From c2ce85745d163aad6b77725754587353247f655b Mon Sep 17 00:00:00 2001 From: Bowen1Zhu <42977266+Bowen1Zhu@users.noreply.github.com> Date: Mon, 8 Jun 2020 22:18:43 -0400 Subject: [PATCH 1/9] Create linear_regression_proposal.md --- .../linear_regression_proposal.md | 28 +++++++++++++++++++ 1 file changed, 28 insertions(+) create mode 100644 LinearRegression/linear_regression_proposal.md diff --git a/LinearRegression/linear_regression_proposal.md b/LinearRegression/linear_regression_proposal.md new file mode 100644 index 0000000..84cfbf8 --- /dev/null +++ b/LinearRegression/linear_regression_proposal.md @@ -0,0 +1,28 @@ +### :pushpin: Step 1 + +**TITLE:** +Intro to Multiple Linear Regression Analysis in Python + +**TOPIC:** +Statistics + +**DESCRIPTION (5-7+ sentences):** +A step-by-step tutorial on multiple linear regression analysis; the process involves checking assumptions, calculating coefficients using different techniques, making predictions, and evaluating performances under different models. These models include OLS, Lasso/Ridge, and Elastic Net. + +### :pushpin: Step 2 + +:family: **TARGET AUDIENCE (3-5+ sentences):** +People who have a basic understanding of elementary statistics topics such as confidence intervals and hypothesis testing, and are interested in obtaining estimates from multiple predictors with basic regression techniques. + +### :pushpin: Step 3 + +> Outline your learning/teaching structure: + +**Beginning (2-3+ sentences):** +Begin by explaining the usage of multiple linear regression analysis and preparing an example dataset. + +**Middle (2-3+ sentences):** +Show how the analysis can be applied to the dataset using a simplest model. Apart from performing the regression itself, its conditions, interpretations, and applications are also explained. + +**End (2-3+ sentences):** +Introduce some more complicated techniques such as stepwise regression and regularizations, and compare their results and performances. \ No newline at end of file From d691f1ef5bdf152b792f34f9993c10104b8b37d2 Mon Sep 17 00:00:00 2001 From: Bowen1Zhu <42977266+Bowen1Zhu@users.noreply.github.com> Date: Mon, 8 Jun 2020 22:39:00 -0400 Subject: [PATCH 2/9] Create Multiple_Linear_Regression.ipynb --- .../Multiple_Linear_Regression.ipynb | 1581 +++++++++++++++++ 1 file changed, 1581 insertions(+) create mode 100644 LinearRegression/Multiple_Linear_Regression.ipynb diff --git a/LinearRegression/Multiple_Linear_Regression.ipynb b/LinearRegression/Multiple_Linear_Regression.ipynb new file mode 100644 index 0000000..469c337 --- /dev/null +++ b/LinearRegression/Multiple_Linear_Regression.ipynb @@ -0,0 +1,1581 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "name": "Multiple_Linear_Regression", + "provenance": [], + "collapsed_sections": [] + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + } + }, + "cells": [ + { + "cell_type": "code", + "metadata": { + "id": "sQ9c41eD2hZ6", + "colab_type": "code", + "outputId": "0a5416d9-eb79-41b2-9855-34507664c7cd", + "colab": { + "resources": { + "http://localhost:8080/nbextensions/google.colab/files.js": { + "data": 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+ "ok": true, + "headers": [ + [ + "content-type", + "application/javascript" + ] + ], + "status": 200, + "status_text": "" + } + }, + "base_uri": "https://localhost:8080/", + "height": 493 + } + }, + "source": [ + "import pandas as pd\n", + "import numpy as np\n", + "from scipy import stats\n", + "import statsmodels.api as sm\n", + "from statsmodels.stats.outliers_influence import variance_inflation_factor\n", + "from sklearn import datasets\n", + "from sklearn import linear_model\n", + "from sklearn import metrics\n", + "from sklearn.preprocessing import StandardScaler\n", + "from sklearn.model_selection import GridSearchCV\n", + "import matplotlib.pyplot as plt\n", + "import seaborn as sn\n", + "from random import uniform\n", + "from google.colab import files\n", + "import io\n", + "\n", + "uploaded = files.upload()\n", + "dataset = pd.read_csv(io.BytesIO(uploaded['Real estate.csv']), delimiter=',')\n", + "\n", + "dataset.head()\n", + "\n", + "dataset.drop(['No'], axis=1)" + ], + "execution_count": 67, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/html": [ + "\n", + " \n", + " \n", + " Upload widget is only available when the cell has been executed in the\n", + " current browser session. Please rerun this cell to enable.\n", + " \n", + " " + ], + "text/plain": [ + "" + ] + }, + "metadata": { + "tags": [] + } + }, + { + "output_type": "stream", + "text": [ + "Saving Real estate.csv to Real estate (3).csv\n" + ], + "name": "stdout" + }, + { + "output_type": "execute_result", + "data": { + "text/html": [ + "
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X1 transaction dateX2 house ageX3 distance to the nearest MRT stationX4 number of convenience storesX5 latitudeX6 longitudeY house price of unit area
02012.91732.084.878821024.98298121.5402437.9
12012.91719.5306.59470924.98034121.5395142.2
22013.58313.3561.98450524.98746121.5439147.3
32013.50013.3561.98450524.98746121.5439154.8
42012.8335.0390.56840524.97937121.5424543.1
........................
4092013.00013.74082.01500024.94155121.5038115.4
4102012.6675.690.45606924.97433121.5431050.0
4112013.25018.8390.96960724.97923121.5398640.6
4122013.0008.1104.81010524.96674121.5406752.5
4132013.5006.590.45606924.97433121.5431063.9
\n", + "

414 rows × 7 columns

\n", + "
" + ], + "text/plain": [ + " X1 transaction date X2 house age \\\n", + "0 2012.917 32.0 \n", + "1 2012.917 19.5 \n", + "2 2013.583 13.3 \n", + "3 2013.500 13.3 \n", + "4 2012.833 5.0 \n", + ".. ... ... \n", + "409 2013.000 13.7 \n", + "410 2012.667 5.6 \n", + "411 2013.250 18.8 \n", + "412 2013.000 8.1 \n", + "413 2013.500 6.5 \n", + "\n", + " X3 distance to the nearest MRT station X4 number of convenience stores \\\n", + "0 84.87882 10 \n", + "1 306.59470 9 \n", + "2 561.98450 5 \n", + "3 561.98450 5 \n", + "4 390.56840 5 \n", + ".. ... ... \n", + "409 4082.01500 0 \n", + "410 90.45606 9 \n", + "411 390.96960 7 \n", + "412 104.81010 5 \n", + "413 90.45606 9 \n", + "\n", + " X5 latitude X6 longitude Y house price of unit area \n", + "0 24.98298 121.54024 37.9 \n", + "1 24.98034 121.53951 42.2 \n", + "2 24.98746 121.54391 47.3 \n", + "3 24.98746 121.54391 54.8 \n", + "4 24.97937 121.54245 43.1 \n", + ".. ... ... ... \n", + "409 24.94155 121.50381 15.4 \n", + "410 24.97433 121.54310 50.0 \n", + "411 24.97923 121.53986 40.6 \n", + "412 24.96674 121.54067 52.5 \n", + "413 24.97433 121.54310 63.9 \n", + "\n", + "[414 rows x 7 columns]" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 67 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "ODM2nIVEbwWY", + "colab_type": "code", + "outputId": "8fa9d34a-20df-4137-f852-e3b96e28be19", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 418 + } + }, + "source": [ + "y = dataset['Y house price of unit area'].values # target vector\n", + "print(dataset['Y house price of unit area'].describe())\n", + "sn.distplot(y, bins = 13)\n", + "plt.show()" + ], + "execution_count": 68, + "outputs": [ + { + "output_type": "stream", + "text": [ + "count 414.000000\n", + "mean 37.980193\n", + "std 13.606488\n", + "min 7.600000\n", + "25% 27.700000\n", + "50% 38.450000\n", + "75% 46.600000\n", + "max 117.500000\n", + "Name: Y house price of unit area, dtype: float64\n" + ], + "name": "stdout" + }, + { + "output_type": "display_data", + "data": { + "image/png": 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dVWFoYLidR3vdLsWYmBfWMQBVfQp4asa0+6Y9HwNumWW5rwFfm2OdDcD5Z1OsOTf1R3vpHBrnlksT+9s/QJrPS1leBm8cswAwZj52JXAS2L6vg/QUDx9YUzp/4wRQXZTJ7hP9jPsDbpdiTEyzAEhwqsoz+05xdW1J3I/4Ga7q4iwm/EHebh1wuxRjYpoFQIJ7u3WAjsExPnLeUrdLWTQ1zhAXrx/pcbkSY2KbBUCC276vA69HuG5dcnT/AGSm+VhXlsurFgDGnJEFQILbvq+DTTWF5Gemul3KorpyZRG7WvoYm7TjAMbMxQIggTV1DnOkaySpun+mXLmyiAl/kDdb+twuxZiYZQGQwH61/xRAQo78OZ+NNYV4PcJr1g1kzJwsABLYrw91snZpDsvyE/vir9nkpKdwfnmeBYAxZ2ABkKBGJ/zsOt7H+1cn7/hJV64sYveJfkbG/W6XYkxMsgBIUPXNvUwGlKtqi90uxTVXrizCH1R22lXBxszKAiBBvXi4izSfh8uqE3Ps/3DULS8kxWvHAYyZiwVAgnr5cDcbawpJT0mOq39nk5Hq5eLKAl5rtgAwZjYWAAno5MBpDncOszmJu3+mXLGyiL1tAwyM2v0BjJnJAiABvXS4G4DNtcl7AHjKlSuLCCrUH7W9AGNmsgBIQC8f7qY4O421S3PcLsV1F1Xlk57isW4gY2ZhAZBgVJVXmrrZXFuMJPCtH8OV5vNyWXWhHQg2ZhYWAAmmqXOYnpEJrlhR5HYpMePyFUU0dgzRPTzudinGxBQLgART79wKcWNN8p7+OdOVK0Nh+Lp1AxnzLhYACeaNo70syU1jeVGm26XEjA3leWSn+awbyJgZLAASiKpSf7SHjTVF1v8/jc/rYVONHQcwZiYLgATS0jvKqcFx6/6ZxRUri2juHqG9/7TbpRgTMywAEkh9c6j//3ILgPeYuibiZecaCWOMBUBCqT/aS2FWKqtKs90uJeasXpJNaU4aLx7ucrsUY2KGBUACeeNYDxurC63/fxYiwubaEl5u6iYQVLfLMSYmWAAkiPb+05zoPW39/2dw9epi+kcn2dc+4HYpxsQEC4AE8Yad/z+v960KDY734iHrBjIGwgwAEdkiIgdFpElE7p1lfpqIPObMrxeRamd6kYg8LyLDIvLtGcu84Kxzt/MojcQbSlb1R3vISfexrizX7VJiVnF2GueX5/KiHQg2BggjAETEC9wPXA+sB24TkfUzmt0F9KnqKuAbwNed6WPAV4A/nWP1t6vqRc6j81zegAmpP9rLZdWhG6GbuW2uLeHN430M220ijQlrD2Aj0KSqzao6ATwKbJ3RZivwsPP8SeA6ERFVHVHVlwkFgYmSrqFxmrtGrPsnDJtri/EHldftojBj8IXRphw4Me11K7Bprjaq6heRAaAImG9f+/siEgB+AnxNVe30jDk8Ut8y57w9baGDmgOjk2dsZ+DS5QVkpHh56XAXH1y/xO1yjHGVmweBb1fVDcBm5/Hp2RqJyN0i0iAiDV1ddvBuNke7R0j1eliWn+F2KTEvzefl8hWFdhzAGMILgDagctrrCmfarG1ExAfkAWfcx1bVNufnEPAIoa6m2do9qKp1qlpXUmJ3uJrNse4Rqooyrf8/TFevLuFo9wgnekfdLsUYV4UTADuBWhGpEZFU4FZg24w224A7nec3AzvO1J0jIj4RKXaepwA3AHvPtngDoxN+OgbHqC7KcruUuDE1LMRLthdgkty8xwCcPv17gO2AF/iequ4Tka8CDaq6DXgI+KGINAG9hEICABE5BuQCqSLyceDDwHFgu/Ph7wWeBf41ou8sSRzvCX2LrSm2AJjuTMdCVJW8jBR+VH88rHV9alNVpMoyJqaEcxAYVX0KeGrGtPumPR8Dbplj2eo5VntpeCWaMznaPYLPI1QUWP9/uESE2tJs9rYPEAiqdZ2ZpGVXAse5o90jVBRkkuK1f8qzsao0m7HJIG19dhzAJC/71Ihj45MB2vtPW/fPOVhVmo0AhzuH3S7FGNdYAMSx472jKNb/fy4yU32UF2RYAJikZgEQx452j+ARqCq0+/+ei9rSbFr7Rjk9EXC7FGNcYQEQx452j1Cen0Gqz/4Zz8Wq0hyCCs3dthdgkpN9csSpCX+Qtj7r/1+IqsJM0nweDp+yADDJyQIgTp3oGyWgSrUFwDnzeoQVJdkc7hzChqEyycgCIE4d7R5BwK4AXqDa0mz6RifpHZlwuxRjFp0FQJw61j1CWV466Slet0uJa7Wl2YCdDmqSkwVAHPIHg7T0jlr/fwQUZqVSkJnC4VNDbpdizKKzAIhDJ3pP4w9a/38khIaFyOFI9wiBoB0HMMnFAiAONXcPI9gFYJFSuySbCX9or8qYZGIBEIeau0L9/5mpYY3lZ+axsiQbj2DdQCbpWADEmclAkBO9o6woyXa7lISRnuKlqjCTQ50WACa5WADEmZbeUfxBZYV1/0TU6iU5tPePMTQ26XYpxiwaC4A409wV6v+3A8CRVbskB4AmOx3UJBELgDjT3DVCeUGGnf8fYWV56WSl+ThoxwFMErEAiCMT/iCtfadZUWz9/5HmEWF1aTZNncMEbVgIkyQsAOLI8Z4RAqqsKLHun2hYvSSH0YkAbX2n3S7FmEVhARBHmp3x/5cX2fj/0TB1lzA7G8gkCwuAONLcNUxFQSZpPuv/j4asNOcuYTY8tEkSFgBxYmwyQFv/aev+ibLVS3I40TvK6ITf7VKMiToLgDhxrGeEoIauWjXRs7o0G8VOBzXJwQIgTjR3jeD1iN3/N8oqCjPJSPFyyLqBTBKwAIgTzd3DVBVmkuK1f7Jo8oiwqjSbw6fsLmEm8dmnSRwYGJ3kZP+YDf+wSFYvyWFo3E/H4JjbpRgTVRYAcaD+aA8KNgDcIqldEtrO1g1kEl1YASAiW0TkoIg0ici9s8xPE5HHnPn1IlLtTC8SkedFZFhEvj1jmUtFZI+zzLdERCLxhhLRa809pHiFyoIMt0tJCrnpKZTlpXPIhoUwCW7eABARL3A/cD2wHrhNRNbPaHYX0Keqq4BvAF93po8BXwH+dJZVPwD8PlDrPLacyxtIBq8d6WF5YRY+6/9fNLWlORzvGWFsMuB2KcZETTifKBuBJlVtVtUJ4FFg64w2W4GHnedPAteJiKjqiKq+TCgI3iEiZUCuqr6uoSNtPwA+vpA3kqg6h8Zo7Biy8/8X2ZqlOQTVbhZvEls4AVAOnJj2utWZNmsbVfUDA0DRPOtsnWedAIjI3SLSICINXV1dYZSbWF5p6gZ+O1yxWRxVzumgjScH3S7FmKiJ+T4FVX1QVetUta6kpMTtchbdS4e6KcxKpSwv3e1SkorXI6xZmsPBU0N2s3iTsMIJgDagctrrCmfarG1ExAfkAT3zrLNinnUmPVXlxcPdXLWqGI8dI190a5eGRgd9s6XP7VKMiYpwAmAnUCsiNSKSCtwKbJvRZhtwp/P8ZmCHnuEqGlU9CQyKyOXO2T93AD8/6+oT3IGTQ3QPj7O5ttjtUpLS6iU5eASePXDK7VKMiYp5A8Dp078H2A4cAB5X1X0i8lURuclp9hBQJCJNwJeAd04VFZFjwD8AnxGR1mlnEH0e+C7QBBwBno7MW0ocLx0OHfPYXJt8XV+xID3FS01xFs8d6HS7FGOiwhdOI1V9CnhqxrT7pj0fA26ZY9nqOaY3AOeHW2gyeulwN6uXZLPU+v9ds3ZpLr/Yc5LjPSMsL7IzsUxiifmDwMnq9ESAN4712rd/l60rywXgWdsLMAnIAiBG1R/tYcIftP5/lxVmpVJbms1zdhzAJCALgBj1wsEu0lM8XL7iTJdTmMVw3bolvHG0l8GxSbdLMSaiLABikKqyo7GTK1cWk55it3902wfXleIPKr8+mHwXIprEZgEQg450jdDSO8o1a0vdLsUAF1cVUJiVat1AJuFYAMSg5xtDBxyvtQCICV6P8IE1JTx/sAt/IOh2OcZEjAVADNrR2MmaJTmU59vwz7Hig+uWMHB6kl3H7apgkzgsAGLM4NgkO4/1WvdPjNlcW0yKV3iu0U4HNYnDAiDGvHy4G39QuWaNnf8fS3LSU7h8RRHP7j9l9wo2CcMCIMbsaOwkN93HpcsL3C7FzPCR85bS3D1it4o0CcMCIIYEg8oLBzu5enWJ3f0rBn3kvKWIwFN7TrpdijERYZ8yMWRP2wDdwxN29k+MKslJY2N1IU/vtQAwicECIIbsaOxEBN6/2vr/Y9VHN5Rx6NQwTZ12w3gT/ywAYsjzBzu5qDKfouw0t0sxc9hy/lIAnt7T4XIlxiycBUCM6Boa5+3WAa5dY90/sWxJbjp1ywt4aq8FgIl/FgAx4oWDofPL7fz/2Hf9hjIOnBzkaPeI26UYsyAWADHi+YOdLMlN47xluW6XYubx0Q2hs4G27W53uxRjFsQCIAZMBoK8dKiba9aUInbz95hXlpfBpppCfr67zS4KM3HNAiAG1Df3MjTut+6fOPLxi8pp7h5hT9uA26UYc84sAGLA9n0dpKd4uNpu/xg3rt9QRqrXw89+0+Z2KcacMwsAlwWDyq/2n+L9q0vISLWbv8SLvIwUrllbwn++ddKGiDZxywLAZXvaBugYHOPD65e6XYo5Sx+/qJzu4XFePdLjdinGnBMLAJdt39eB1yNct876/+PNNWtLyUn3WTeQiVsWAC57Zv8pNtUUkp+Z6nYp5iylp3i56cJlPL33JAOn7YbxJv743C4gkT1S33LG+V1D4zR1DrNuac68bU1suvWyKn5U38K23W18+opqt8sx5qzYHoCL9p8cBGBdmV38Fa/OL89lfVkuj+484XYpxpy1sAJARLaIyEERaRKRe2eZnyYijznz60Wketq8LzvTD4rIR6ZNPyYie0Rkt4g0ROLNxJu9bQNUFmRY908cExFu21jJvvZB9to1ASbOzBsAIuIF7geuB9YDt4nI+hnN7gL6VHUV8A3g686y64FbgfOALcB3nPVNuUZVL1LVugW/kzjTMzxOW/9pzi/Pc7sUs0A3XVROms/Dj9+wbjwTX8LZA9gINKlqs6pOAI8CW2e02Qo87Dx/ErhOQmMabAUeVdVxVT0KNDnrS3pT3xYtAOJfXkYKH9tQxrbd7YyM+90ux5iwhRMA5cD0Ds5WZ9qsbVTVDwwARfMsq8AzIrJLRO6e65eLyN0i0iAiDV1dXWGUGx/2tIe6fwqs+ych3H75cobG/fzkzVa3SzEmbG4eBL5KVS8h1LX0BRG5erZGqvqgqtapal1JSWIMldAzPE57/xgb7Nt/wrh0eQEXVebz/VeOEQzaAHEmPoQTAG1A5bTXFc60WduIiA/IA3rOtKyqTv3sBH5GEnUN7bHun4T02atqONo9wo7GTrdLMSYs4QTATqBWRGpEJJXQQd1tM9psA+50nt8M7NDQOLnbgFuds4RqgFrgDRHJEpEcABHJAj4M7F3424kPe9oGqCrMtLN/Esz15y+lLC+d771y1O1SjAnLvAHg9OnfA2wHDgCPq+o+EfmqiNzkNHsIKBKRJuBLwL3OsvuAx4H9wC+BL6hqAFgCvCwibwFvAL9Q1V9G9q3Fpo7BMU4OjHFBhX37TzQpXg93XFHNq0d62N8+6HY5xswrrCuBVfUp4KkZ0+6b9nwMuGWOZf8K+KsZ05qBC8+22ESwu6UPj8AFFflul2LCdDZXaad6PaT6PPyvn7zNbRur3jP/U5veO80Yt9iVwIsoqMruE/2sWZJDdpqNwpGIMlK9XLGiiL3OKK/GxDILgEV0pGuYwTE/F1cVuF2KiaLNq4pJ9XnYceCU26UYc0YWAIvoNy39pKd4WLs0x+1STBRlpvm4cmURe9sHOTlw2u1yjJmTBcAiGZ8MsK99gAvK8/F5bbMnuqtWlZDm8/DsATsl1MQu+yRaJG+3DTAZUC6usoO/ySAj1cvm2hIOnBykqXPY7XKMmZUFwCJQVV5v7mFpbjpVhZlul2MWyebaYgqzUvnPt9rxB+2+wSb2WAAsghO9o5wcGGPTikJCY+SZZJDi9XDDhjK6hsd5tcnuG2xijwXAInj9aC9pPg8XVVr3T7JZW5bL2qU57GjspH90wu1yjHkXC4AoGx73s6dtgEuqCkjzeedfwCYE9NQAAAu4SURBVCScGy5YBgKPN5zAH7CuIBM7LACirOFYL4GgsmlFodulGJcUZqWy9cJlHOsZ5Z92NLldjjHvsACIogl/kFeP9LCqJJvSnHS3yzEuuriqgIsr8/mnHYd5vdmOB5jYYAEQRTuP9TI87ueataVul2JiwE0XLqO6KIvP/fsumjqH3C7HGAuAaBmbDPDi4S5qirOoKc5yuxwTA9JSvHz/v1+Gz+PhjofeoL3frhI27rIAiJInGk4wNObnWvv2b6ZZXpTFw5+9jKExP59+qJ42CwHjIguAKBibDPDAC0dYXpjJCvv2b2Y4b1keD33mMjoHx/n4/a+wp3XA7ZJMkrIAiIIHXjhC+8AYH1y/xC78MrPaWFPITz5/JaleD//tX17jyV2thG6iZ8zisQCIsOM9Izzw6yPceOEyVpZku12OiWGrl+TwH194Hxsq8vjTJ97irocbOGX3EDCLyAIgglSV+36+j1Svh//9sXVul2PiQElOGo/+/uV85Yb1vHqkm2v+7gX+/pmDDI5Nul2aSQIWABH0X2+f5NeHuvjjD61mSa6d92/C4/EId11Vwy+/eDXXrC3ln3Y0cfX/e56/3d5Ix4DtEZjosfsSRkhT5zBf/ukeLqrM584rlrtdjolR891f+H0ri6kuzOL5g5185/kjPPDCEdYszeXCijzWLs0l1ffb72x2f2GzUBYAETA87udz/76LNJ+HB373Ervhi1mQ8oIMfvfy5fSOTFDf3MPu1n4OnBwk1ethXVkOF1Tks6rUji+ZhbMAWKDJQJAvPbab5q5h/v2uTZTlZbhdkkkQhVmpXL+hjI+cv5Sj3SO83TrA3rYB3modINXr4ZWmbq5dW8q1a0sptS5Hcw4sABZgbDLAPY+8ybMHOvmLG9dz5apit0syCcgjwsqSbFaWZHPjhWUc6RyhsWOQvW0DPLM/dOP5DeV5XLu2lOvWlXL+sjw8Hjv92MzPAuAcDYxO8vlHdvFKUw//d+t5fPqKardLMknA5/GwZmkOa5bmcNvGSho7htjR2MmOxk6+teMw33zuMCU5aVy7ppRr15Vy1apistLsv7mZnf1lnIMdjaf48k/30D08wd/fciGfuLTC7ZJMEhIR1pXlsq4sly9cs4qe4XF+faiL5xo7eWrvSR5rOEGq18OmFYVct7aU69YtodJuSWqmkXi6+rCurk4bGhpc+/1vnejnn399hKf3drBmSQ5/d8uFbKjIm7P9fGd8GBMtgaByvGeExo4hGjuG6B4eB6A0J421S3NYvTSHyoJMUrweO5soCYjILlWtmzk9rD0AEdkCfBPwAt9V1b+ZMT8N+AFwKdADfFJVjznzvgzcBQSAP1LV7eGsM1a09Izy7IFTPL33JDuP9ZGT7uOL19Xy+WtW2h2+TMzyeoQVJdmsKMnmoxvK6B4e52DHEAc7hnilqYcXD3fj9Qjl+Rkc6xnhkqoCLq7KpzQnLamHLwkGlcGxSbqHJ+gZHqdnZIKRcT/j/iBjkwHG/UEmA0FSfR4yU7xkpHpJT/GSneajICuVwsxUCrJSyU33xcV2nHcPQES8wCHgQ0ArsBO4TVX3T2vzeeACVf2ciNwK/I6qflJE1gM/BjYCy4BngdXOYmdc52wWsgegqviDij+gTASC+ANBJgPKZCDI6ckA/aOT9I1O0DEwRlv/aQ6dGmJf+yBdQ6FvTqtKs/lkXSW3bqwkJz0lrN9pewAmFo1NBmjuGuF47wgtPaOcHBhjwrlVZWaql+VFWdQUZ7K8KItleenkZaaSl5FCfkYKeRkppKd4SfEKPq8n9NMT+rnYH3iqSlBDeztBVQJBJaBKMPjb5xP+IKMTAX72Zhvj/iAT/gCjEwGGx/2MjPudn87ridC0YAQ6RXweoSArlaKsVAoyUynMDoVDYda7HwWZqWSkhrZnqtdDitdDii+0PVM8nogdzF/IHsBGoElVm50VPQpsBaZ/WG8F/o/z/Eng2xL6a9gKPKqq48BREWly1kcY64yYLf/4Io0d4d+AI9XnoaYoi82rirmgIo9r1payvMhG9TSJIT3Fy/pluaxflgvAJy4tZ2/bAHvbBjnWM8Kx7hEaTw7xzL5T+M/i09DrEbwiMMdn1myT58oMmWMlQf3th/1CP6jTfB6y0nzvfHuvKMggO833zrSsNB9ZaV7SfN53Bd3vXr6ciUAoWE5PBjg94Wd4PEDfyAS9U4/RCfpGJugZCf08cHKQ3pEJ+kfPbogPkdBZYALs/cuPkJ4S2V6HcAKgHDgx7XUrsGmuNqrqF5EBoMiZ/vqMZcud5/OtEwARuRu423k5LCIHw6h5wQ5D8TPQvRi/K4KKsZqjLd7qhXlqvn0RCzkLMbud75x7VlRrzvjrBS0+6/AEMX8WkKo+CDy42L9XRBpm22WKZVZz9MVbvWA1L5Z4rDmcMQvagMppryucabO2EREfkEfoYPBcy4azTmOMMVEUTgDsBGpFpEZEUoFbgW0z2mzjt3tGNwM7NHR0eRtwq4ikiUgNUAu8EeY6jTHGRNG8XUBOn/49wHZCp2x+T1X3ichXgQZV3QY8BPzQOcjbS+gDHafd44QO7vqBL6hqAGC2dUb+7S3Ionc7RYDVHH3xVi9YzYsl7mqOqwvBjDHGRI6NW2yMMUnKAsAYY5KUBcAMIrJFRA6KSJOI3Ot2PbMRkUoReV5E9ovIPhH5ojO9UER+JSKHnZ8Fbtc6k4h4ReQ3IvJfzusaEal3tvdjzkkBMUNE8kXkSRFpFJEDInJFrG9nEflj5+9ir4j8WETSY207i8j3RKRTRPZOmzbrdpWQbzm1vy0il8RIvX/r/F28LSI/E5H8afO+7NR7UEQ+stj1hssCYBpn2Iv7geuB9cBtznAWscYP/ImqrgcuB77g1Hkv8Jyq1gLPOa9jzReBA9Nefx34hqquAvoIjRsVS74J/FJV1wIXEqo9ZreziJQDfwTUqer5hE6yuJXY287/BmyZMW2u7Xo9oTMIawldFPrAItU43b/x3np/BZyvqhcQGtrmywDO/8VbgfOcZb7jfLbEHAuAd3tn2AtVnQCmhqiIKap6UlXfdJ4PEfpQKidU68NOs4eBj7tT4exEpAL4GPBd57UA1xIaPgRirGYRyQOuJnSWG6o6oar9xPh2JnR2X4ZzTU4mcJIY286q+iKhMwanm2u7bgV+oCGvA/kiUrY4lYbMVq+qPqOqfufl64SuZ4JpQ+Co6lFg+hA4McUC4N1mG/aifI62MUFEqoGLgXpgiaqedGZ1AEtcKmsu/wj8GRB0XhcB/dP+E8Xa9q4BuoDvO91W3xWRLGJ4O6tqG/B3QAuhD/4BYBexvZ2nzLVd4+H/5WeBp53n8VAvYAEQ10QkG/gJ8D9VdXD6POdCvJg5x1dEbgA6VXWX27WcBR9wCfCAql4MjDCjuycGt3MBoW+gNYRG4M3ivV0XMS/WtuuZiMifE+qW/ZHbtZwtC4B3i5shKkQkhdCH/49U9afO5FNTu8bOz0636pvF+4CbROQYoa61awn1r+c7XRUQe9u7FWhV1Xrn9ZOEAiGWt/MHgaOq2qWqk8BPCW37WN7OU+barjH7/1JEPgPcANyuv72oKmbrnckC4N3iYogKp+/8IeCAqv7DtFnTh+S4E/j5Ytc2F1X9sqpWqGo1oe26Q1VvB54nNHwIxF7NHcAJEVnjTLqO0FXtMbudCXX9XC4imc7fyVTNMbudp5lru24D7nDOBrocGJjWVeQaCd3U6s+Am1R1dNqsuYbAiT2qao9pD+CjhI7oHwH+3O165qjxKkK7x28Du53HRwn1qT8HHCZ0851Ct2udo/4PAP/lPF9B6D9HE/AEkOZ2fTNqvQhocLb1fwAFsb6dgb8EGoG9wA+BtFjbzoRuFHUSmCS0p3XXXNuV0K0E7nf+T+4hdIZTLNTbRKivf+r/4D9Pa//nTr0Hgevd/puY62FDQRhjTJKyLiBjjElSFgDGGJOkLACMMSZJWQAYY0ySsgAwxpgkZQFgjDFJygLAGGOS1P8HouLTC1K8ER0AAAAASUVORK5CYII=\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "WPiAKFpzcf4U", + "colab_type": "code", + "outputId": "256cb956-e362-40dd-aae5-65cb89f4b406", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 470 + } + }, + "source": [ + "df = pd.DataFrame(dataset,columns=['X1 transaction date', 'X2 house age', 'X3 distance to the nearest MRT station', 'X4 number of convenience stores', 'X5 latitude', 'X6 longitude']) # regressor matrix\n", + "corrMatrix = df.corr()\n", + "sn.heatmap(corrMatrix, annot=True) # visualize the correlation matrix using a heatmap" + ], + "execution_count": 69, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 69 + }, + { + "output_type": "display_data", + "data": { + "image/png": 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VIF FactorPredictor
11.014674X1 transaction date
21.014287X2 house age
34.323019X3 distance to the nearest MRT station
41.617038X4 number of convenience stores
51.610234X5 latitude
62.926302X6 longitude
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" + ], + "text/plain": [ + " VIF Factor Predictor\n", + "1 1.014674 X1 transaction date\n", + "2 1.014287 X2 house age\n", + "3 4.323019 X3 distance to the nearest MRT station\n", + "4 1.617038 X4 number of convenience stores\n", + "5 1.610234 X5 latitude\n", + "6 2.926302 X6 longitude" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 70 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "6eOByNtRqzG1", + "colab_type": "code", + "outputId": "9aaa25e1-3691-4a1c-e094-72ea66044369", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 444 + } + }, + "source": [ + "df = pd.DataFrame(dataset,columns=['X1 transaction date', 'X2 house age', 'X4 number of convenience stores', 'X5 latitude', 'X6 longitude']) # regressor matrix\n", + "corrMatrix = df.corr()\n", + "sn.heatmap(corrMatrix, annot=True) # visualize the correlation matrix using a heatmap" + ], + "execution_count": 71, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 71 + }, + { + "output_type": "display_data", + "data": { + "image/png": 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\n", 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" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "RUSAN1_lFVqX", + "colab_type": "code", + "outputId": "dedb63f1-52c9-434c-d177-edfd7ad203b3", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 204 + } + }, + "source": [ + "X = dataset[['X1 transaction date', 'X2 house age', 'X4 number of convenience stores', 'X5 latitude', 'X6 longitude']]\n", + "X_aug = sm.add_constant(X) # augmented regressor matrix with a column of ones inserted at the front\n", + "vif = pd.DataFrame()\n", + "vif['VIF Factor'] = [variance_inflation_factor(X_aug.values, i) for i in range(X_aug.shape[1])]\n", + "vif['Predictor'] = X_aug.columns\n", + "vif = vif.drop(0)\n", + "vif" + ], + "execution_count": 72, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/html": [ + "
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VIF FactorPredictor
11.005277X1 transaction date
21.012527X2 house age
31.398292X4 number of convenience stores
41.349140X5 latitude
51.365232X6 longitude
\n", + "
" + ], + "text/plain": [ + " VIF Factor Predictor\n", + "1 1.005277 X1 transaction date\n", + "2 1.012527 X2 house age\n", + "3 1.398292 X4 number of convenience stores\n", + "4 1.349140 X5 latitude\n", + "5 1.365232 X6 longitude" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 72 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "mtuKLp1upZob", + "colab_type": "code", + "outputId": "90478839-ac46-49a0-b657-1a951487429b", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 136 + } + }, + "source": [ + "regressor = linear_model.LinearRegression()\n", + "regressor.fit(X, y)\n", + "coeff_df = pd.DataFrame(regressor.coef_, X.columns, columns=['Coefficient'])\n", + "# print the calculated coefficients as well as the intercept\n", + "print('Intercept %.6f' %(regressor.intercept_))\n", + "print(coeff_df)" + ], + "execution_count": 73, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Intercept -42310.207230\n", + " Coefficient\n", + "X1 transaction date 4.209764\n", + "X2 house age -0.279726\n", + "X4 number of convenience stores 1.565796\n", + "X5 latitude 337.629436\n", + "X6 longitude 209.338154\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "Jv9fR3k4FrEf", + "colab_type": "code", + "outputId": "99dc9c80-e038-425a-a878-d18b021e7a4e", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 1000 + } + }, + "source": [ + "y_hat = regressor.predict(X) # predicted values\n", + "df_comparison = pd.DataFrame({'Actual': y, 'Predicted': y_hat}) # put the actual and predicted values together\n", + "df_comparison = df_comparison.head(50) # show top 50 rows of this data frame\n", + "print(df_comparison)\n", + "df_comparison.plot(kind = 'bar') # visualize the comparison\n", + "plt.grid(which = 'major', linestyle = '-', linewidth = '0.5', color = 'green')\n", + "plt.grid(which = 'minor', linestyle = ':', linewidth = '0.5', color = 'black')" + ], + "execution_count": 74, + "outputs": [ + { + "output_type": "stream", + "text": [ + " Actual Predicted\n", + "0 37.9 48.404279\n", + "1 42.2 49.290901\n", + "2 47.3 50.890731\n", + "3 54.8 50.541321\n", + "4 43.1 47.018079\n", + "5 32.1 30.828825\n", + "6 40.3 39.923115\n", + "7 46.7 47.081491\n", + "8 18.8 14.384292\n", + "9 22.1 32.889071\n", + "10 41.4 29.658713\n", + "11 58.1 53.456919\n", + "12 39.3 39.269362\n", + "13 23.8 27.573710\n", + "14 34.3 48.325797\n", + "15 50.5 38.696363\n", + "16 70.1 51.532243\n", + "17 37.4 33.168931\n", + "18 42.3 47.268804\n", + "19 47.7 46.197155\n", + "20 29.3 34.528204\n", + "21 51.6 50.308416\n", + "22 24.6 30.417507\n", + "23 47.9 49.014246\n", + "24 38.8 33.751416\n", + "25 27.0 29.968922\n", + "26 56.2 47.656063\n", + "27 33.6 38.653993\n", + "28 47.0 41.601329\n", + "29 57.1 47.160289\n", + "30 22.1 15.896112\n", + "31 25.0 42.328283\n", + "32 34.2 27.555088\n", + "33 49.3 46.873734\n", + "34 55.1 48.514296\n", + "35 27.3 46.313934\n", + "36 22.9 28.890080\n", + "37 25.3 32.225209\n", + "38 47.7 46.930124\n", + "39 46.2 46.404920\n", + "40 15.9 16.628513\n", + "41 18.2 18.236063\n", + "42 34.7 34.247509\n", + "43 34.1 42.865920\n", + "44 53.9 48.680398\n", + "45 38.3 41.336871\n", + "46 42.0 48.451930\n", + "47 61.5 36.028046\n", + "48 13.4 15.523962\n", + "49 13.2 13.216184\n" + ], + "name": "stdout" + }, + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "91uqmsQ6l210", + "colab_type": "code", + "outputId": "53e48100-7327-4ce3-f539-a9eb6f351615", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 282 + } + }, + "source": [ + "epsilon_hat = y - y_hat # residuals\n", + "plt.grid(color = 'b', linestyle= '--' , linewidth = 0.5)\n", + "plt.scatter(y_hat, epsilon_hat) # scatter plot" + ], + "execution_count": 75, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 75 + }, + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "iBqjnpxOFwrO", + "colab_type": "code", + "outputId": "3e45301f-00a1-49bf-986f-4a2b6f161c23", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 549 + } + }, + "source": [ + "pp = sm.ProbPlot(epsilon_hat, fit=True)\n", + "pp.ppplot(line='45') # normal probability plot" + ], + "execution_count": 76, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "image/png": 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "rzyVsxoCYlhw", + "colab_type": "code", + "outputId": "65ee71c9-f172-4bfb-8fd9-c68fae115584", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 119 + } + }, + "source": [ + "random = []\n", + "# generate random inputs\n", + "for i in range(X.shape[1]):\n", + " random.append(uniform(X.iloc[:, i].min(), X.iloc[:, i].max()))\n", + "# print the random inputs generated\n", + "print('random input:', random)\n", + "random.insert(0, 1) # insert 1 at the front\n", + "X_aug = sm.add_constant(X) # insert 1 at the front\n", + "est = sm.OLS(y, X_aug).fit()\n", + "prediction = est.get_prediction(np.reshape(random, (1, 6)))\n", + "pd.set_option('display.max_columns', None)\n", + "print(prediction.summary_frame(alpha = 0.05))" + ], + "execution_count": 82, + "outputs": [ + { + "output_type": "stream", + "text": [ + "random input: [2013.3002540225928, 19.80124894778612, 2.2810358454108703, 24.979226201571294, 121.53197772366114]\n", + " mean mean_se mean_ci_lower mean_ci_upper obs_ci_lower \\\n", + "0 38.346671 0.809233 36.755885 39.937457 20.070918 \n", + "\n", + " obs_ci_upper \n", + "0 56.622423 \n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "LxUcy5kfNFdl", + "colab_type": "code", + "outputId": "a9950dbc-b29b-446b-e2c1-3c3a687c3d38", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 544 + } + }, + "source": [ + "print(est.summary())" + ], + "execution_count": 83, + "outputs": [ + { + "output_type": "stream", + "text": [ + " OLS Regression Results \n", + "==============================================================================\n", + "Dep. Variable: y R-squared: 0.542\n", + "Model: OLS Adj. R-squared: 0.537\n", + "Method: Least Squares F-statistic: 96.68\n", + "Date: Mon, 08 Jun 2020 Prob (F-statistic): 5.12e-67\n", + "Time: 23:11:27 Log-Likelihood: -1505.9\n", + "No. Observations: 414 AIC: 3024.\n", + "Df Residuals: 408 BIC: 3048.\n", + "Df Model: 5 \n", + "Covariance Type: nonrobust \n", + "===================================================================================================\n", + " coef std err t P>|t| [0.025 0.975]\n", + "---------------------------------------------------------------------------------------------------\n", + "const -4.231e+04 5333.483 -7.933 0.000 -5.28e+04 -3.18e+04\n", + "X1 transaction date 4.2098 1.621 2.598 0.010 1.024 7.395\n", + "X2 house age -0.2797 0.040 -6.949 0.000 -0.359 -0.201\n", + "X4 number of convenience stores 1.5658 0.183 8.558 0.000 1.206 1.925\n", + "X5 latitude 337.6294 42.654 7.916 0.000 253.780 421.479\n", + "X6 longitude 209.3382 34.696 6.033 0.000 141.132 277.544\n", + "==============================================================================\n", + "Omnibus: 240.224 Durbin-Watson: 2.171\n", + "Prob(Omnibus): 0.000 Jarque-Bera (JB): 3935.913\n", + "Skew: 2.113 Prob(JB): 0.00\n", + "Kurtosis: 17.502 Cond. No. 2.36e+07\n", + "==============================================================================\n", + "\n", + "Warnings:\n", + "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", + "[2] The condition number is large, 2.36e+07. This might indicate that there are\n", + "strong multicollinearity or other numerical problems.\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "dBp3VR4j5nhs", + "colab_type": "code", + "outputId": "d35dfc91-2118-404b-8807-ee285e3f5e4d", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 102 + } + }, + "source": [ + "X_ = dataset[['X1 transaction date', 'X2 house age', 'X3 distance to the nearest MRT station', 'X4 number of convenience stores', 'X5 latitude', 'X6 longitude']]\n", + "X_aug_ = sm.add_constant(X_) # augmented regressor matrix with a column of ones inserted at the front\n", + "min_r_cv = 0\n", + "# calculate the initial risk estimator with all predictors included\n", + "for i in range(X_.shape[0]):\n", + " X_cv = X_aug_.drop(X_aug_.index[i])\n", + " X_cv.reset_index(inplace=True)\n", + " X_cv = X_cv.drop('index', axis=1)\n", + " y_cv = np.delete(y, i)\n", + " est_cv = sm.OLS(y_cv, X_cv).fit()\n", + " prediction_cv = est_cv.get_prediction(X_aug_.iloc[[i]]).predicted_mean\n", + " min_r_cv += (y[i] - prediction_cv)**2\n", + "print('original risk estimator:', min_r_cv)\n", + "\n", + "variables = X_.shape[1]\n", + "min_index = -1\n", + "# keep deleting a predictor until we can't improve the model anymore\n", + "while (min_index != 0):\n", + " min_index = 0\n", + " # calculate the risk estimator when the j-th predictor is removed\n", + " for j in range(1, variables + 1):\n", + " r_cv = 0\n", + " for i in range(X_.shape[0]):\n", + " X_cv = X_aug_.drop(X_aug_.index[i]) # remove the i-th data point\n", + " X_cv.reset_index(inplace = True)\n", + " X_cv = X_cv.drop('index', axis = 1)\n", + " X_cv.drop(X_cv.columns[[j]], axis=1, inplace=True) # remove the j-th column\n", + " y_cv = np.delete(y, i) # remove the i-th data point\n", + " # refit the model and make the prediction\n", + " est_cv = sm.OLS(y_cv, X_cv).fit()\n", + " X_aug_copy = X_aug_.iloc[[i]].copy()\n", + " X_aug_copy.drop(X_aug_copy.columns[[j]], axis=1, inplace=True)\n", + " prediction_cv = est_cv.get_prediction(X_aug_copy).predicted_mean\n", + " # the risk estimator is calculated as the sum of the squared differences between each removed point and the prediction for this point\n", + " r_cv += (y[i] - prediction_cv)**2\n", + " # update the optimal predictor to drop if the risk estimator becomes lower\n", + " if (r_cv < min_r_cv):\n", + " min_index = j\n", + " min_r_cv = r_cv\n", + " # update the regressor matrix and the number of variables if deleting a predictor leads to a better model\n", + " if (min_index != 0):\n", + " X_aug_.drop(X_aug_.columns[[min_index]], axis=1, inplace=True)\n", + " variables -= 1\n", + "print('improved risk estimator:', min_r_cv)\n", + "print('remaining predictors:', X_aug_.columns.values)" + ], + "execution_count": 84, + "outputs": [ + { + "output_type": "stream", + "text": [ + "original risk estimator: [33075.17492263]\n", + "improved risk estimator: [32951.59783497]\n", + "remaining predictors: ['const' 'X1 transaction date' 'X2 house age'\n", + " 'X3 distance to the nearest MRT station'\n", + " 'X4 number of convenience stores' 'X5 latitude']\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "4n6OUTHbGLcI", + "colab_type": "code", + "outputId": "ddd641c6-a17a-402d-e62d-3b814a4d925a", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 544 + } + }, + "source": [ + "est_ = sm.OLS(y, X_aug_).fit()\n", + "print(est_.summary())" + ], + "execution_count": 85, + "outputs": [ + { + "output_type": "stream", + "text": [ + " OLS Regression Results \n", + "==============================================================================\n", + "Dep. Variable: y R-squared: 0.582\n", + "Model: OLS Adj. R-squared: 0.577\n", + "Method: Least Squares F-statistic: 113.8\n", + "Date: Mon, 08 Jun 2020 Prob (F-statistic): 4.47e-75\n", + "Time: 23:12:05 Log-Likelihood: -1487.0\n", + "No. Observations: 414 AIC: 2986.\n", + "Df Residuals: 408 BIC: 3010.\n", + "Df Model: 5 \n", + "Covariance Type: nonrobust \n", + "==========================================================================================================\n", + " coef std err t P>|t| [0.025 0.975]\n", + "----------------------------------------------------------------------------------------------------------\n", + "const -1.596e+04 3233.450 -4.936 0.000 -2.23e+04 -9602.961\n", + "X1 transaction date 5.1348 1.555 3.303 0.001 2.079 8.191\n", + "X2 house age -0.2694 0.038 -7.003 0.000 -0.345 -0.194\n", + "X3 distance to the nearest MRT station -0.0044 0.000 -8.887 0.000 -0.005 -0.003\n", + "X4 number of convenience stores 1.1361 0.188 6.056 0.000 0.767 1.505\n", + "X5 latitude 226.8816 44.174 5.136 0.000 140.044 313.719\n", + "==============================================================================\n", + "Omnibus: 232.810 Durbin-Watson: 2.154\n", + "Prob(Omnibus): 0.000 Jarque-Bera (JB): 3644.713\n", + "Skew: 2.038 Prob(JB): 0.00\n", + "Kurtosis: 16.953 Cond. No. 1.77e+07\n", + "==============================================================================\n", + "\n", + "Warnings:\n", + "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", + "[2] The condition number is large, 1.77e+07. This might indicate that there are\n", + "strong multicollinearity or other numerical problems.\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "FD2sFRnOGNR4", + "colab_type": "code", + "colab": {} + }, + "source": [ + "X_std = StandardScaler().fit_transform(X_)" + ], + "execution_count": 0, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "pr14L41BGEPE", + "colab_type": "code", + "outputId": "d2e13cbf-ce73-4229-d205-2288416c7cae", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 367 + } + }, + "source": [ + "coefs = []\n", + "alphas = np.logspace(-2, 1, 30) # the range of the parameter\n", + "for a in alphas:\n", + " l = linear_model.Lasso(alpha=a, fit_intercept=False)\n", + " l.fit(X_std, y)\n", + " coefs.append(l.coef_)\n", + "# plot log lambda on x-axis and the corresponding values of coefficients on y-axis\n", + "ax = plt.gca()\n", + "ax.plot(alphas, coefs)\n", + "ax.set_xscale('log')\n", + "plt.xlabel('Log lambda')\n", + "plt.ylabel('Coefficients')\n", + "plt.title('Coefficients as a function of lambda')\n", + "plt.axis('tight')" + ], + "execution_count": 87, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "(0.00707945784384138,\n", + " 14.12537544622754,\n", + " -6.055023647908607,\n", + " 3.7774646433491075)" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 87 + }, + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "V9UTN6veGYtg", + "colab_type": "code", + "outputId": "d3b67ca9-6f42-48be-a28d-50f7b1f4c009", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 51 + } + }, + "source": [ + "parameters_lasso = [{'alpha': alphas}]\n", + "cv_lasso = GridSearchCV(linear_model.Lasso(), parameters_lasso, scoring = 'neg_mean_squared_error')\n", + "cv_lasso.fit(X_std, y)\n", + "scores_lasso = cv_lasso.cv_results_['mean_test_score'] # the scores are negative\n", + "scores_lasso = np.negative(scores_lasso) # reverse the sign of the score\n", + "scores_std_lasso = cv_lasso.cv_results_['std_test_score'] # standard deviation\n", + "# print the optimal values\n", + "print('best score:', np.negative(cv_lasso.best_score_))\n", + "print('lambda:', cv_lasso.best_params_.get('alpha'))" + ], + "execution_count": 88, + "outputs": [ + { + "output_type": "stream", + "text": [ + "best score: 78.31608978858921\n", + "lambda: 0.05298316906283707\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "vynCAYy4Gtjv", + "colab_type": "code", + "outputId": "e62f05f4-d06c-4ee0-c7f8-e7c69a1b2dd9", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 316 + } + }, + "source": [ + "# plot the cross validation score against log lambda\n", + "fig_lasso = plt.figure()\n", + "plt.semilogx(alphas, scores_lasso)\n", + "std_error_lasso = scores_std_lasso / np.sqrt(X_.shape[0])\n", + "# shade the region within 1 std err\n", + "plt.semilogx(alphas, scores_lasso + std_error_lasso, 'b--')\n", + "plt.semilogx(alphas, scores_lasso - std_error_lasso, 'b--')\n", + "plt.fill_between(alphas, scores_lasso + std_error_lasso, scores_lasso - std_error_lasso, alpha = 0.25)\n", + "plt.ylabel('CV score +/- std error')\n", + "plt.xlabel('Log lambda')\n", + "plt.axhline(np.min(scores_lasso), linestyle='--', color='.5')\n", + "plt.xlim([alphas[0], alphas[-1]])\n", + "plt.title('CV score as a function of lambda')" + ], + "execution_count": 89, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "Text(0.5, 1.0, 'CV score as a function of lambda')" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 89 + }, + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "tMFZgiDEG059", + "colab_type": "code", + "outputId": "e4a6fc31-d0ff-47a0-d2ee-0e8e2a11b304", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 187 + } + }, + "source": [ + "# print the standardized coefficients\n", + "print('Lasso Results:')\n", + "print('(Standardized)')\n", + "lasso = linear_model.Lasso(alpha = cv_lasso.best_params_.get('alpha'))\n", + "lasso.fit(X_std, y)\n", + "lasso_df = pd.DataFrame(lasso.coef_, X_.columns, columns=['Coefficient'])\n", + "print('Intercept %.6f' %(lasso.intercept_))\n", + "print(lasso_df)" + ], + "execution_count": 91, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Lasso Results:\n", + "(Standardized)\n", + "Intercept 37.980193\n", + " Coefficient\n", + "X1 transaction date 1.392322\n", + "X2 house age -3.008603\n", + "X3 distance to the nearest MRT station -5.468975\n", + "X4 number of convenience stores 3.311749\n", + "X5 latitude 2.782846\n", + "X6 longitude -0.000000\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "cYEx491nG7pd", + "colab_type": "code", + "outputId": "ca0d1dfa-63ae-49ff-f6d8-4492bc8093d5", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 170 + } + }, + "source": [ + "# back-convert for ease of interpretation\n", + "# beta_real = beta_std / std err\n", + "# intercept_real = intercept_std - sum of (mean * beta_std / stderr)\n", + "print('(Real)')\n", + "lasso_real = lasso_df.copy()\n", + "intercept_real = lasso.intercept_\n", + "count_lasso = lasso_real.shape[0]\n", + "for i in range(lasso_real.shape[0]):\n", + " # decrement the total number of predictors if the coefficient is reduced to zero\n", + " if lasso_real.iloc[i, 0] == 0:\n", + " count_lasso -= 1\n", + " lasso_real.iloc[i, 0] /= np.std(X_.iloc[:, i])\n", + " intercept_real -= (lasso_real.iloc[i, 0] * np.mean(X_.iloc[:, i]))\n", + "print('Intercept %.6f' %(intercept_real))\n", + "print(lasso_real)" + ], + "execution_count": 92, + "outputs": [ + { + "output_type": "stream", + "text": [ + "(Real)\n", + "Intercept -15515.768488\n", + " Coefficient\n", + "X1 transaction date 4.943862\n", + "X2 house age -0.264406\n", + "X3 distance to the nearest MRT station -0.004338\n", + "X4 number of convenience stores 1.125679\n", + "X5 latitude 224.509957\n", + "X6 longitude -0.000000\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "rAdP1sYCHCd_", + "colab_type": "code", + "outputId": "f0d02f31-affd-4f5b-d347-3bf185feab79", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 673 + } + }, + "source": [ + "print('Ridge Results:')\n", + "alphas_ridge = np.logspace(-2, 5, 30) # the range of the parameter\n", + "parameters_ridge = [{'alpha': alphas_ridge}]\n", + "cv_ridge = GridSearchCV(linear_model.Ridge(), parameters_ridge, scoring = 'neg_mean_squared_error')\n", + "cv_ridge.fit(X_std, y)\n", + "scores_ridge = cv_ridge.cv_results_['mean_test_score'] # the scores are negative\n", + "scores_ridge = np.negative(scores_ridge) # reverse the sign of the score\n", + "scores_std_ridge = cv_ridge.cv_results_['std_test_score'] # standard deviation\n", + "\n", + "# plot the cross validation score against log lambda\n", + "fig_ridge = plt.figure()\n", + "plt.semilogx(alphas_ridge, scores_ridge)\n", + "std_error_ridge = scores_std_ridge / np.sqrt(X_.shape[0])\n", + "# shade the region within 1 std err\n", + "plt.semilogx(alphas_ridge, scores_ridge + std_error_ridge, 'b--')\n", + "plt.semilogx(alphas_ridge, scores_ridge - std_error_ridge, 'b--')\n", + "plt.fill_between(alphas_ridge, scores_ridge + std_error_ridge, scores_ridge - std_error_ridge, alpha = 0.25)\n", + "plt.ylabel('CV score +/- std error')\n", + "plt.xlabel('Log lambda')\n", + "plt.axhline(np.min(scores_ridge), linestyle='--', color='.5')\n", + "plt.xlim([alphas_ridge[0], alphas_ridge[-1]])\n", + "plt.title('CV score as a function of lambda')\n", + "plt.show()\n", + "# print the optimal values\n", + "print('best score:', np.negative(cv_ridge.best_score_))\n", + "print('lambda:', cv_ridge.best_params_.get('alpha'))\n", + "\n", + "# print the standardized coefficients\n", + "print('(Standardized)')\n", + "ridge = linear_model.Ridge(alpha = cv_ridge.best_params_.get('alpha'))\n", + "ridge.fit(X_std, y)\n", + "ridge_df = pd.DataFrame(ridge.coef_, X_.columns, columns=['Coefficient'])\n", + "print('Intercept %.6f' %(ridge.intercept_))\n", + "print(ridge_df)\n", + "\n", + "# back-convert for ease of interpretation\n", + "# beta_real = beta_std / std err\n", + "# intercept_real = intercept_std - sum of (mean * beta_std / stderr)\n", + "print('\\n(Real)')\n", + "ridge_real = ridge_df.copy()\n", + "ridge_intercept_real = ridge.intercept_\n", + "count_ridge = ridge_real.shape[0]\n", + "for i in range(count_ridge):\n", + " ridge_real.iloc[i, 0] /= np.std(X_.iloc[:, i])\n", + " ridge_intercept_real -= (ridge_real.iloc[i, 0] * np.mean(X_.iloc[:, i]))\n", + "print('Intercept %.6f' %(ridge_intercept_real))\n", + "print(ridge_real)" + ], + "execution_count": 93, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Ridge Results:\n" + ], + "name": "stdout" + }, + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + }, + { + "output_type": "stream", + "text": [ + "best score: 78.32898324034278\n", + "lambda: 2.592943797404667\n", + "(Standardized)\n", + "Intercept 37.980193\n", + " Coefficient\n", + "X1 transaction date 1.436194\n", + "X2 house age -3.048938\n", + "X3 distance to the nearest MRT station -5.543872\n", + "X4 number of convenience stores 3.336385\n", + "X5 latitude 2.806742\n", + "X6 longitude -0.104249\n", + "\n", + "(Real)\n", + "Intercept -15050.879394\n", + " Coefficient\n", + "X1 transaction date 5.099639\n", + "X2 house age -0.267951\n", + "X3 distance to the nearest MRT station -0.004398\n", + "X4 number of convenience stores 1.134053\n", + "X5 latitude 226.437833\n", + "X6 longitude -6.800912\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "qGSTHaMbLIJ8", + "colab_type": "code", + "outputId": "20032b37-bdb9-4735-cf58-1e2db11e5a8c", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 673 + } + }, + "source": [ + "print('Elastic Net Results:')\n", + "alphas_elastic_net = np.logspace(-2, 1, 30) # the range of the parameter\n", + "parameters_elastic_net = [{'alpha': alphas_elastic_net}]\n", + "cv_elastic_net = GridSearchCV(linear_model.ElasticNet(), parameters_elastic_net, scoring = 'neg_mean_squared_error')\n", + "cv_elastic_net.fit(X_std, y)\n", + "scores_elastic_net = cv_elastic_net.cv_results_['mean_test_score'] # the scores are negative\n", + "scores_elastic_net = np.negative(scores_elastic_net) # reverse the sign of the score\n", + "scores_std_elastic_net = cv_elastic_net.cv_results_['std_test_score'] # standard deviation\n", + "\n", + "# plot the cross validation score against log lambda\n", + "fig_elastic_net = plt.figure()\n", + "plt.semilogx(alphas_elastic_net, scores_elastic_net)\n", + "std_error_elastic_net = scores_std_elastic_net / np.sqrt(X_.shape[0])\n", + "# shade the region within 1 std err\n", + "plt.semilogx(alphas_elastic_net, scores_elastic_net + std_error_elastic_net, 'b--')\n", + "plt.semilogx(alphas_elastic_net, scores_elastic_net - std_error_elastic_net, 'b--')\n", + "plt.fill_between(alphas_elastic_net, scores_elastic_net + std_error_elastic_net, scores_elastic_net - std_error_elastic_net, alpha = 0.25)\n", + "plt.ylabel('CV score +/- std error')\n", + "plt.xlabel('Log lambda')\n", + "plt.axhline(np.min(scores_elastic_net), linestyle='--', color='.5')\n", + "plt.xlim([alphas_elastic_net[0], alphas_elastic_net[-1]])\n", + "plt.title('CV score as a function of lambda')\n", + "plt.show()\n", + "# print the optimal values\n", + "print('best score:', np.negative(cv_elastic_net.best_score_))\n", + "print('lambda:', cv_elastic_net.best_params_.get('alpha'))\n", + "\n", + "# print the standardized coefficients\n", + "print('(Standardized)')\n", + "elastic = linear_model.ElasticNet(alpha = cv_elastic_net.best_params_.get('alpha'))\n", + "elastic.fit(X_std, y)\n", + "elastic_df = pd.DataFrame(elastic.coef_, X_.columns, columns=['Coefficient'])\n", + "print('Intercept %.6f' %(elastic.intercept_))\n", + "print(elastic_df)\n", + "\n", + "# back-convert for ease of interpretation\n", + "# beta_real = beta_std / std err\n", + "# intercept_real = intercept_std - sum of (mean * beta_std / stderr)\n", + "print('\\n(Real)')\n", + "elastic_real = elastic_df.copy()\n", + "elastic_intercept_real = elastic.intercept_\n", + "count_elastic = elastic_real.shape[0]\n", + "for i in range(count_elastic):\n", + " elastic_real.iloc[i, 0] /= np.std(X_.iloc[:, i])\n", + " elastic_intercept_real -= (elastic_real.iloc[i, 0] * np.mean(X_.iloc[:, i]))\n", + "print('Intercept %.6f' %(elastic_intercept_real))\n", + "print(elastic_real)" + ], + "execution_count": 94, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Elastic Net Results:\n" + ], + "name": "stdout" + }, + { + "output_type": "display_data", + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + }, + { + "output_type": "stream", + "text": [ + "best score: 78.32578208939992\n", + "lambda: 0.020433597178569417\n", + "(Standardized)\n", + "Intercept 37.980193\n", + " Coefficient\n", + "X1 transaction date 1.417179\n", + "X2 house age -3.024698\n", + "X3 distance to the nearest MRT station -5.430362\n", + "X4 number of convenience stores 3.333001\n", + "X5 latitude 2.811782\n", + "X6 longitude -0.003293\n", + "\n", + "(Real)\n", + "Intercept -15725.668991\n", + " Coefficient\n", + "X1 transaction date 5.032121\n", + "X2 house age -0.265821\n", + "X3 distance to the nearest MRT station -0.004308\n", + "X4 number of convenience stores 1.132902\n", + "X5 latitude 226.844458\n", + "X6 longitude -0.214813\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "Kd0WjA_kLSQW", + "colab_type": "code", + "outputId": "4fc30baf-8999-4168-b623-bee31aa34ec7", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 68 + } + }, + "source": [ + "y_pred_lasso = lasso.predict(X_std) # predictions\n", + "r2_lasso = metrics.r2_score(y, y_pred_lasso) # R-squared\n", + "adj_r2_lasso = 1 - (1 - r2_lasso) * (X_.shape[0] - 1) / (X_.shape[0] - count_lasso - 1) # adjusted R-squared\n", + "print('Lasso adj. R2:', adj_r2_lasso)\n", + "\n", + "y_pred_ridge = ridge.predict(X_std) # predictions\n", + "r2_ridge = metrics.r2_score(y, y_pred_ridge) # R-squared\n", + "adj_r2_ridge = 1 - (1 - r2_ridge) * (X_.shape[0] - 1) / (X_.shape[0] - count_ridge - 1) # adjusted R-squared\n", + "print('Ridge adj. R2:', adj_r2_ridge)\n", + "\n", + "y_pred_elastic = elastic.predict(X_std) # predictions\n", + "r2_elastic = metrics.r2_score(y, y_pred_elastic) # R-squared\n", + "adj_r2_elastic = 1 - (1 - r2_elastic) * (X_.shape[0] - 1) / (X_.shape[0] - count_elastic - 1) # adjusted R-squared\n", + "print('Elastic Net adj. R2:', adj_r2_elastic)" + ], + "execution_count": 95, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Lasso adj. R2: 0.5771295619995425\n", + "Ridge adj. R2: 0.576190574926105\n", + "Elastic Net adj. R2: 0.5761109296860583\n" + ], + "name": "stdout" + } + ] + } + ] +} \ No newline at end of file From e046e78769c4c16a3b03d0f8bd230a1f9fe3b788 Mon Sep 17 00:00:00 2001 From: Bowen1Zhu <42977266+Bowen1Zhu@users.noreply.github.com> Date: Tue, 9 Jun 2020 14:06:36 -0400 Subject: [PATCH 3/9] Create blog --- LinearRegression/Blog/1.png | Bin 0 -> 8481 bytes LinearRegression/Blog/10.png | Bin 0 -> 3739 bytes LinearRegression/Blog/11.png | Bin 0 -> 9029 bytes LinearRegression/Blog/12.png | Bin 0 -> 26251 bytes LinearRegression/Blog/13.png | Bin 0 -> 7250 bytes LinearRegression/Blog/14.png | Bin 0 -> 3977 bytes LinearRegression/Blog/15.png | Bin 0 -> 6582 bytes LinearRegression/Blog/16.png | Bin 0 -> 6236 bytes LinearRegression/Blog/17.png | Bin 0 -> 19402 bytes LinearRegression/Blog/18.png | Bin 0 -> 14047 bytes LinearRegression/Blog/19.png | Bin 0 -> 2106 bytes LinearRegression/Blog/2.png | Bin 0 -> 2125 bytes LinearRegression/Blog/20.png | Bin 0 -> 12350 bytes LinearRegression/Blog/21.png | 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+\begin{document} +\newgeometry{top=3.5cm} +\maketitle + +\textbf{Linear Regression models} allow us to summarize and study relationships between variables by fitting a straight line to the observed data. You may have heard of \textbf{simple linear regression}, which establishes the relationship between two quantitative variables--one predictor variable and one target variable. + +However, in reality, it is rare that a target variable is explained by only one predictor. So what if we want to estimate a continuous variable using more than one predictors? If two or more predictor variables have a linear relationship with the target variable, a \textbf{multiple linear regression analysis} allows us to quantify the strength of the relationship and estimate the target variable at a certain value of the predictor variables. + +This tutorial will show you step-by-step how to perform a multiple linear regression analysis using Python, from checking assumptions to evaluating performance. +\section*{Getting Started} +\subsection*{Import Libraries} +First, let's important all necessary libraries in the beginning to keep our code organized: +\begin{figure}[H]\includegraphics[width=\linewidth]{1}\end{figure} +\restoregeometry +\subsection*{Read Dataset} +For this analysis, I will use a real estate dataset that can be downloaded from \href{https://www.kaggle.com/quantbruce/real-estate-price-prediction}{here}. I choose to upload it to Google Colab from local drive. Of course, you can also replace the first argument in read\_csv() with the filepath or URL to the dataset that you'd like to use instead. The delimiter parameter is set to comma by default, but you can change it depending on the delimiter of your csv file. +\begin{figure}[H]\includegraphics[width=\linewidth]{2}\end{figure} +We can take a look at what the data looks like: +\begin{figure}[H]\includegraphics[width=\linewidth]{3}\end{figure} +\begin{figure}[H]\includegraphics[width=\linewidth]{4}\end{figure} +As you can see, the first column in the real estate data set is redundant, so we should probably remove it. Otherwise, this data set seems directly usable. However, it's likely that your own data set will require more preprocessing--dealing with missing/invalid values, restructuring the data, and encoding dummy variables, etc. +\begin{figure}[H]\includegraphics[width=\linewidth]{5}\end{figure} +After data preprocessing, we can use the describe() function to obtain some summary statistics of our target variable, and the displot() function from the seaborn library to plot its distribution. +\begin{figure}[H]\includegraphics[width=1.1\linewidth]{6}\end{figure} +\begin{figure}[H]\centering\includegraphics[width=0.5\linewidth]{7}\end{figure} +We see that the values of house price of unit area are normally distributed with perhaps a few outliers on the right. +\section*{Checking Multicollinearity} +Before the analysis, it is important to verify several regression conditions so as to make sure that our analysis is valid. Most of the conditions in linear regression can be checked easily with the residuals--the only snag is that we get the residuals only \textit{after} we perform the regression. Still, "no multicollinearity" is the condition that we are able to check beforehand, without using the residuals. + +Since a multiple regression involves more than one predictor variables, multicollinearity occurs when some of them are highly correlated with each other, which means each of these predictors will account for similar variance in the target variable. Therefore, though the presence of multicollinearity will not affect the predictive power of our model, it will make it more difficult for us to assess the individual influence of a predictor on our target variable. We can detect multicollinearity using either a correlation matrix or VIF factors. +\subsection*{Correlation Matrix} +The correlation coefficient is a statistic that measures linear correlation between two variables. Its value lies between -1 and +1. The absolute value gives the strength of the relationship between the two variables. The larger its magnitude, the stronger their relationship. In general, a correlation coefficient above +0.8 or below -0.8 indicates a strong correlation, and we should take some measures to reduce multicollinearity before we continue. + +The pandas corr() function calculates the correlations among all variables in the dataframe. We can visualize the resulting correlation matrix using a heatmap from the seaborn library. The diagonal values should always equal 1 since they are the correlations of a variable with itself. +\begin{figure}[H]\includegraphics[width=1.1\linewidth]{8}\end{figure} +\begin{figure}[H]\includegraphics[width=0.9\linewidth]{9}\end{figure} +\subsection*{VIF Factors} +VIF factor is an alternative measure for multicollinearity, which ranges from 1 upwards. A rule of thumb used in practice is if a VIF value is greater than 4, then multicollinearity is a problem. We can check VIF factors using the variance\_inflation\_factor() function from the statsmodels package. +\begin{figure}[H]\includegraphics[width=\linewidth]{10}\end{figure} +\begin{figure}[H]\centering\includegraphics[width=0.5\linewidth]{11}\end{figure} +You should see in the correlation matrix that the correlation coefficient between X3 and X6 is $-0.81 < -0.8$, and the VIF factor for X3 is also slightly higher than 4, which is unfavorable. A simple solution is to remove one of the correlated variables from our model. After removing X3 from the list of column names and rerunning the previous code, the new correlation matrix should show no significant multicollinearity, and the VIF factors of all the remaining variables are around 1, so we are in good shape, and can proceed with our regression. +\begin{figure}[H]\includegraphics[width=0.8\linewidth]{12}\end{figure} +\begin{figure}[H]\centering\includegraphics[width=0.5\linewidth]{13}\end{figure} +But wait, you may ask, why did I choose to delete X3 rather than X6? Indeed, my choice was kind of arbitrary here. To remove the redundant variables more carefully, we can consider using stepwise regression to only keep the predictors that lead to the best performance; I will describe backwards stepwise regression later. + +Another way to deal with multicollinearity without having to drop your predictors before the analysis is to perform regression with regularization techniques (such as Lasso and Ridge) which I will also describe at the end of the article. Regularization can help you handle multicollinearity, so if you don't want to delete any variables, you may choose to skip the OLS model below and directly jump to the Lasso/Ridge/Elastic Net regression presented in the end. + +\section*{Performing the Regression} +\subsection*{A Bit of Math} +Now it's finally time to introduce our regression model. Under the linear model, the actual value of our target variable should be a linear combination of all predictor variables plus a constant (intercept) as well as some errors. Thus it can be written in the form of an equation $y = \beta_0 + \beta_1 X_1 + \beta_2 X_2 + \dots + \epsilon_i$, and our goal is to estimate $\beta_0$, $\beta_1$, $\beta_2$, ... + +Assuming you’re not scared of matrices, let's first understand some mathematical background for linear regression in linear algebra. More generally speaking, suppose our data consisits of $n$ observations, each of which contains the values of $k$ predictor variables (not including the intercept) as well as the corresponding value of the target variable. In matrix notation, we can write the regressor matrix $\text{X}$ as +$\begin{bmatrix} +1 & X_{11} & \dots & X_{1k} \\ +1 & X_{21} & \dots & X_{2k} \\ +\vdots & \vdots & \ddots & \vdots \\ +1 & X_{n1} & \dots & X_{nk} \\ +\end{bmatrix}$, the target vector $\mathbf{y}$ as +$\begin{bmatrix} +y_1 \\ +y_2 \\ +\vdots \\ +y_n \\ +\end{bmatrix}$, the coefficient vector $\bm{\beta}$ as +$\begin{bmatrix} +\beta_0 \\ +\beta_1 \\ +\vdots \\ +\beta_k \\ +\end{bmatrix}$, and the residual vector $\bm{\epsilon}$ as +$\begin{bmatrix} +\epsilon_1 \\ +\epsilon_2 \\ +\vdots \\ +\epsilon_n \\ +\end{bmatrix}$. Then, our linear model can be rewritten as the following: +$\begin{bmatrix} +y_1 \\ +y_2 \\ +\vdots \\ +y_n \\ +\end{bmatrix} = +\begin{bmatrix} +1 & X_{11} & \dots & X_{1k} \\ +1 & X_{21} & \dots & X_{2k} \\ +\vdots & \vdots & \ddots & \vdots \\ +1 & X_{n1} & \dots & X_{nk} \\ +\end{bmatrix} +\begin{bmatrix} +\beta_0 \\ +\beta_1 \\ +\vdots \\ +\beta_k \\ +\end{bmatrix} + +\begin{bmatrix} +\epsilon_1 \\ +\epsilon_2 \\ +\vdots \\ +\epsilon_n \\ +\end{bmatrix}$. Or, more simply, as $\mathbf{y} = \text{X} \bm{\beta} + \bm{\epsilon}$, where for each $i \in [1, n]$, $y_i = \beta_0 + \beta_1 X_{i1} + \beta_2 X_{i2} + \dots + \beta_k X_{ik} + \epsilon_i$. + +The simplest model that we're going to start with is the ordinary least squares (OLS) regression, which aims to minimize the sum of the squared residuals $\norm{\epsilon}^2$, which is equivalent to $\norm{\mathbf{y} - \text{X} \bm{\beta}}^2$. It can be shown via matrix calculus that the least squares estimator for our coefficient vector $\bm{\beta}$ is given by $\bm{\hat{\beta}} = (\text{X}^\intercal \text{X})^{-1} \text{X}^\intercal \mathbf{y}$. +\subsection*{Getting the Coefficients} +The above calculation has already been implemented in the scikit-learn library so we don't need to calculate $\bm{\hat{\beta}}$ manually. After instantiating the LinearRegression class, we can easily obtain the coefficients along with the intercept by calling the fit() method along with our data. +\begin{figure}[H]\includegraphics[width=\linewidth]{14}\end{figure} +\begin{figure}[H]\centering\includegraphics[width=0.6\linewidth]{15}\end{figure} +This means, for example, that for every one unit of change in X1 transaction date, the change in the house price of unit area is approximately 4.21. + +We can compare and visualize some predicted values of the house price with the corresponding actual values in a bar graph: +\begin{figure}[H]\includegraphics[width=\linewidth]{16}\end{figure} +\vspace*{-2cm} +\begin{figure}[H]\includegraphics[width=0.25\linewidth]{17}\end{figure} +\begin{figure}[H]\includegraphics[width=\linewidth]{18}\end{figure} + +\section*{Checking the Residuals} +Congrats! You have successfully obtained the regression line. But remember that we still need to check the residuals of the regression to ensure its validity. + +First, we can use the scatter() function from the matplotlib library to plot the residuals (between the actual and predicted values) against the predicted values. We expect to see that the points are randomly distributed in the scatter plot. More specifically, they should show no curvature (which ensures linearity), and constant variation along the predicted value (which ensures homoscedasticity). +\begin{figure}[H]\centering\includegraphics[width=0.9\linewidth]{19}\end{figure} +\begin{figure}[H]\centering\includegraphics[width=0.6\linewidth]{20}\end{figure} +Finally, let's generate a normal probability plot using probplot() to test the normality of the residuals. If the residuals are normally distributed, the points in the normal probability plot should stick to the red diagonal line as closely as possible. As shown in the plot below, the residuals of our real estate model show a slight deviation from the ideal line, but the deviation or bend is not very serious. +\begin{figure}[H]\centering\includegraphics[width=\linewidth]{21}\end{figure} +\begin{figure}[H]\centering\includegraphics[width=0.6\linewidth]{22}\end{figure} +The above procedure indicates that our residuals satisfy the regression conditions. If, however, your residuals do show some strong patterns, you should consider transforming your data using negative reciprocal, logarithm, square root, square, or exponentiation and then redo the regression. If none of the above transformation options can solve the problem, it's possible that your data set does not fit the linear model, and you may resort to a nonlinear model. + +\section*{Making Predictions} +After all the previous conditions have been verified, you now have a trustworthy regression equation which enables you to make some predictions if given an extra piece of data. While we can use predict() in scikit-learn to get the mean of our prediction (like what we did when comparing the predicted values with the actual values right after we've got the coefficients), confidence intervals are available via the get\_prediction() in the statsmodels package. However, unlike the scikit-learn library, statsmodels does not add a column of ones to the regressor matrix by default, so before calling get\_prediction() we need to add the ones using the add\_constant() function. +\begin{figure}[H]\centering\includegraphics[width=\linewidth]{23}\end{figure} +\begin{figure}[H]\centering\includegraphics[width=1.05\linewidth]{24}\end{figure} +Note that apart from the mean and standard error, summary\_frame() spits out two intervals at 95\% confidence level (we have set alpha = 0.05). The first pair of lower bound and upper bound forms a confidence interval, which is an estimate of the mean price of all the houses that match our randomly generated data. The second pair, on the other hand, forms a prediction interval, which estimate the price of a particular house with this set of data. Because individual values vary more than means, we can expect the prediction interval to be wider than the confidence interval at the same confidence level. + +\section*{Evaluations} +While it is relatively straightforward to obtain regression lines and predictions, there are numerous evaluation metrics to measure the accuracy of our model. In fact, the summary() function from statsmodels provides you with an overwhelming amount of data: +\begin{figure}[H]\includegraphics[width=\linewidth]{25}\end{figure} +Don't panic, let's interpret some important values one by one. +\subsubsection*{R-squared and Adjusted R-squared} +\begin{figure}[H]\includegraphics[width=0.5\linewidth]{26}\end{figure} +R-squared, a.k.a. coefficient of determination, measures the proportion of the variance of the target variable that can be explained by the predictors in our model. It is calculated as $1 - \frac{\text{Sum of Squares Error (SSE)}}{\text{Sum of Squares Total (SST)}}$, and ranges from 0 to 100\%. The higher $R^2$, the better the model. An $R^2$ of 100\%, for example, means the model explains all the variation of the target variable, whereas a value of 0\% indicates zero predictive capability. +Our model has $R^2 = 0.542$, so approximately 54\% of the variation in the house price can be accounted for by our OLS model. + +Note that there's an adjusted $R^2 = 0.537$ in the second row which is slightly smaller than $R^2$. This is because $R^2$ only works as intended in a simple linear regression model where there's only one predictor. In a multiple regression, when a new predictor is added to the model, $R^2$ can only increase but never decrease. This implies that a model may seem to have a better fit simply because it has more predictors. Thus the adjusted $R^2$, calculated as $1 - \frac{\text{Mean Squares Error (MSE)}}{\text{Mean Squares Total (MST)}}$ or $1 - \frac{(1 - R^2)(n - 1)}{n - k - 1}$ if we already know $R^2$, takes into account the number of predictors $k$ and the number of data points $n$ in the model. It only increases if the new predictor improves the model more than expected by chance and decreases if it fails to do so. As a result, adjusted $R^2$ should always be less than or equal to $R^2$. +\subsubsection*{F-statistic} +\begin{figure}[H]\includegraphics[width=0.5\linewidth]{27}\end{figure} +Below $R^2$ and the adjusted $R^2$ is the F-statistic which is the statistic of an F-test checking whether our model fits the data well. The null hypothesis of the F-test is that the model with no predictors but only an intercept can fit the data as well as the proposed one. To put it simply, it's testing whether $R^2$ is significantly greater than zero. The F-statistic is the ratio of the explained variance to the unexplained variance, so a higher value of F-statistic is evidence against the null hypothesis. + +The fourth row on the right gives the p-value corresponding to the F-statistic. Our model yields a very small p-value of 5.12e-67, so there is sufficient evidence to reject the null hypothesis and conclude that our model does have some predictive power. +\subsubsection*{Confidence Intervals and t-tests} +\begin{figure}[H]\includegraphics[width=\linewidth]{28}\end{figure} +Perhaps the most important information is located in the central part of the summary. We can see the estimated values of each coefficient in the first column, followed by an estimate of the standard deviation of the coefficient. The last two columns provide 95\% confidence intervals constructed from the coefficients and their standard errors in the first two columns. + +The two columns in the middle are the results of t-tests checking for the relevancy of each coefficient. The null hypothesis of each t-test is that the corresponding coefficient equals zero, meaning no linear relationship between this predictor and the target variable. The t-statistic is the value in the first column (mean) divided by the second column (standard error); the p-values corresponding to each t-statistic are presented in the next column. You can see that the p-values of all our coefficients except X1 are smaller than .01, so we can safely reject the null hypotheses and say that they are indeed relevant to predicting our target variable. However, X1 may be a redundant variable at .01 significance level. + +\section*{Stepwise Regression} +The results of the OLS regression seem significant but the real estate data set involves only 6 predictors. When we have a substantial number of predictors in the model, it's unlikely that all of them will have significant p-values. Oftentimes, there exist predictors that give redundant information. As the model increases in complexity, the variance of our estimator can get very large. Thus we may consider getting rid of some of the predictors in order to simplify the model and prevent overfitting. + +In theory, you could try all the possible combinations of your predictors and select the one that you believe is the best (for example, the model that yields the highest adjusted $R^2$). However, imagine your data set contains have 20 predictors, then you would need to compare $2^{20} > 1,000,000$ potential models! + +An easier predictor selection procedure, as I mentioned previously, is backwards stepwise regression. Starting with all predictors in the model, in each iteration we find out which predictor to delete, if any, will lead to the best model. We repeat this step until we can't improve our model by removing any variables. (Similarly, there is also forward stepwise regression that works in the reverse way.) + +The question then arises: how do we determine quantitatively which model is the best? There are numerous methods that can provide a quantitative measure of the model performance. The one I present here is leave-one-out cross-validation. Its procedure is as follows: in each iteration, we pick a data point (a row of $X_{i\cdot}$ and $y_i$) from our data set, and refit an OLS model on the remaining data points. Based on this model, we make a prediction $\hat{y}_{i}$ for the data point $y_i$ that we picked in the current iteration. We sum up the squared differences between each data point and its predicted value, i.e. $\sum_{i=1}^{n} (y_i - \hat{y}_i)^2$ as our evaluation metric, called the risk estimator. A good model should yield small difference between each pair of predicted and actual values, thus a smaller risk estimator is preferred. + +Using leave-one-out cross-validation, we are able to quantitatively compare the models during each iteration of backwards stepwise regression. This procedure is not supported in Python libraries, so we have to implement the process by ourselves: +\begin{figure}[H]\centering\includegraphics[width=1.1\linewidth]{29.1}\end{figure} +\begin{figure}[H]\centering\includegraphics[width=1.1\linewidth]{29.2}\end{figure} +We can apply the above function to our real estate data, though it is too small in size to let the above algorithm run for many rounds and make significant improvement. Still, backwards stepwise regression reveals that X6 is the only predictor among X1-X6 that should be dropped so that the risk estimator can be improved from 33075 to 32952 (obviously, very little improvement here). +\begin{figure}[H]\includegraphics[width=0.8\linewidth]{30}\end{figure} +We can try to rerun the OLS regression with X6 removed from the model. The adjusted $R^2$ now increases to 0.577. Thus to reduce multicollinearity, deleting X6 is perhaps a better option than X3. +\begin{figure}[H]\includegraphics[width=1.1\linewidth]{31}\end{figure} +\begin{figure}[H]\includegraphics[width=\linewidth]{32}\end{figure} + +\section*{Regularization} +However, stepwise regression has many potential drawbacks. For example, as a greedy search algorithm, it is not guaranteed to find the best model, especially when predictors are correlated. + +Another approach that performs predictor selection and also works in the presence of multicollinearity is regularization, a technique for reducing the complexity of the model by adding an extra penalty term to the errors. More specifically, our objective here is still to minimize $\norm{\mathbf{y} - \text{X} \bm{\beta}}^2$ (same as the OLS model), but we now impose an additional constraint that the coefficients should not exceed some threshold. The specific constraint depends on the type of the regularization. Below I will mention three popular regularization techniques--Lasso, Ridge, and Elastic Net. + +(I will stick to the real estate data as our example data set. But normally, these techniques are used when we have a substantial number of predictors in a complex model, avoiding the risk of overfitting. Thus it would probably be a little bit of overkill in this case where only 6 predictor variables are involved.) + +First, since the new model will penalize large coefficients, we need to standardize our predictor variables to ensure that the penalty is applied fairly across all predictors. By standardization I mean converting the values in each column of the regressor matrix into z-scores, so the standard score of $x$ is calculated as $z = \frac{x - \mu}{\sigma}$, where $\mu$ is the mean of all values in the same column and $\sigma$ is their standard deviation. +\begin{figure}[H]\includegraphics[width=0.6\linewidth]{33}\end{figure} +After the standardization, we are ready to choose a specific model to perform. Let's start with Lasso regression. Lasso regression requires that the sum of the absolute values of the coefficients $\norm{\beta}_1$ is no larger than some prespecified value. Using Lagrange Multiplier, we can write our objective function to minimize as $\norm{\mathbf{y} - \text{X} \bm{\beta}}^2_2 + \lambda \norm{\beta}_1$. $\lambda \norm{\beta}_1$ is the extra penalty term here and can be controlled by changing the value of $\lambda$. When $\lambda$ is zero, the model reduces to OLS; when $\lambda$ tends to infinity, all coefficients approach zero. You can imagine that, as I gradually increase $\lambda$, the magnitude of my coefficients has to decrease towards zero. This can be illustrated by the code below: +\begin{figure}[H]\includegraphics[width=0.8\linewidth]{34}\end{figure} +\begin{figure}[H]\centering\includegraphics[width=0.5\linewidth]{35}\end{figure} +To improve the predictive power of our model, we can again resort to cross-validation and choose the $\lambda$ that optimizes some evaluation metrics, such as the cross-validated sum of squared residuals. This can be done by the GridSearchCV() function in scikit-learn. It searches over some range of $\lambda$ to find the optimal evaluation score. Note that the scoring metric is negative mean squared error since the scoring API is designed to maximize rather than minimize the score. Of course, we can easily convert the score back to positive using the negative() function in numpy. +\begin{figure}[H]\centering\includegraphics[width=\linewidth]{36}\end{figure} +\begin{figure}[H]\includegraphics[width=0.5\linewidth]{37}\end{figure} +We can visualize where the optimal value of $\lambda$ is located in the interval: +\begin{figure}[H]\includegraphics[width=\linewidth]{38}\end{figure} +\begin{figure}[H]\centering\includegraphics[width=0.6\linewidth]{39}\end{figure} +Putting the optimal value of $\lambda$ in the parameter of Lasso(), we can obtain the coefficients under the Lasso model: +\begin{figure}[H]\includegraphics[width=\linewidth]{40}\end{figure} +\begin{figure}[H]\includegraphics[width=0.75\linewidth]{41}\end{figure} +Note that X6 is again reduced to zero. The significant changes in the magnitude of other coefficients is due to the fact that we have standardized our predictors before the regression. To recover the interpretability of our results, we may choose to back-convert the coefficients (by dividing by the standard deviation) and the intercept (by subtracting all the coefficients times the means of the corresponding predictors and divided by the corresponding standard deviations): +\begin{figure}[H]\includegraphics[width=\linewidth]{42}\end{figure} +\begin{figure}[H]\includegraphics[width=0.75\linewidth]{43}\end{figure} +We can also try Ridge and Elastic Net regression. Their procedures are exactly the same except that we need to call different functions for different types of regressions. + +For Ridge regression, the only difference is that the objective now becomes $\min\limits_{\beta} \norm{Y - X\beta}^2_2 + \lambda \norm{\beta}^2_2$. (The constraint is now on the sum of squared coefficients.) While Lasso promotes predictor selection, Ridge will decrease the values of coefficients but is unable to force a coefficient to exactly 0. +\begin{figure}[H]\includegraphics[width=\linewidth]{44.1}\end{figure} +\begin{figure}[H]\includegraphics[width=\linewidth]{44.2}\end{figure} +\begin{figure}[H]\includegraphics[width=0.63\linewidth]{45}\end{figure} +Lastly, Elastic Net regression is a combination of Lasso and Ridge--the objective is $\min\limits_{\beta} \norm{Y - X\beta}^2_2 + \lambda \left(\alpha \norm{\beta}_1 + \frac{1 - \alpha}{2} \norm{\beta}^2_2\right)$, and $\alpha = 0.5$ by default. +\begin{figure}[H]\includegraphics[width=1.1\linewidth]{46.1}\end{figure} +\begin{figure}[H]\includegraphics[width=1.1\linewidth]{46.2}\end{figure} +\begin{figure}[H]\includegraphics[width=0.6\linewidth]{47}\end{figure} +Again, we can calculate the adjusted $R^2$ of each of these regressions. You can see that their values are all around 0.576, which is better than the adjusted $R^2$ of our initial OLS model. +\begin{figure}[H]\includegraphics[width=1\linewidth]{48}\end{figure} +\begin{figure}[H]\includegraphics[width=0.6\linewidth]{49}\end{figure} +That's it for a complete procedure to perform linear regression analysis in Python! We have checked the necessary conditions, calculated the coefficients under different models, and compared their performance. If you want to find an even better regression model, perhaps you could go on to try some nonlinear models in the future! +\end{document} diff --git a/LinearRegression/linear_regression_blog.md b/LinearRegression/linear_regression_blog.md new file mode 100644 index 0000000..33d015c --- /dev/null +++ b/LinearRegression/linear_regression_blog.md @@ -0,0 +1,718 @@ +# Intro to Multiple Linear Regression Analysis in Python + +**Linear Regression models** allow us to summarize and study relationships between variables +by fitting a straight line to the observed data. You may have heard of **simple linear regression**, +which establishes the relationship between two quantitative variables–one predictor variable and +one target variable. + +However, in reality, it is rare that a target variable is explained by only one predictor. So +what if we want to estimate a continuous variable using more than one predictors? If two or +more predictor variables have a linear relationship with the target variable, a **multiple linear +regression analysis** allows us to quantify the strength of the relationship and estimate the target +variable at a certain value of the predictor variables. + +This tutorial will show you step-by-step how to perform a multiple linear regression analysis +using Python, from checking assumptions to evaluating performance. + + + +## Getting Started + +### Import Libraries + +First, let’s important all necessary libraries in the beginning to keep our code organized: + +```python +import pandas as pd +import numpy as np +from scipy import stats +import statsmodels.api as sm +from statsmodels.stats.outliers_influence import variance_inflation_factor +from sklearn import datasets +from sklearn import linear_model +from sklearn import metrics +from sklearn.preprocessing import StandardScaler +from sklearn.model_selection import GridSearchCV +import matplotlib.pyplot as plt +import seaborn as sn +from random import uniform +from google.colab import files +import io +``` + +### Read Dataset + +For this analysis, I will use a real estate dataset that can be downloaded from here. I choose to +upload it to Google Colab from local drive. Of course, you can also replace the first argument in +read csv() with the filepath or URL to the dataset that you’d like to use instead. The delimiter +parameter is set to comma by default, but you can change it depending on the delimiter of your +csv file. + +```python +uploaded = files.upload() +dataset = pd.read_csv(io.BytesIO(uploaded['Real estate.csv']), delimiter=',') +``` + +We can take a look at what the data looks like: + +```python +dataset.head() +``` + +![](Blog/4.png) + +As you can see, the first column in the real estate data set is redundant, so we should probably +remove it. Otherwise, this data set seems directly usable. However, it’s likely that your own data +set will require more preprocessing–dealing with missing/invalid values, restructuring the data, and +encoding dummy variables, etc. + +```python +dataset.drop(['No'], axis=1) +``` + +After data preprocessing, we can use the describe() function to obtain some summary statistics +of our target variable, and the displot() function from the seaborn library to plot its distribution. + +```python +y = dataset['Y house price of unit area'].values # target vector +print(dataset['Y house price of unit area'].describe()) +sn.distplot(y, bins = 13) +``` + + + +We see that the values of house price of unit area are normally distributed with perhaps a few +outliers on the right. + + + +## Checking Multicollinearity + +Before the analysis, it is important to verify several regression conditions so as to make sure that +our analysis is valid. Most of the conditions in linear regression can be checked easily with the +residuals–the only snag is that we get the residuals only after we perform the regression. Still, ”no +multicollinearity” is the condition that we are able to check beforehand, without using the residuals. + +Since a multiple regression involves more than one predictor variables, multicollinearity occurs +when some of them are highly correlated with each other, which means each of these predictors +will account for similar variance in the target variable. Therefore, though the presence of multi- +collinearity will not affect the predictive power of our model, it will make it more difficult for us to +assess the individual influence of a predictor on our target variable. We can detect multicollinearity +using either a correlation matrix or VIF factors. + +### Correlation Matrix + +The correlation coefficient is a statistic that measures linear correlation between two variables. Its +value lies between -1 and +1. The absolute value gives the strength of the relationship between the +two variables. The larger its magnitude, the stronger their relationship. In general, a correlation +coefficient above +0.8 or below -0.8 indicates a strong correlation, and we should take some measures +to reduce multicollinearity before we continue. + +The pandas corr() function calculates the correlations among all variables in the dataframe. +We can visualize the resulting correlation matrix using a heatmap from the seaborn library. The +diagonal values should always equal 1 since they are the correlations of a variable with itself. + +```python +df = pd.DataFrame(dataset,columns=['X1 transaction date', 'X2 house age', 'X3 distance to the nearest MRT station', 'X4 number of convenience stores', 'X5 latitude', 'X6 longitude']) # regressor matrix +corrMatrix = df.corr() +sn.heatmap(corrMatrix, annot=True) # visualize the correlation matrix using a heatmap +``` + + + +### VIF Factors + +VIF factor is an alternative measure for multicollinearity, which ranges from 1 upwards. A rule of +thumb used in practice is if a VIF value is greater than 4, then multicollinearity is a problem. We +can check VIF factors using the variance inflation factor() function from the statsmodels package. + +```python +X = dataset[['X1 transaction date', 'X2 house age', 'X3 distance to the nearest MRT station', 'X4 number of convenience stores', 'X5 latitude', 'X6 longitude']] +X2 = sm.add_constant(X) # augmented regressor matrix +vif = pd.DataFrame() +vif['VIF Factor'] = [variance_inflation_factor(X2.values, i) for i in range(X2.shape[1])] +vif['Predictor'] = X2.columns +vif = vif.drop(0) +vif +``` + +![](Blog/11.png) + +You should see in the correlation matrix that the correlation coefficient between X3 and X6 is +−0.81 < −0.8, and the VIF factor for X3 is also slightly higher than 4, which is unfavorable. A +simple solution is to remove one of the correlated variables from our model. After removing X3 +from the list of column names and rerunning the previous code, the new correlation matrix should +show no significant multicollinearity, and the VIF factors of all the remaining variables are around +1, so we are in good shape, and can proceed with our regression. + + + +![](Blog/13.png) + +But wait, you may ask, why did I choose to delete X3 rather than X6? Indeed, my choice was +kind of arbitrary here. To remove the redundant variables more carefully, we can consider using +stepwise regression to only keep the predictors that lead to the best performance; I will describe +backwards stepwise regression later. + +Another way to deal with multicollinearity without having to drop your predictors before the +analysis is to perform regression with regularization techniques (such as Lasso and Ridge) which I +will also describe at the end of the article. Regularization can help you handle multicollinearity, so +if you don’t want to delete any variables, you may choose to skip the OLS model below and directly +jump to the Lasso/Ridge/Elastic Net regression presented in the end. + + + +## Performing the Regression + +### A Bit of Math + +Now it’s finally time to introduce our regression model. Under the linear model, the actual value +of our target variable should be a linear combination of all predictor variables plus a constant +(intercept) as well as some errors. Thus it can be written in the form of an equation $y = \beta_0 + \beta_1 X_1 + \beta_2 X_2 + \dots + \epsilon_i$, and our goal is to estimate $\beta_0$, $\beta_1$, $\beta_2$, ... + +Assuming you’re not scared of matrices, let's first understand some mathematical background for linear regression in linear algebra. More generally speaking, suppose our data consisits of $n$ observations, each of which contains the values of $k$ predictor variables (not including the intercept) as well as the corresponding value of the target variable. In matrix notation, we can write the regressor matrix $\text{X}$ as $\begin{bmatrix} +1 & X_{11} & \dots & X_{1k} \\ +1 & X_{21} & \dots & X_{2k} \\ +\vdots & \vdots & \ddots & \vdots \\ +1 & X_{n1} & \dots & X_{nk} \\ +\end{bmatrix}$, the target vector $\mathbf{y}$ as $\begin{bmatrix} +y_1 \\ +y_2 \\ +\vdots \\ +y_n \\ +\end{bmatrix}$, the coefficient vector $\mathbf{\beta}$ as $\begin{bmatrix} +\beta_0 \\ +\beta_1 \\ +\vdots \\ +\beta_k \\ +\end{bmatrix}$, and the residual vector $\mathbf{\epsilon}$ as $\begin{bmatrix} +\epsilon_1 \\ +\epsilon_2 \\ +\vdots \\ +\epsilon_n \\ +\end{bmatrix}$. Then, our linear model can be rewritten as the following: $\begin{bmatrix} +y_1 \\ +y_2 \\ +\vdots \\ +y_n \\ +\end{bmatrix} = +\begin{bmatrix} +1 & X_{11} & \dots & X_{1k} \\ +1 & X_{21} & \dots & X_{2k} \\ +\vdots & \vdots & \ddots & \vdots \\ +1 & X_{n1} & \dots & X_{nk} \\ +\end{bmatrix} +\begin{bmatrix} +\beta_0 \\ +\beta_1 \\ +\vdots \\ +\beta_k \\ +\end{bmatrix} + +\begin{bmatrix} +\epsilon_1 \\ +\epsilon_2 \\ +\vdots \\ +\epsilon_n \\ +\end{bmatrix}$. Or, more simply, as $\mathbf{y} = \text{X} \mathbf{\beta} + \mathbf{\epsilon}$, where for each $i \in [1, n]$, $y_i = \beta_0 + \beta_1 X_{i1} + \beta_2 X_{i2} + \dots + \beta_k X_{ik} + \epsilon_i$. + +The simplest model that we're going to start with is the ordinary least squares (OLS) regression, which aims to minimize the sum of the squared residuals $||\epsilon||^2$, which is equivalent to $|\mathbf{y} - \text{X} \mathbf{\beta}||^2$. It can be shown via matrix calculus that the least squares estimator for our coefficient vector $\mathbf{\beta}$ is given by $\mathbf{\hat{\beta}} = (\text{X}^\intercal \text{X})^{-1} \text{X}^\intercal \mathbf{y}$. + +### Getting the Coefficients + +The above calculation has already been implemented in the scikit-learn library so we don't need to calculate $\mathbf{\hat{\beta}}$ manually. After instantiating the LinearRegression class, we can easily obtain the coefficients along with the intercept by calling the fit() method along with our data. + +```python +regressor = linear_model.LinearRegression() +regressor.fit(X, y) +coeff_df = pd.DataFrame(regressor.coef_, X.columns, columns=['Coefficient']) +# print the calculated coefficients as well as the intercept +print('Intercept %.6f' %(regressor.intercept_)) +print(coeff_df) +``` + + + +This means, for example, that for every one unit of change in X1 transaction date, the change +in the house price of unit area is approximately 4.21. + +We can compare and visualize some predicted values of the house price with the corresponding +actual values in a bar graph: + +```python +y_hat = regressor.predict(X) # predicted values +df_comparison = pd.DataFrame({'Actual': y, 'Predicted': y_hat}) # put the actual and predicted values together +df_comparison = df_comparison.head(50) # show top 50 rows of this data frame +print(df_comparison) +df_comparison.plot(kind = 'bar') # visualize the comparison +plt.grid(which = 'major', linestyle = '-', linewidth = '0.5', color = 'green') +plt.grid(which = 'minor', linestyle = ':', linewidth = '0.5', color = 'black') +``` + + + +![](Blog/18.png) + + + +## Checking the Residuals + +Congrats! You have successfully obtained the regression line. But remember that we still need to +check the residuals of the regression to ensure its validity. + +First, we can use the scatter() function from the matplotlib library to plot the residuals (be- +tween the actual and predicted values) against the predicted values. We expect to see that the +points are randomly distributed in the scatter plot. More specifically, they should show no cur- +vature (which ensures linearity), and constant variation along the predicted value (which ensures +homoscedasticity). + +```python +epsilon_hat = y - y_hat # residuals +plt.grid(color = 'b', linestyle= '--' , linewidth = 0.5) +plt.scatter(y_hat, epsilon_hat) # scatter plot +``` + +![](Blog/20.png) + +Finally, let’s generate a normal probability plot using probplot() to test the normality of the +residuals. If the residuals are normally distributed, the points in the normal probability plot should +stick to the red diagonal line as closely as possible. As shown in the plot below, the residuals of +our real estate model show a slight deviation from the ideal line, but the deviation or bend is not +very serious. + +```python +pp = sm.ProbPlot(epsilon_hat, fit=True) +pp.ppplot(line='45') # normal probability plot +``` + +![](Blog/22.png) + +The above procedure indicates that our residuals satisfy the regression conditions. If, however, +your residuals do show some strong patterns, you should consider transforming your data using +negative reciprocal, logarithm, square root, square, or exponentiation and then redo the regression. +If none of the above transformation options can solve the problem, it’s possible that your data set +does not fit the linear model, and you may resort to a nonlinear model. + + + +## Making Predictions + +After all the previous conditions have been verified, you now have a trustworthy regression equation +which enables you to make some predictions if given an extra piece of data. While we can use +predict() in scikit-learn to get the mean of our prediction (like what we did when comparing the +predicted values with the actual values right after we’ve got the coefficients), confidence intervals +are available via the get prediction() in the statsmodels package. However, unlike the scikit-learn +library, statsmodels does not add a column of ones to the regressor matrix by default, so before +calling get prediction() we need to add the ones using the add constant() function. + +```python +random = [] +# generate random inputs +for i in range(X.shape[1]): + random.append(uniform(X.iloc[:, i].min(), X.iloc[:, i].max())) +# print the random inputs generated +print('random input:', random) +random.insert(0, 1) # insert 1 at the front +X_aug = sm.add_constant(X) # insert 1 at the front +est = sm.OLS(y, X_aug).fit() +prediction = est.get_prediction(np.reshape(random, (1, 6))) +pd.set_option('display.max_columns', None) +print(prediction.summary_frame(alpha = 0.05)) +``` + +![](Blog/24.png) + +Note that apart from the mean and standard error, summary frame() spits out two intervals at +95% confidence level (we have set alpha = 0.05). The first pair of lower bound and upper bound +forms a confidence interval, which is an estimate of the mean price of all the houses that match our +randomly generated data. The second pair, on the other hand, forms a prediction interval, which +estimate the price of a particular house with this set of data. Because individual values vary more +than means, we can expect the prediction interval to be wider than the confidence interval at the +same confidence level. + + + +## Evaluations + +While it is relatively straightforward to obtain regression lines and predictions, there are numerous +evaluation metrics to measure the accuracy of our model. In fact, the summary() function from +statsmodels provides you with an overwhelming amount of data: + +```python +print(est.summary()) +``` + +![](Blog/25+.png) + +Don’t panic, let’s interpret some important values one by one. + +### R-squared and Adjusted R-squared + + + +R-squared, a.k.a. coefficient of determination, measures the proportion of the variance of the target variable that can be explained by the predictors in our model. It is calculated as $1 - \frac{\text{Sum of Squares Error (SSE)}}{\text{Sum of Squares Total (SST)}}$, and ranges from 0 to 100%. The higher $R^2$, the better the model. An $R^2$ of 100%, for example, means the model explains all the variation of the target variable, whereas a value of 0% indicates zero predictive capability. Our model has $R^2 = 0.542$, so approximately 54% of the variation in the house price can be accounted for by our OLS model. + +Note that there's an adjusted $R^2 = 0.537$ in the second row which is slightly smaller than $R^2$. This is because $R^2$ only works as intended in a simple linear regression model where there's only one predictor. In a multiple regression, when a new predictor is added to the model, $R^2$ can only increase but never decrease. This implies that a model may seem to have a better fit simply because it has more predictors. Thus the adjusted $R^2$, calculated as $1 - \frac{\text{Mean Squares Error (MSE)}}{\text{Mean Squares Total (MST)}}$ or $1 - \frac{(1 - R^2)(n - 1)}{n - k - 1}$ if we already know $R^2$, takes into account the number of predictors $k$ and the number of data points $n$ in the model. It only increases if the new predictor improves the model more than expected by chance and decreases if it fails to do so. As a result, adjusted $R^2$ should always be less than or equal to $R^2$. + +### F-statistic + + + +Below $R^2$ and the adjusted $R^2$ is the F-statistic which is the statistic of an F-test checking whether our model fits the data well. The null hypothesis of the F-test is that the model with no predictors but only an intercept can fit the data as well as the proposed one. To put it simply, it's testing whether $R^2$ is significantly greater than zero. The F-statistic is the ratio of the explained variance to the unexplained variance, so a higher value of F-statistic is evidence against the null hypothesis. + +The fourth row on the right gives the p-value corresponding to the F-statistic. Our model yields a very small p-value of 5.12e-67, so there is sufficient evidence to reject the null hypothesis and conclude that our model does have some predictive power. + +### Confidence Intervals and t-tests + + + +Perhaps the most important information is located in the central part of the summary. We can see +the estimated values of each coefficient in the first column, followed by an estimate of the standard +deviation of the coefficient. The last two columns provide 95% confidence intervals constructed +from the coefficients and their standard errors in the first two columns. + +The two columns in the middle are the results of t-tests checking for the relevancy of each +coefficient. The null hypothesis of each t-test is that the corresponding coefficient equals zero, +meaning no linear relationship between this predictor and the target variable. The t-statistic is +the value in the first column (mean) divided by the second column (standard error); the p-values +corresponding to each t-statistic are presented in the next column. You can see that the p-values +of all our coefficients except X1 are smaller than .01, so we can safely reject the null hypotheses +and say that they are indeed relevant to predicting our target variable. However, X1 may be a +redundant variable at .01 significance level. + + + +## Stepwise Regression + +The results of the OLS regression seem significant but the real estate data set involves only 6 predictors. When we have a substantial number of predictors in the model, it's unlikely that all of them will have significant p-values. Oftentimes, there exist predictors that give redundant information. As the model increases in complexity, the variance of our estimator can get very large. Thus we may consider getting rid of some of the predictors in order to simplify the model and prevent overfitting. + +In theory, you could try all the possible combinations of your predictors and select the one that you believe is the best (for example, the model that yields the highest adjusted $R^2$). However, imagine your data set contains have 20 predictors, then you would need to compare $2^{20} > 1,000,000$ potential models! + +An easier predictor selection procedure, as I mentioned previously, is backwards stepwise regression. Starting with all predictors in the model, in each iteration we find out which predictor to delete, if any, will lead to the best model. We repeat this step until we can't improve our model by removing any variables. (Similarly, there is also forward stepwise regression that works in the reverse way.) + +The question then arises: how do we determine quantitatively which model is the best? There are numerous methods that can provide a quantitative measure of the model performance. The one I present here is leave-one-out cross-validation. Its procedure is as follows: in each iteration, we pick a data point (a row of $X_{i\cdot}$ and $y_i$) from our data set, and refit an OLS model on the remaining data points. Based on this model, we make a prediction $\hat{y}_{i}$ for the data point $y_i$ that we picked in the current iteration. We sum up the squared differences between each data point and its predicted value, i.e. $\sum_{i=1}^{n} (y_i - \hat{y}_i)^2$ as our evaluation metric, called the risk estimator. A good model should yield small difference between each pair of predicted and actual values, thus a smaller risk estimator is preferred. + +Using leave-one-out cross-validation, we are able to quantitatively compare the models during each iteration of backwards stepwise regression. This procedure is not supported in Python libraries, so we have to implement the process by ourselves: + +```python +X_ = dataset[['X1 transaction date', 'X2 house age', 'X3 distance to the nearest MRT station', 'X4 number of convenience stores', 'X5 latitude', 'X6 longitude']] +X_aug_ = sm.add_constant(X_) # augmented regressor matrix with a column of ones inserted at the front +min_r_cv = 0 +# calculate the initial risk estimator with all predictors included +for i in range(X_.shape[0]): + X_cv = X_aug_.drop(X_aug_.index[i]) + X_cv.reset_index(inplace=True) + X_cv = X_cv.drop('index', axis=1) + y_cv = np.delete(y, i) + est_cv = sm.OLS(y_cv, X_cv).fit() + prediction_cv = est_cv.get_prediction(X_aug_.iloc[[i]]).predicted_mean + min_r_cv += (y[i] - prediction_cv)**2 +print('original risk estimator:', min_r_cv) + +variables = X_.shape[1] +min_index = -1 +# keep deleting a predictor until we can't improve the model anymore +while (min_index != 0): + min_index = 0 + # calculate the risk estimator when the j-th predictor is removed + for j in range(1, variables + 1): + r_cv = 0 + for i in range(X_.shape[0]): + X_cv = X_aug_.drop(X_aug_.index[i]) # remove the i-th data point + X_cv.reset_index(inplace = True) + X_cv = X_cv.drop('index', axis = 1) + X_cv.drop(X_cv.columns[[j]], axis=1, inplace=True) # remove the j-th column + y_cv = np.delete(y, i) # remove the i-th data point + # refit the model and make the prediction + est_cv = sm.OLS(y_cv, X_cv).fit() + X_aug_copy = X_aug_.iloc[[i]].copy() + X_aug_copy.drop(X_aug_copy.columns[[j]], axis=1, inplace=True) + prediction_cv = est_cv.get_prediction(X_aug_copy).predicted_mean + # the risk estimator is calculated as the sum of the squared differences between each removed point and the prediction for this point + r_cv += (y[i] - prediction_cv)**2 + # update the optimal predictor to drop if the risk estimator becomes lower + if (r_cv < min_r_cv): + min_index = j + min_r_cv = r_cv + # update the regressor matrix and the number of variables if deleting a predictor leads to a better model + if (min_index != 0): + X_aug_.drop(X_aug_.columns[[min_index]], axis=1, inplace=True) + variables -= 1 +print('improved risk estimator:', min_r_cv) +print('remaining predictors:', X_aug_.columns.values) +``` + +We can apply the above function to our real estate data, though it is too small in size to let the +above algorithm run for many rounds and make significant improvement. Still, backwards stepwise +regression reveals that X6 is the only predictor among X1-X6 that should be dropped so that the +risk estimator can be improved from 33075 to 32952 (obviously, very little improvement here). + + + +We can try to rerun the OLS regression with X6 removed from the model. The adjusted $R^2$ now increases to 0.577. Thus to reduce multicollinearity, deleting X6 is perhaps a better option than X3. + +```python +est_ = sm.OLS(y, X_aug_).fit() +print(est_.summary()) +``` + +![](Blog/32.png) + + + +## Regularization + +However, stepwise regression has many potential drawbacks. For example, as a greedy search algorithm, it is not guaranteed to find the best model, especially when predictors are correlated. + +Another approach that performs predictor selection and also works in the presence of multicollinearity is regularization, a technique for reducing the complexity of the model by adding an extra penalty term to the errors. More specifically, our objective here is still to minimize $||\mathbf{y} - \text{X} \mathbf{\beta}||^2$ (same as the OLS model), but we now impose an additional constraint that the coefficients should not exceed some threshold. The specific constraint depends on the type of the regularization. Below I will mention three popular regularization techniques--Lasso, Ridge, and Elastic Net. + +(I will stick to the real estate data as our example data set. But normally, these techniques are used when we have a substantial number of predictors in a complex model, avoiding the risk of overfitting. Thus it would probably be a little bit of overkill in this case where only 6 predictor variables are involved.) + +First, since the new model will penalize large coefficients, we need to standardize our predictor variables to ensure that the penalty is applied fairly across all predictors. By standardization I mean converting the values in each column of the regressor matrix into z-scores, so the standard score of $x$ is calculated as $z = \frac{x - \mu}{\sigma}$, where $\mu$ is the mean of all values in the same column and $\sigma$ is their standard deviation. + +```python +X_std = StandardScaler().fit_transform(X_) +``` + +### Lasso + +After the standardization, we are ready to choose a specific model to perform. Let's start with Lasso regression. Lasso regression requires that the sum of the absolute values of the coefficients $||\beta||_1$ is no larger than some prespecified value. Using Lagrange Multiplier, we can write our objective function to minimize as $||\mathbf{y} - \text{X} \mathbf{\beta}||^2_2 + \lambda ||\beta||_1$. $\lambda ||\beta||_1$ is the extra penalty term here and can be controlled by changing the value of $\lambda$. When $\lambda$ is zero, the model reduces to OLS; when $\lambda$ tends to infinity, all coefficients approach zero. You can imagine that, as I gradually increase $\lambda$, the magnitude of my coefficients has to decrease towards zero. This can be illustrated by the code below: + +```python +coefs = [] +alphas = np.logspace(-2, 1, 30) # the range of the parameter +for a in alphas: + l = linear_model.Lasso(alpha=a, fit_intercept=False) + l.fit(X_std, y) + coefs.append(l.coef_) +# plot log lambda on x-axis and the corresponding values of coefficients on y-axis +ax = plt.gca() +ax.plot(alphas, coefs) +ax.set_xscale('log') +plt.xlabel('Log lambda') +plt.ylabel('Coefficients') +plt.title('Coefficients as a function of lambda') +plt.axis('tight') +``` + +![](Blog/35+.png) + +To improve the predictive power of our model, we can again resort to cross-validation and choose the $\lambda$ that optimizes some evaluation metrics, such as the cross-validated sum of squared residuals. This can be done by the GridSearchCV() function in scikit-learn. It searches over some range of $\lambda$ to find the optimal evaluation score. Note that the scoring metric is negative mean squared error since the scoring API is designed to maximize rather than minimize the score. Of course, we can easily convert the score back to positive using the negative() function in numpy. + +```python +parameters_lasso = [{'alpha': alphas}] +cv_lasso = GridSearchCV(linear_model.Lasso(), parameters_lasso, scoring = 'neg_mean_squared_error') +cv_lasso.fit(X_std, y) +scores_lasso = cv_lasso.cv_results_['mean_test_score'] # the scores are negative +scores_lasso = np.negative(scores_lasso) # reverse the sign of the score +scores_std_lasso = cv_lasso.cv_results_['std_test_score'] # standard deviation +# print the optimal values +print('best score:', np.negative(cv_lasso.best_score_)) +print('lambda:', cv_lasso.best_params_.get('alpha')) +``` + + + +We can visualize where the optimal value of $\lambda$ is located in the interval: + +```python +# plot the cross validation score against log lambda +fig_lasso = plt.figure() +plt.semilogx(alphas, scores_lasso) +std_error_lasso = scores_std_lasso / np.sqrt(X_.shape[0]) +# shade the region within 1 std err +plt.semilogx(alphas, scores_lasso + std_error_lasso, 'b--') +plt.semilogx(alphas, scores_lasso - std_error_lasso, 'b--') +plt.fill_between(alphas, scores_lasso + std_error_lasso, scores_lasso - std_error_lasso, alpha = 0.25) +plt.ylabel('CV score +/- std error') +plt.xlabel('Log lambda') +plt.axhline(np.min(scores_lasso), linestyle='--', color='.5') +plt.xlim([alphas[0], alphas[-1]]) +plt.title('CV score as a function of lambda') +``` + +![](Blog/39.png) + +Putting the optimal value of $\lambda$ in the parameter of Lasso(), we can obtain the coefficients under the Lasso model: + +```python +# print the standardized coefficients +print('Lasso Results:') +print('(Standardized)') +lasso = linear_model.Lasso(alpha = cv_lasso.best_params_.get('alpha')) +lasso.fit(X_std, y) +lasso_df = pd.DataFrame(lasso.coef_, X_.columns, columns=['Coefficient']) +print('Intercept %.6f' %(lasso.intercept_)) +print(lasso_df) +``` + + + +Note that X6 is again reduced to zero. The significant changes in the magnitude of other +coefficients is due to the fact that we have standardized our predictors before the regression. To +recover the interpretability of our results, we may choose to back-convert the coefficients (by dividing +by the standard deviation) and the intercept (by subtracting all the coefficients times the means of +the corresponding predictors and divided by the corresponding standard deviations): + +```python +# back-convert for ease of interpretation +# beta_real = beta_std / std err +# intercept_real = intercept_std - sum of (mean * beta_std / stderr) +print('(Real)') +lasso_real = lasso_df.copy() +intercept_real = lasso.intercept_ +count_lasso = lasso_real.shape[0] +for i in range(lasso_real.shape[0]): + # decrement the total number of predictors if the coefficient is reduced to zero + if lasso_real.iloc[i, 0] == 0: + count_lasso -= 1 + lasso_real.iloc[i, 0] /= np.std(X_.iloc[:, i]) + intercept_real -= (lasso_real.iloc[i, 0] * np.mean(X_.iloc[:, i])) +print('Intercept %.6f' %(intercept_real)) +print(lasso_real) +``` + + + +We can also try Ridge and Elastic Net regression. Their procedures are exactly the same except that we need to call different functions for different types of regressions. + +### Ridge + +For Ridge regression, the only difference is that the objective now becomes $\min\limits_{\beta} ||Y - X\beta||^2_2 + \lambda ||\beta||^2_2$. (The constraint is now on the sum of squared coefficients.) While Lasso promotes predictor selection, Ridge will decrease the values of coefficients but is unable to force a coefficient to exactly 0. + +```python +print('Ridge Results:') +alphas_ridge = np.logspace(-2, 5, 30) # the range of the parameter +parameters_ridge = [{'alpha': alphas_ridge}] +cv_ridge = GridSearchCV(linear_model.Ridge(), parameters_ridge, scoring = 'neg_mean_squared_error') +cv_ridge.fit(X_std, y) +scores_ridge = cv_ridge.cv_results_['mean_test_score'] # the scores are negative +scores_ridge = np.negative(scores_ridge) # reverse the sign of the score +scores_std_ridge = cv_ridge.cv_results_['std_test_score'] # standard deviation + +# plot the cross validation score against log lambda +fig_ridge = plt.figure() +plt.semilogx(alphas_ridge, scores_ridge) +std_error_ridge = scores_std_ridge / np.sqrt(X_.shape[0]) +# shade the region within 1 std err +plt.semilogx(alphas_ridge, scores_ridge + std_error_ridge, 'b--') +plt.semilogx(alphas_ridge, scores_ridge - std_error_ridge, 'b--') +plt.fill_between(alphas_ridge, scores_ridge + std_error_ridge, scores_ridge - std_error_ridge, alpha = 0.25) +plt.ylabel('CV score +/- std error') +plt.xlabel('Log lambda') +plt.axhline(np.min(scores_ridge), linestyle='--', color='.5') +plt.xlim([alphas_ridge[0], alphas_ridge[-1]]) +plt.title('CV score as a function of lambda') +plt.show() +# print the optimal values +print('best score:', np.negative(cv_ridge.best_score_)) +print('lambda:', cv_ridge.best_params_.get('alpha')) + +# print the standardized coefficients +print('(Standardized)') +ridge = linear_model.Ridge(alpha = cv_ridge.best_params_.get('alpha')) +ridge.fit(X_std, y) +ridge_df = pd.DataFrame(ridge.coef_, X_.columns, columns=['Coefficient']) +print('Intercept %.6f' %(ridge.intercept_)) +print(ridge_df) + +# back-convert for ease of interpretation +# beta_real = beta_std / std err +# intercept_real = intercept_std - sum of (mean * beta_std / stderr) +print('\n(Real)') +ridge_real = ridge_df.copy() +ridge_intercept_real = ridge.intercept_ +count_ridge = ridge_real.shape[0] +for i in range(count_ridge): + ridge_real.iloc[i, 0] /= np.std(X_.iloc[:, i]) + ridge_intercept_real -= (ridge_real.iloc[i, 0] * np.mean(X_.iloc[:, i])) +print('Intercept %.6f' %(ridge_intercept_real)) +print(ridge_real) +``` + + + +### Elastic Net + +Lastly, Elastic Net regression is a combination of Lasso and Ridge--the objective is $\min\limits_{\beta} ||Y - X\beta||^2_2 + \lambda \left(\alpha ||\beta||_1 + \frac{1 - \alpha}{2} ||\beta||^2_2\right)$, and $\alpha = 0.5$ by default. + +```python +print('Elastic Net Results:') +alphas_elastic_net = np.logspace(-2, 1, 30) # the range of the parameter +parameters_elastic_net = [{'alpha': alphas_elastic_net}] +cv_elastic_net = GridSearchCV(linear_model.ElasticNet(), parameters_elastic_net, scoring = 'neg_mean_squared_error') +cv_elastic_net.fit(X_std, y) +scores_elastic_net = cv_elastic_net.cv_results_['mean_test_score'] # the scores are negative +scores_elastic_net = np.negative(scores_elastic_net) # reverse the sign of the score +scores_std_elastic_net = cv_elastic_net.cv_results_['std_test_score'] # standard deviation + +# plot the cross validation score against log lambda +fig_elastic_net = plt.figure() +plt.semilogx(alphas_elastic_net, scores_elastic_net) +std_error_elastic_net = scores_std_elastic_net / np.sqrt(X_.shape[0]) +# shade the region within 1 std err +plt.semilogx(alphas_elastic_net, scores_elastic_net + std_error_elastic_net, 'b--') +plt.semilogx(alphas_elastic_net, scores_elastic_net - std_error_elastic_net, 'b--') +plt.fill_between(alphas_elastic_net, scores_elastic_net + std_error_elastic_net, scores_elastic_net - std_error_elastic_net, alpha = 0.25) +plt.ylabel('CV score +/- std error') +plt.xlabel('Log lambda') +plt.axhline(np.min(scores_elastic_net), linestyle='--', color='.5') +plt.xlim([alphas_elastic_net[0], alphas_elastic_net[-1]]) +plt.title('CV score as a function of lambda') +plt.show() +# print the optimal values +print('best score:', np.negative(cv_elastic_net.best_score_)) +print('lambda:', cv_elastic_net.best_params_.get('alpha')) + +# print the standardized coefficients +print('(Standardized)') +elastic = linear_model.ElasticNet(alpha = cv_elastic_net.best_params_.get('alpha')) +elastic.fit(X_std, y) +elastic_df = pd.DataFrame(elastic.coef_, X_.columns, columns=['Coefficient']) +print('Intercept %.6f' %(elastic.intercept_)) +print(elastic_df) + +# back-convert for ease of interpretation +# beta_real = beta_std / std err +# intercept_real = intercept_std - sum of (mean * beta_std / stderr) +print('\n(Real)') +elastic_real = elastic_df.copy() +elastic_intercept_real = elastic.intercept_ +count_elastic = elastic_real.shape[0] +for i in range(count_elastic): + elastic_real.iloc[i, 0] /= np.std(X_.iloc[:, i]) + elastic_intercept_real -= (elastic_real.iloc[i, 0] * np.mean(X_.iloc[:, i])) +print('Intercept %.6f' %(elastic_intercept_real)) +print(elastic_real) +``` + + + +### Comparing Performances + +Again, we can calculate the adjusted $R^2$ of each of these regressions. You can see that their values are all around 0.576, which is better than the adjusted $R^2$ of our initial OLS model. + +```python +y_pred_lasso = lasso.predict(X_std) # predictions +r2_lasso = metrics.r2_score(y, y_pred_lasso) # R-squared +adj_r2_lasso = 1 - (1 - r2_lasso) * (X_.shape[0] - 1) / (X_.shape[0] - count_lasso - 1) # adjusted R-squared +print('Lasso adj. R2:', adj_r2_lasso) + +y_pred_ridge = ridge.predict(X_std) # predictions +r2_ridge = metrics.r2_score(y, y_pred_ridge) # R-squared +adj_r2_ridge = 1 - (1 - r2_ridge) * (X_.shape[0] - 1) / (X_.shape[0] - count_ridge - 1) # adjusted R-squared +print('Ridge adj. R2:', adj_r2_ridge) + +y_pred_elastic = elastic.predict(X_std) # predictions +r2_elastic = metrics.r2_score(y, y_pred_elastic) # R-squared +adj_r2_elastic = 1 - (1 - r2_elastic) * (X_.shape[0] - 1) / (X_.shape[0] - count_elastic - 1) # adjusted R-squared +print('Elastic Net adj. R2:', adj_r2_elastic) +``` + + + + + +That’s it for a complete procedure to perform linear regression analysis in Python! We have +checked the necessary conditions, calculated the coefficients under different models, and compared +their performance. If you want to find an even better regression model, perhaps you could go on +to try some nonlinear models in the future! \ No newline at end of file From 576a23e601dafdd70e4b799bfe7098656e234758 Mon Sep 17 00:00:00 2001 From: Bowen1Zhu <42977266+Bowen1Zhu@users.noreply.github.com> Date: Mon, 27 Jul 2020 20:40:43 -0400 Subject: [PATCH 4/9] Upload blog --- Bullet-Dodging Game in Processing.md | 2191 ++++++++++++++++++++++++++ draft9/data/background.png | Bin 0 -> 772402 bytes draft9/data/blue1.png | Bin 0 -> 138101 bytes draft9/data/blue2.png | Bin 0 -> 129956 bytes draft9/data/bullet1.png | Bin 0 -> 21411 bytes draft9/data/bullet2.png | Bin 0 -> 16647 bytes draft9/data/green1.png | Bin 0 -> 6045 bytes draft9/data/green2.png | Bin 0 -> 1506 bytes draft9/data/heart1.png | Bin 0 -> 33979 bytes draft9/data/heart2.png | Bin 0 -> 47017 bytes draft9/data/obstacle.png | Bin 0 -> 16558 bytes draft9/data/player1.png | Bin 0 -> 14051 bytes draft9/data/player2.png | Bin 0 -> 4042 bytes draft9/data/red.png | Bin 0 -> 13553 bytes draft9/draft9.pde | 895 +++++++++++ images/editor1.png | Bin 0 -> 58858 bytes images/editor2.png | Bin 0 -> 23066 bytes images/image.png | Bin 0 -> 978637 bytes images/image1.png | Bin 0 -> 1007643 bytes images/image2.png | Bin 0 -> 992520 bytes images/image3.png | Bin 0 -> 985074 bytes 21 files changed, 3086 insertions(+) create mode 100644 Bullet-Dodging Game in Processing.md create mode 100644 draft9/data/background.png create mode 100644 draft9/data/blue1.png create mode 100644 draft9/data/blue2.png create mode 100644 draft9/data/bullet1.png create mode 100644 draft9/data/bullet2.png create mode 100644 draft9/data/green1.png create mode 100644 draft9/data/green2.png create mode 100644 draft9/data/heart1.png create mode 100644 draft9/data/heart2.png create mode 100644 draft9/data/obstacle.png create mode 100644 draft9/data/player1.png create mode 100644 draft9/data/player2.png create mode 100644 draft9/data/red.png create mode 100644 draft9/draft9.pde create mode 100644 images/editor1.png create mode 100644 images/editor2.png create mode 100644 images/image.png create mode 100644 images/image1.png create mode 100644 images/image2.png create mode 100644 images/image3.png diff --git a/Bullet-Dodging Game in Processing.md b/Bullet-Dodging Game in Processing.md new file mode 100644 index 0000000..81ef799 --- /dev/null +++ b/Bullet-Dodging Game in Processing.md @@ -0,0 +1,2191 @@ +# Bullet-Dodging Game in Processing + +Processing is an open-source graphical library that uses the Java language. Designed for the visual arts community, Processing can be used to create interactive graphics such as data visualizations, digital art, and video games. In this blog, we're going to build a simple bullet-dodging game from scratch in Processing. All of the built-in functions mentioned below can be found on the [Processing reference page](https://processing.org/reference/). + + + +## Table of contents: + +* [Part I: Getting Started](#part-i:-getting-started) +* [Part II: Adding the Player and the Bullets](#part-ii:-adding-the-player-and-the-bullets) + +* [Part III: Adding a Life and Scoring System](#part-iii:-adding-a-life-and-scoring-system) + +* [Part IV: Adding Enemies and Shooting](#part-iv:-adding-enemies-and-shooting) + +* [Part V: Implementing More Subclasses](#part-v:-implementing-more-subclasses) + +* [Part VI: Adding Images](#part-vi:-adding-images) + +* [Part VII: Adding Obstacles](#part-vii:-adding-obstacles) + +* [Part VIII: Pausing and Restarting the Game](#part-viii:-pausing-and-restarting-the-game) + + + +## Part I: Getting Started + +The Processing Development Environment (PDE) can be downloaded from [here](https://processing.org/download/). + +After launching the editor, you will see a text editor, a compiler, and a display window. Programs are written in the text editor and started by pressing the Run button. + +The program runs by automatically calling two special functions: `setup()` and `draw()`. The `setup()` function is run once, when the program starts, so it's where we initialize the canvas and variables. After running the `setup()` function, the code inside `draw()` will run continuously from top to bottom until the program is stopped. Let's write down the two function names first. + +If we run the program by pressing the Run button on the upper left corner (or Ctrl + R), a small canvas with the default size will appear. + +![](images/editor1.png) + +First, let's use `size()` and `background()` and to set up the size and color of our canvas. The `size()` function takes two arguments--width and height, whereas the `background()` function can take either RGB or the gray parameter (0-255, where 0 means black and 255 means white) depending on the number of arguments. Since the canvas size will stay the same, we should put `size()` in the `setup()` function. On the other hand, since we will clear the contents of the window and redraw the screen each time `draw()` is called, `background()` should be put at the beginning of the `draw()` function. + +![](images/editor2.png) + + + +## Part II: Adding the Player and the Bullets + +Now that the canvas has been set up, let's add the player on the screen. For simplicity, let's temporarily represent the player using `circle()`. + +We can define a Player class with two functions--`update()` and `show()`. `update()` moves the player's position when the user presses the arrow keys and the `constrain()` function in it keeps the player within bounds; `show()` draws a circle to show the player's current position. + +``` +class Player { + int size = 100; + int xpos = int(random(size, width - size)); + int ypos = 1000; + + void update() { + if (keyPressed) { + if (keyCode == LEFT) { + xpos -= 10; + } else if (keyCode == RIGHT) { + xpos += 10; + } else if (keyCode == UP) { + ypos -= 10; + } else if (keyCode == DOWN) { + ypos += 10; + } + } + // prevent the player from moving off-screen + xpos = constrain(xpos, size / 2, width - size / 2); + } + + void show() { + fill(0); // filled with black + circle(xpos, ypos, size); + } +} +``` + +We can now declare an instance `Player player;` at the top of the code as a global variable and initialize it in `setup()`: ` player = new Player();`. Then by calling `player.update();player.show();` in `draw()`, we should be able to control the player's movement now. + + + +Likewise, we can also define a Bullet class with functions `update()`, `show()` and `check_collision()`. The bullets will drop from top to bottom (vertical position increases from 0 to height) at a speed of 5 and at the same time will check if they have hit the player. + +``` +class Bullet { + int size = 10; + int xpos = int(random(size, width - size)); + int ypos; + + Bullet(int ypos) { + this.ypos = ypos; + } + + void update() { + ypos += 5; + if (ypos > height + size / 2) { // reuse the bullets + xpos = int(random(size, width - size)); + ypos = - size / 2; + } + } + + void show() { + fill(255); + stroke(255, 0, 0); + strokeWeight(5); + circle(xpos, ypos, size); + noStroke(); + } + + boolean check_collision() { + if (dist(xpos, ypos, player.xpos, player.ypos) < (size + player.size) / 2) { + return true; + } + return false; + } +} +``` + +We can now declare an array of Bullet at the top of the code as global variables: + +``` +int MAX_BULLET = 25; +Bullet bullets[] = new Bullet[MAX_BULLET]; +``` + +Let's initialize the bullets with varying initial vertical positions in `setup()`: + +``` +for (int i = 0; i < MAX_BULLET; i++) { + bullets[i] = new Bullet(- i * height / MAX_BULLET); +} +``` + +Then we can `update()`, `show()` and `check_collision()` in `draw()`: + +``` +for (int i = 0; i < MAX_BULLET; i++) { + bullets[i].update(); + bullets[i].show(); + if (bullets[i].check_collision()) { + exit(); + } +} +``` + +We haven't dealt with the case when the bullet hits the player, but at least we already have a rather primitive version of the game to play now. + + + +## Part III: Adding a Life and Scoring System + +Without a second chance, however, the player in our initial version of the game seems prone to death. So let's add a life system to make the game more enjoyable. + +To start, [here](https://github.com/Bowen1Zhu/Bullet-Dodging-Game/blob/master/data/heart1.png) & [here](https://github.com/Bowen1Zhu/Bullet-Dodging-Game/blob/master/data/heart2.png) are the heart icons that I used in the life system. To add an image to the program, simply drag it into the Processing editor, and when you save the project, a data folder containing the image will automatically appear in the project folder next to the Processing code file. + +To load the image in the program, first declare + +``` +PImage heart1; +PImage heart2; +``` + +at the top of the code, and then call `loadImage()` in `setup()`: + +``` +heart1 = loadImage("heart1.png"); +heart2 = loadImage("heart2.png"); +``` + +Then we can draw the images at the specified position (upper left corner) by calling the`image()` function: `image(heart1, 20, 19, 45, 45);`. + + + +Next, we will draw a hitpoint bar next to the icon. After declaring relevant variables at the top: + +``` +int MAX_HP = 6; +int hp = 6; +``` + +and add the following lines of actions when `bullets[i].check_collision()` returns true: + +``` +hp --; +bullets[i].ypos = - bullets[i].size; +if (hp == 0) { + exit(); +} +``` + +we can manually draw the bar in `draw()`: + +``` +fill(255); +stroke(0); +strokeWeight(3); +rect(80, 28, 145, 27, 5); +fill(255, 0, 0); +noStroke(); +rect(82, 30, 142 * hp / MAX_HP, 24, 3); +fill(0); +strokeWeight(5); +textSize(24); +text(hp + " / 6", 125, 50); +``` + + + +Now that the player has multiple lives, we can also enable the player to collect extra lives during the game. + +We define the Life class below: + +``` +class Life { + int size = 60; // size of the icon + float xpos = random(size / 2, width - size / 2); // randomize horizontal position of the icon + float ypos = random(size / 2, height - size / 2); // randomize vertical position of the icon + + // draw the icon + void show() { + image(heart2, xpos, ypos, size, size); + } + + // increment hp and return true if the player has touched the icon + boolean check_collision() { + if (dist(xpos, ypos, player.xpos, player.ypos) < (size + player.size) / 2) { + if (hp < MAX_HP) { + hp ++; + } + return true; //return true so that the icon will be reinitialized + } + return false; + } +} +``` + +Again we declare `Life life;` at the top, initialize the object `life = new Life();` in `setup()`, and check for collision in `draw()`: + +``` +life.show(); +if (life.check_collision()) { + life = new Life(); +} +``` + + + +With the life system, it is natural to add a scoring system as well. Simply declare a score variable `int score = 0;` at the top, and at the end of the draw function increment the variable ` score ++;`. We can show the player's score at the top right corner of the screen: `text("Score: " + score, 1000, 50);`. + + + +Here's our code so far: + +``` +PImage heart1; +PImage heart2; + +Player player; +Life life; + +int MAX_BULLET = 25; +Bullet bullets[] = new Bullet[MAX_BULLET]; +int MAX_HP = 6; +int hp = 6; +int score = 0; + +class Player { + int size = 100; + int xpos = int(random(size, width - size)); + int ypos = 1000; + + void update() { + if (keyPressed) { + if (keyCode == LEFT) { + xpos -= 10; + } else if (keyCode == RIGHT) { + xpos += 10; + } else if (keyCode == UP) { + ypos -= 10; + } else if (keyCode == DOWN) { + ypos += 10; + } + } + // prevent the player from moving off-screen + xpos = constrain(xpos, size / 2, width - size / 2); + } + + void show() { + fill(0); // filled with black + circle(xpos, ypos, size); + } +} + +class Bullet { + int size = 10; + int xpos = int(random(size, width - size)); + int ypos; + + Bullet(int ypos) { + this.ypos = ypos; + } + + void update() { + ypos += 5; + if (ypos > height + size / 2) { // reuse the bullets + xpos = int(random(size, width - size)); + ypos = - size / 2; + } + } + + void show() { + fill(255); + stroke(255, 0, 0); + strokeWeight(5); + circle(xpos, ypos, size); + noStroke(); + } + + boolean check_collision() { + if (dist(xpos, ypos, player.xpos, player.ypos) < (size + player.size) / 2) { + return true; + } + return false; + } +} + +class Life { + int size = 60; // size of the icon + float xpos = random(size / 2, width - size / 2); // randomize horizontal position of the icon + float ypos = random(size / 2, height - size / 2); // randomize vertical position of the icon + + // draw the icon + void show() { + image(heart2, xpos, ypos, size, size); + } + + // increment hp and return true if the player has touched the icon + boolean check_collision() { + if (dist(xpos, ypos, player.xpos, player.ypos) < (size + player.size) / 2) { + if (hp < MAX_HP) { + hp ++; + } + return true; //return true so that the icon will be reinitialized + } + return false; + } +} + +void setup() { + size(1200, 1200); // 1200 x 1200 canvas size + heart1 = loadImage("heart1.png"); + heart2 = loadImage("heart2.png"); + player = new Player(); + life = new Life(); + for (int i = 0; i < MAX_BULLET; i++) { + bullets[i] = new Bullet(- i * height / MAX_BULLET); + } +} + +void draw() { + background(255); // white background + player.update(); + player.show(); + for (int i = 0; i < MAX_BULLET; i++) { + bullets[i].update(); + bullets[i].show(); + if (bullets[i].check_collision()) { + hp --; + bullets[i].ypos = - bullets[i].size; + if (hp == 0) { + exit(); + } + } + } + life.show(); + if (life.check_collision()) { + life = new Life(); + } + show_status(); + score ++; +} + +void show_status() { + fill(255); + stroke(0); + strokeWeight(3); + rect(80, 28, 145, 27, 5); + image(heart1, 20, 19, 45, 45); + fill(255, 0, 0); + noStroke(); + rect(82, 30, 142 * hp / MAX_HP, 24, 3); + fill(0); + strokeWeight(5); + textSize(24); + text(hp + " / 6", 125, 50); + text("Score: " + score, 1000, 50); +} +``` + + + +## Part IV: Adding Enemies and Shooting + +We have already implemented all the essential functions of a simple bullet-dodging game. If you're ready for a more advanced program, it is now time to add enemies to the game and make it a shooting game. + +First of all, it is imperative that we declare a global time variable `int time = 0;` and increment it (`time ++;`) at the end of `draw()`, so that we can decide when the enemy will fire the next bullet regularly. + +We would like to have different kinds of enemies shooting different kinds of bullets, so we will abandon our previous Bullet class as well as the bullet array. Instead, let's first define the following two abstract classes--Bullet and Enemy--which requires support for the basic functions such as `update()` and `show()`. Each subclass will have its own attributes--size, speed, etc. + +``` +abstract class Bullet { + int size, speed, damage; + float xpos, ypos, xspeed, yspeed; + + // decrement hp and return true if the bullet hits the player + boolean check_collision() { + if (dist(xpos, ypos, player.xpos, player.ypos) < player.size / 2) { + hp -= damage; + return true; + } + return false; + } + + abstract boolean update(); // update the position of the bullet + abstract void show(); // draw the bullet on the screen +} + +abstract class Enemy { + int size, speed, max_hp, hp, appear_time = time; + float xpos, ypos; + + // draw the hp bar above the enemy + void show_hp() { + fill(255); + stroke(0); + strokeWeight(2); + rect(xpos - 60, ypos - 100, 120, 10); // total hit points + noStroke(); + fill(255, 0, 0); + rect(xpos - 59, ypos - 99, 119 * hp / max_hp, 8); // remaining hit points + } + + abstract void update(); // update the position of the bullet + abstract void show(); // draw the enemy on the screen + abstract void shoot(); // fire a bullet +} +``` + +Abstract classes cannot be instantiated, we are able to create arrays holding objects of their subclasses: + +``` +import java.util.List; +import java.util.ArrayList; +import java.util.Iterator; + +List my_bullets = new ArrayList(); +List bullets = new ArrayList(); +List enemies = new ArrayList(); +``` + +Next, let's implement a simple subclass of Enemy along with its Bullet. This particular enemy will move around the screen in counterclockwise direction starting from the upper right: + +``` +class Green_Enemy extends Enemy { + int dist = 200; // margin between its path and the boundary of the arena + int pos = 3; // position of the enemy: 0--right; 1--bottom; 2--left; 3--top + Green_Enemy() { + size = 120; // size of the enemy + speed = 5; // velocity of the enemy + max_hp = 5; // total hit points + hp = 5; // current hit points + xpos = width + size / 2; // horizontal position of the enemy + ypos = dist; // vertical position of the enemy + } + + // the enemy moves in counterclockwise direction, starting from the upper right + void update() { + if (pos == 3) { // top + xpos -= speed; // move leftward + if (xpos <= dist) { + pos = 2; // turn left at the upper left corner + } + } else if (pos == 2) { // left + ypos += speed; // move downward + if (ypos >= height - dist) { + pos = 1; // turn left at the lower left corner + } + } else if (pos == 1) { // bottom + xpos += speed; // move rightward + if (xpos >= width - dist) { + pos = 0; // turn left at the lower right corner + } + } else { // right + ypos -= speed; // move upward + if (ypos <= dist) { + pos = 3; // turn left at the upper right corner + } + } + + if ((time - appear_time) % 30 == 0) { + shoot(); // fire a bullet + } + } + + // draw the enemy on the screen + void show() { + fill(255, 0, 0); + stroke(0); + strokeWeight(5); + circle(xpos, ypos, size); + noStroke(); + show_hp(); + } + + // fire a bullet + void shoot() { + bullets.add(new Red_Bullet(xpos, ypos)); + } +} +``` + +This enemy will fire a particular kind of bullet towards the player: + +``` +class Green_Bullet extends Bullet { + Green_Bullet(float xpos, float ypos) { + size = 12; // size of the bullet + speed = 6; // total velocity of the bullet + damage = 1; // damage of the bullet + this.xpos = xpos; // horizontal position of the bullet + this.ypos = ypos; // vertical position of the bullet + // calculate the horizontal and vertical speed of the bullet + float x_dist = player.xpos - xpos; + float y_dist = player.ypos - ypos; + xspeed = speed * x_dist / dist(xpos, ypos, player.xpos, player.ypos); + yspeed = speed * y_dist / dist(xpos, ypos, player.xpos, player.ypos); + } + + // update the position of the bullet + boolean update() { + xpos += xspeed; + ypos += yspeed; + // return true if the bullet hits the boundary + if (xpos < - size / 2 || xpos > width + size / 2 || ypos < - size / 2 || ypos > height + size / 2) { + return true; + } + return false; + } + + // draw the bullet on the screen + void show() { + fill(0, 200, 0); + stroke(50); + strokeWeight(5); + circle(xpos, ypos, size); + noStroke(); + } +} +``` + + + +Since we are using ArrayList now, the code for updating enemies and bullets in `draw()` becomes the following: + +``` +// create a new enemy after a certain time interval +if (time % 800 == 0) { + enemies.add(new Green_Enemy()); +} +// update and draw all the existing bullets shot by the enemies; remove the bullet that has hit the player, the boundary +Iterator itr = bullets.iterator(); +while (itr.hasNext()) { + Bullet b = (Bullet)itr.next(); + if (b.update()) { + itr.remove(); + } else { + b.show(); + if (b.check_collision()) { + itr.remove(); + if (hp == 0) { + exit(); + } + } + } +} +// update and draw all the existing enemies +itr = enemies.iterator(); +while (itr.hasNext()) { + Enemy e = (Enemy)itr.next(); + e.update(); + e.show(); +} +``` + + + +Now that we have let the enemies fire bullets towards the player, it would be unfair if the player cannot shoot back. So let's implement the player's bullet as well to make it a shooting game: + +``` +class My_Bullet extends Bullet { + My_Bullet(float xpos, float ypos) { + size = 12; // size of the bullet + speed = 10; // total velocity of the bullet + damage = 1; // damage of the bullet + this.xpos = xpos; // horizontal position of the bullet + this.ypos = ypos; // vertical position of the bullet + // calculate the horizontal and vertical speed of the bullet + float x_dist = mouseX - player.xpos; + float y_dist = mouseY - player.ypos; + xspeed = speed * x_dist / dist(player.xpos, player.ypos, mouseX, mouseY); + yspeed = speed * y_dist / dist(player.xpos, player.ypos, mouseX, mouseY); + } + + // update the position of the bullet + boolean update() { + xpos += xspeed; + ypos += yspeed; + // return true if the bullet hits the boundary + if (xpos < - size / 2 || xpos > width + size / 2 || ypos < - size / 2 || ypos > height + size / 2) { + return true; + } + return false; + } + + // draw the bullet on the screen + void show() { + fill(0); + circle(xpos, ypos, size); + } + + // check if the player's bullet has hit any enemy + boolean check_hit() { + // traverse the enemy array + Iterator itr = enemies.iterator(); + while (itr.hasNext()) { + Enemy e = (Enemy)itr.next(); + // if the bullet touches an enemy, decrement its hp, increment the number of bullets that hit the target + if (dist(xpos, ypos, e.xpos, e.ypos) < (size + e.size) / 2) { + e.hp --; + // if the enemy's hp is reduced to zero, remove it from the array, increment the score and the number of enemies destroyed + if (e.hp == 0) { + score += 500; + itr.remove(); + } + return true; // return true so that the bullet will be removed from the bullet array + } + } + return false; + } +} +``` + +Similar to the bullets and enemies array, we need to iterate through the my_bullet array in `draw()` to update the player's bullets: + +``` +// update and draw all the existing bullets shot by the player; remove the bullet that has hit the enemies or the boundary +itr = my_bullets.iterator(); +while (itr.hasNext()) { + My_Bullet b = (My_Bullet)itr.next(); + if (b.update()) { + itr.remove(); + } else { + b.show(); + if (b.check_hit()) { + itr.remove(); + } + } +} +``` + +To shoot a bullet, we first need to add a `shoot()` function to the Player class: + +``` +void shoot() { + my_bullets.add(new My_Bullet(xpos, ypos)); +} +``` + +Finally, we need to resort to the `MousePressed()` function, which is called once after every time a mouse button is pressed. By calling `player.shoot()` in `mousePressed()`, a bullet will be shot towards the position of the cursor whenever the player presses the mouse. + +``` +// the player fires a bullet when the mouse is pressed +void mousePressed() { + player.shoot(); +} +``` + + + +## Part V: Implementing More Subclasses + +In the previous section, we have improved our bullet-dodging game and made it more like a shooting game. Likewise, you may use your imagination to create all kinds of enemies and bullets. For example, in the code below I also implemented enemies that follow the player and shoot bouncing bullets, and enemies that head slowly towards a fixed position and shoot homing bullets. + +``` +import java.util.List; +import java.util.ArrayList; +import java.util.Iterator; + +List my_bullets = new ArrayList(); +List bullets = new ArrayList(); +List enemies = new ArrayList(); + +PImage heart1; +PImage heart2; + +Player player; +Life life; + +int MAX_HP = 6; // total hit points +int hp = 6; // remaining hit points +int score = 0; // current score +int time = 0; // time elapsed +int last_time = 0; // time when the last enemy appears + +class Player { + int size = 100; + int xpos = int(random(size, width - size)); + int ypos = 1000; + + void update() { + if (keyPressed) { + if (keyCode == LEFT) { + xpos -= 10; + } else if (keyCode == RIGHT) { + xpos += 10; + } else if (keyCode == UP) { + ypos -= 10; + } else if (keyCode == DOWN) { + ypos += 10; + } + } + // prevent the player from moving off-screen + xpos = constrain(xpos, size / 2, width - size / 2); + ypos = constrain(ypos, size / 2, height - size / 2); + } + + void show() { + fill(0); // filled with black + circle(xpos, ypos, size); + } + + void shoot() { + my_bullets.add(new My_Bullet(xpos, ypos)); + } +} + +abstract class Bullet { + int size, speed, damage; + float xpos, ypos, xspeed, yspeed; + + // decrement hp and return true if the bullet hits the player + boolean check_collision() { + if (dist(xpos, ypos, player.xpos, player.ypos) < player.size / 2) { + hp -= damage; + return true; + } + return false; + } + + abstract boolean update(); // update the position of the bullet + abstract void show(); // draw the bullet on the screen +} + +// player's bullet +class My_Bullet extends Bullet { + My_Bullet(float xpos, float ypos) { + size = 12; // size of the bullet + speed = 10; // total velocity of the bullet + damage = 1; // damage of the bullet + this.xpos = xpos; // horizontal position of the bullet + this.ypos = ypos; // vertical position of the bullet + // calculate the horizontal and vertical speed of the bullet + float x_dist = mouseX - player.xpos; + float y_dist = mouseY - player.ypos; + xspeed = speed * x_dist / dist(player.xpos, player.ypos, mouseX, mouseY); + yspeed = speed * y_dist / dist(player.xpos, player.ypos, mouseX, mouseY); + } + + // update the position of the bullet + boolean update() { + xpos += xspeed; + ypos += yspeed; + // return true if the bullet hits the boundary + if (xpos < - size / 2 || xpos > width + size / 2 || ypos < - size / 2 || ypos > height + size / 2) { + return true; + } + return false; + } + + // draw the bullet on the screen + void show() { + fill(0); + circle(xpos, ypos, size); + } + + // check if the player's bullet has hit any enemy + boolean check_hit() { + // traverse the enemy array + Iterator itr = enemies.iterator(); + while (itr.hasNext()) { + Enemy e = (Enemy)itr.next(); + // if the bullet touches an enemy, decrement its hp, increment the number of bullets that hit the target + if (dist(xpos, ypos, e.xpos, e.ypos) < (size + e.size) / 2) { + e.hp --; + // if the enemy's hp is reduced to zero, remove it from the array, increment the score and the number of enemies destroyed + if (e.hp == 0) { + if (e.max_hp == 5) { + score += 500; + } else if (e.max_hp == 4) { + score += 750; + } else { + score += 1000; + } + itr.remove(); + } + return true; // return true so that the bullet will be removed from the bullet array + } + } + return false; + } +} + +// green bullet with no special effect and little damage +class Green_Bullet extends Bullet { + Green_Bullet(float xpos, float ypos) { + size = 12; // size of the bullet + speed = 6; // total velocity of the bullet + damage = 1; // damage of the bullet + this.xpos = xpos; // horizontal position of the bullet + this.ypos = ypos; // vertical position of the bullet + // calculate the horizontal and vertical speed of the bullet + float x_dist = player.xpos - xpos; + float y_dist = player.ypos - ypos; + xspeed = speed * x_dist / dist(xpos, ypos, player.xpos, player.ypos); + yspeed = speed * y_dist / dist(xpos, ypos, player.xpos, player.ypos); + } + + // update the position of the bullet + boolean update() { + xpos += xspeed; + ypos += yspeed; + // return true if the bullet hits the boundary + if (xpos < - size / 2 || xpos > width + size / 2 || ypos < - size / 2 || ypos > height + size / 2) { + return true; + } + return false; + } + + // draw the bullet on the screen + void show() { + fill(0, 200, 0); + stroke(50); + strokeWeight(5); + circle(xpos, ypos, size); + noStroke(); + } +} + +// bouncing bullet +class Red_Bullet extends Bullet { + boolean bounced = false; // whether the bullet has touched any wall once + Red_Bullet(float xpos, float ypos) { + size = 24; // size of the bullet + speed = 8; // total velocity of the bullet + damage = 2; // damage of the bullet + this.xpos = xpos; // horizontal position of the bullet + this.ypos = ypos; // vertical position of the bullet + // calculate the horizontal and vertical speed of the bullet + float x_dist = player.xpos - xpos; + float y_dist = player.ypos - ypos; + xspeed = speed * x_dist / dist(xpos, ypos, player.xpos, player.ypos); + yspeed = speed * y_dist / dist(xpos, ypos, player.xpos, player.ypos); + } + + // update the position of the bullet + boolean update() { + xpos += xspeed; + ypos += yspeed; + // if the bullet hits the boundary or the obstacle + if (xpos <= size / 2 || xpos >= width - size / 2) { // left & right boundary + if (bounced == false) { // if the bullet hasn't bounced, reverse the horizontal velocity and mark it as bounced + bounced = true; + xspeed = - xspeed; + } else { + return true; // return true if the bullet has bounced once and hit the boundary again + } + } else if (ypos <= size / 2 || ypos >= height - size / 2) { // upper & lower boundary + if (bounced == false) { // if the bullet hasn't bounced, reverse the vertical velocity and mark it as bounced + bounced = true; + yspeed = - yspeed; + } else { + return true; // return true if the bullet has bounced once and hit the boundary again + } + } + return false; + } + + // draw the bullet on the screen + void show() { + stroke(0); + strokeWeight(1); + fill(220, 50, 50); + circle(xpos, ypos, size); + noStroke(); + } +} + +// homing bullet +class Blue_Bullet extends Bullet { + int remaining_time = 300; // the remaining time before the bullet disappears + List path = new ArrayList(); // the trajectory of the bullet + Blue_Bullet(float xpos, float ypos) { + size = 25; // size of the bullet + speed = 4; // total velocity of the bullet + damage = 2; // damage of the bullet + this.xpos = xpos; // horizontal position of the bullet + this.ypos = ypos; // vertical position of the bullet + } + + boolean update() { + remaining_time --; // decrement the remaining time + // return true if the time reduces to zero so that the bullet will be removed from the bullet array + if (remaining_time == 0) { + return true; + } else if (remaining_time > 75) { + // update the horizontal and vertical speed of the bullet + float x_dist = player.xpos - xpos; + float y_dist = player.ypos - ypos; + xspeed = speed * x_dist / dist(xpos, ypos, player.xpos, player.ypos); + yspeed = speed * y_dist / dist(xpos, ypos, player.xpos, player.ypos); + } + xpos += xspeed; + ypos += yspeed; + // update the trajectory of the bullet + path.add(new Path(xpos, ypos)); + update_path(); + // return true if the bullet hits the boundary (seems impossible) + if (xpos < - size / 2 || xpos > width + size / 2 || ypos < - size / 2 || ypos > height + size / 2) { + return true; + } + return false; + } + + // draw the bullet on the screen + void show() { + fill(50, 50, 255); + stroke(0); + strokeWeight(5); + circle(xpos, ypos, size); + noStroke(); + } + + // update the trajectory of the bullet + void update_path() { + Iterator itr = path.iterator(); + while (itr.hasNext()) { + Path p = (Path)itr.next(); + p.update(); + p.show(); + // remove the object if it has become transparent + if (p.alpha == 0) { + itr.remove(); + } + } + } +} + +// the trajectory of the homing bullet +class Path { + float xpos, ypos; + int size = 25, alpha = 255; + Path(float xpos, float ypos) { + this.xpos = xpos; + this.ypos = ypos; + } + + // the path will gradually become transparent + void update() { + alpha -= 12; + } + + void show() { + fill(0, 0, 200, alpha); + stroke(50, 50, 150, alpha); + strokeWeight(5); + circle(xpos, ypos, size); + noStroke(); + } +} + +abstract class Enemy { + int size, speed, max_hp, hp, appear_time = time; + float xpos, ypos; + + // draw the hp bar above the enemy + void show_hp() { + fill(255); + stroke(0); + strokeWeight(2); + rect(xpos - 60, ypos - 100, 120, 10); // total hit points + noStroke(); + fill(255, 0, 0); + rect(xpos - 59, ypos - 99, 119 * hp / max_hp, 8); // remaining hit points + } + + abstract void update(); // update the position of the bullet + abstract void show(); // draw the enemy on the screen + abstract void shoot(); // fire a bullet +} + +// fast enemy moving around the arena +class Green_Enemy extends Enemy { + int dist = 200; // margin between its path and the boundary of the arena + int pos = 3; // position of the enemy: 0--right; 1--bottom; 2--left; 3--top + Green_Enemy() { + size = 120; // size of the enemy + speed = 5; // velocity of the enemy + max_hp = 5; // total hit points + hp = 5; // current hit points + xpos = width + size / 2; // horizontal position of the enemy + ypos = dist; // vertical position of the enemy + } + + // the enemy moves in counterclockwise direction, starting from the upper right + void update() { + if (pos == 3) { // top + xpos -= speed; // move leftward + if (xpos <= dist) { + pos = 2; // turn left at the upper left corner + } + } else if (pos == 2) { // left + ypos += speed; // move downward + if (ypos >= height - dist) { + pos = 1; // turn left at the lower left corner + } + } else if (pos == 1) { // bottom + xpos += speed; // move rightward + if (xpos >= width - dist) { + pos = 0; // turn left at the lower right corner + } + } else { // right + ypos -= speed; // move upward + if (ypos <= dist) { + pos = 3; // turn left at the upper right corner + } + } + + if ((time - appear_time) % 30 == 0) { + shoot(); // fire a bullet + } + } + + // draw the enemy on the screen + void show() { + fill(0, 255, 0); + stroke(0); + strokeWeight(5); + circle(xpos, ypos, size); + noStroke(); + show_hp(); + } + + // fire a bullet + void shoot() { + bullets.add(new Green_Bullet(xpos, ypos)); + } +} + +// enemy that follows the player and shoots bouncing bullets +class Red_Enemy extends Enemy { + float xspeed, yspeed; // directional velocities of the enemy + Red_Enemy() { + size = 120; // size of the enemy + speed = 3; // total velocity of the enemy + max_hp = 4; // total hit points + hp = 4; // current hit points + xpos = random(size / 2, height - size / 2); // horizontal position of the enemy + ypos = int(random(2)) * width; // vertical position of the enemy + } + + // the enemy follows the player's position + void update() { + // update the horizontal and vertical velocities according to the player's position + float x_dist = player.xpos - xpos; + float y_dist = player.ypos - ypos; + xspeed = speed * x_dist / dist(xpos, ypos, player.xpos, player.ypos); + yspeed = speed * y_dist / dist(xpos, ypos, player.xpos, player.ypos); + xpos += xspeed; + ypos += yspeed; + + if ((time - appear_time) % 60 == 0) { + shoot(); // fire a bullet + } + } + + // draw the enemy on the screen + void show() { + fill(255, 0, 0); + stroke(0); + strokeWeight(5); + circle(xpos, ypos, size); + noStroke(); + show_hp(); + } + + // fire a bouncing bullet + void shoot() { + bullets.add(new Red_Bullet(xpos, ypos)); + } +} + +// slow enemy that heads towards a fixed position and shoots homing bullets +class Blue_Enemy extends Enemy { + float xtarget, ytarget, xspeed, yspeed; // target position and directional velocities of the enemy + Blue_Enemy() { + size = 135; // size of the enemy + speed = 2; // total velocity of the enemy + max_hp = 7; // total hit points + hp = 7; // current hit points + // randomize the target position in the middle of the field + xtarget = random(300, 900); + ytarget = random(300, 900); + xpos = int(random(2)) * height; // horizontal position of the enemy + ypos = random(size / 2, width - size / 2); // vertical position of the enemy + // calculate the horizontal and vertical velocities + float x_dist = xtarget - xpos; + float y_dist = ytarget - ypos; + xspeed = speed * x_dist / dist(xpos, ypos, xtarget, ytarget); + yspeed = speed * y_dist / dist(xpos, ypos, xtarget, ytarget); + } + + // the enemy heads towards its target position + void update() { + // update the position if it hasn't reached the target point + if (abs(xpos - xtarget) > 1) { + xpos += xspeed; + ypos += yspeed; + } + + if ((time - appear_time) % 100 == 0) { + shoot(); // fire a bullet + } + } + + // draw the enemy on the screen + void show() { + fill(0, 0, 255); + stroke(0); + strokeWeight(10); + circle(xpos, ypos, size); + noStroke(); + show_hp(); + } + + // fire a homing bullet + void shoot() { + bullets.add(new Blue_Bullet(xpos, ypos)); + } +} + +class Life { + int size = 60; // size of the icon + float xpos = random(size / 2, width - size / 2); // randomize horizontal position of the icon + float ypos = random(size / 2, height - size / 2); // randomize vertical position of the icon + + // draw the icon + void show() { + image(heart2, xpos, ypos, size, size); + } + + // increment hp and return true if the player has touched the icon + boolean check_collision() { + if (dist(xpos, ypos, player.xpos, player.ypos) < (size + player.size) / 2) { + if (hp < MAX_HP) { + hp ++; + } + return true; //return true so that the icon will be reinitialized + } + return false; + } +} + +void setup() { + size(1200, 1200); // 1200 x 1200 canvas size + heart1 = loadImage("heart1.png"); + heart2 = loadImage("heart2.png"); + player = new Player(); + life = new Life(); +} + +void draw() { + background(255); // white background + player.update(); + player.show(); + life.show(); + if (life.check_collision()) { + life = new Life(); + } + // create a new enemy after a certain time interval or if all enemies have been destroyed + boolean next_enemy = false; + if (enemies.isEmpty()) { + next_enemy = true; + } + if (time < 3000) { + if ((time - last_time) % 1000 == 0) { + next_enemy = true; + } + } else { + if ((time - last_time) % 500 == 0) { + next_enemy = true; + } + } + // probability: 40% green enemy; 40% red enemy; 20% blue enemy + if (next_enemy) { + float rand = random(1); + if (rand < 0.4) { + enemies.add(new Green_Enemy()); + } else if (rand < 0.8) { + enemies.add(new Red_Enemy()); + } else { + enemies.add(new Blue_Enemy()); + } + last_time = time; // record the time when the last enemy was created + } + // update and draw all the existing bullets shot by the enemies; remove the bullet that has hit the player or the boundary + Iterator itr = bullets.iterator(); + while (itr.hasNext()) { + Bullet b = (Bullet)itr.next(); + if (b.update()) { + itr.remove(); + } else { + b.show(); + if (b.check_collision()) { + itr.remove(); + if (hp <= 0) { + hp = 0; + exit(); + } + } + } + } + // update and draw all the existing enemies + itr = enemies.iterator(); + while (itr.hasNext()) { + Enemy e = (Enemy)itr.next(); + e.update(); + e.show(); + } + // update and draw all the existing bullets shot by the player; remove the bullet that has hit the enemies or the boundary + itr = my_bullets.iterator(); + while (itr.hasNext()) { + My_Bullet b = (My_Bullet)itr.next(); + if (b.update()) { + itr.remove(); + } else { + b.show(); + if (b.check_hit()) { + itr.remove(); + } + } + } + show_status(); + score ++; + time ++; +} + +void show_status() { + fill(255); + stroke(0); + strokeWeight(3); + rect(80, 28, 145, 27, 5); + image(heart1, 20, 19, 45, 45); + fill(255, 0, 0); + noStroke(); + rect(82, 30, 142 * hp / MAX_HP, 24, 3); + fill(0); + strokeWeight(5); + textSize(24); + text(hp + " / 6", 125, 50); + text("Score: " + score, 1000, 50); +} + +// the player fires a bullet when the mouse is pressed +void mousePressed() { + player.shoot(); +} +``` + + + +## Part VI: Adding Images + +So far we have already completed the basic code structure of the program. Now it is time to get as creative as you can to make the program looks like a real game! `loadImage()` would be a very useful function in adding aesthetic elements to your game. You may customize the background image, use your favorite characters to replace the ugly circles, and add some small features according to your theme. + +For example, below is the code of my version of tank battle game. Apart from adding background and tank images, I have also implemented some minor functions such as keeping track of the number of bullets, enemies destroyed, and shooting accuracy. + +``` +import java.util.List; +import java.util.ArrayList; +import java.util.Iterator; + +PImage heart1; +PImage heart2; +PImage bullet1; +PImage bullet2; +PImage background; +PImage green1; +PImage green2; +PImage red; +PImage blue1; +PImage blue2; +PImage player1; +PImage player2; + +Player player; +Life_Icon life; +Bullet_Icon bul; +List my_bullets = new ArrayList(); +int my_bullet_count = 0; +List bullets = new ArrayList(); +int bullet_count = 0; +List enemies = new ArrayList(); +int enemy_count = 0; + +int MAX_HP = 6; +int hp = 6; +int MAX_BULLET = 60; +int bullet_num = 60; +int score = 0; +int enemies_destroyed = 0; +int hit = 0; +int total = 0; +int time = 0; +int last_time = 0; + +class Player { + int size = 150; + float xpos = width / 2; + float ypos = height / 2; + + void update() { + if (keyPressed) { + if (keyCode == LEFT) { + xpos -= 10; + } else if (keyCode == RIGHT) { + xpos += 10; + } else if (keyCode == UP) { + ypos -= 10; + } else if (keyCode == DOWN) { + ypos += 10; + } + } + xpos = constrain(xpos, 50, width - 50); + ypos = constrain(ypos, 50, height - 50); + } + + void show() { + pushMatrix(); + translate(xpos, ypos); + float angle = 0; + if (keyCode == LEFT) { + angle = - PI / 2; + } else if (keyCode == RIGHT) { + angle = PI / 2; + } else if (keyCode == DOWN) { + angle = PI; + } + rotate(angle); + image(player1, - size / 2, - size / 2, size, size); + rotate(- angle + calculate_angle(xpos, ypos, mouseX, mouseY)); + image(player2, -30, -90, 60, 120); + popMatrix(); + } + + void shoot() { + if (bullet_num > 0) { + float angle = calculate_angle_(xpos, ypos, mouseX, mouseY); + float turret_length = 80; + my_bullets.add(new My_Bullet(xpos + turret_length * sin(angle), ypos + turret_length * cos(angle))); + my_bullet_count ++; + bullet_num --; + } + } +} + +abstract class Bullet { + int size, speed, damage; + float xpos, ypos, xspeed, yspeed; + + boolean check_collision() { + if (dist(xpos, ypos, player.xpos, player.ypos) < player.size / 2) { + hp -= damage; + return true; + } + return false; + } + + abstract boolean update(); + abstract void show(); +} + +class My_Bullet extends Bullet { + My_Bullet(float xpos, float ypos) { + size = 12; + speed = 10; + damage = 1; + this.xpos = xpos; + this.ypos = ypos; + float x_dist = mouseX - player.xpos; + float y_dist = mouseY - player.ypos; + xspeed = speed * x_dist / dist(player.xpos, player.ypos, mouseX, mouseY); + yspeed = speed * y_dist / dist(player.xpos, player.ypos, mouseX, mouseY); + } + + boolean update() { + xpos += xspeed; + ypos += yspeed; + if (xpos < - size / 2 || xpos > width + size / 2 || ypos < - size / 2 || ypos > height + size / 2) { + return true; + } + return false; + } + + void show() { + fill(0); + circle(xpos, ypos, size); + } + + boolean check_hit() { + Iterator itr = enemies.iterator(); + while (itr.hasNext()) { + Enemy e = (Enemy)itr.next(); + if (dist(xpos, ypos, e.xpos, e.ypos) < (size + e.size) / 2) { + e.hp --; + if (e.hp == 0) { + if (e.max_hp == 5) { + score += 500; + } else if (e.max_hp == 4) { + score += 750; + } else { + score += 1000; + } + itr.remove(); + enemies_destroyed ++; + } + hit ++; + return true; + } + } + return false; + } +} + +class Green_Bullet extends Bullet { + Green_Bullet(float xpos, float ypos) { + size = 12; + speed = 6; + damage = 1; + this.xpos = xpos; + this.ypos = ypos; + float x_dist = player.xpos - xpos; + float y_dist = player.ypos - ypos; + xspeed = speed * x_dist / dist(xpos, ypos, player.xpos, player.ypos); + yspeed = speed * y_dist / dist(xpos, ypos, player.xpos, player.ypos); + } + + boolean update() { + xpos += xspeed; + ypos += yspeed; + if (xpos < - size / 2 || xpos > width + size / 2 || ypos < - size / 2 || ypos > height + size / 2) { + return true; + } + return false; + } + + void show() { + fill(0, 200, 0); + stroke(50); + strokeWeight(5); + circle(xpos, ypos, size); + noStroke(); + } +} + +class Red_Bullet extends Bullet { + boolean bounced = false; + Red_Bullet(float xpos, float ypos) { + size = 24; + speed = 8; + damage = 2; + this.xpos = xpos; + this.ypos = ypos; + float x_dist = player.xpos - xpos; + float y_dist = player.ypos - ypos; + xspeed = speed * x_dist / dist(xpos, ypos, player.xpos, player.ypos); + yspeed = speed * y_dist / dist(xpos, ypos, player.xpos, player.ypos); + } + + boolean update() { + xpos += xspeed; + ypos += yspeed; + if (xpos <= size / 2 || xpos >= width - size / 2) { + if (bounced == false) { + bounced = true; + xspeed = - xspeed; + } else { + return true; + } + } else if (ypos <= size / 2 || ypos >= height - size / 2) { + if (bounced == false) { + bounced = true; + yspeed = - yspeed; + } else { + return true; + } + } + return false; + } + + void show() { + stroke(0); + strokeWeight(1); + fill(220, 50, 50); + circle(xpos, ypos, size); + noStroke(); + } +} + +class Blue_Bullet extends Bullet { + int remaining_time = 300; + List path = new ArrayList(); + Blue_Bullet(float xpos, float ypos) { + size = 25; + speed = 4; + damage = 2; + this.xpos = xpos; + this.ypos = ypos; + } + + boolean update() { + remaining_time --; + if (remaining_time == 0) { + return true; + } else if (remaining_time > 75) { + float x_dist = player.xpos - xpos; + float y_dist = player.ypos - ypos; + xspeed = speed * x_dist / dist(xpos, ypos, player.xpos, player.ypos); + yspeed = speed * y_dist / dist(xpos, ypos, player.xpos, player.ypos); + } + xpos += xspeed; + ypos += yspeed; + path.add(new Path(xpos, ypos)); + update_path(); + if (xpos < - size / 2 || xpos > width + size / 2 || ypos < - size / 2 || ypos > height + size / 2) { + return true; + } + return false; + } + + void show() { + fill(50, 50, 255); + stroke(0); + strokeWeight(5); + circle(xpos, ypos, size); + noStroke(); + } + + void update_path() { + Iterator itr = path.iterator(); + while (itr.hasNext()) { + Path p = (Path)itr.next(); + p.update(); + p.show(); + if (p.alpha == 0) { + itr.remove(); + } + } + } +} + +class Path { + float xpos, ypos; + int size = 25, alpha = 255; + Path(float xpos, float ypos) { + this.xpos = xpos; + this.ypos = ypos; + } + + void update() { + alpha -= 12; + } + + void show() { + fill(0, 0, 200, alpha); + stroke(50, 50, 150, alpha); + strokeWeight(5); + circle(xpos, ypos, size); + noStroke(); + } +} + +abstract class Enemy { + int size, speed, max_hp, hp, appear_time = time; + float xpos, ypos; + void show_hp() { + fill(255); + stroke(0); + strokeWeight(2); + rect(xpos - 60, ypos - 100, 120, 10); + noStroke(); + fill(255, 0, 0); + rect(xpos - 59, ypos - 99, 119 * hp / max_hp, 8); + } + abstract void update(); + abstract void show(); + abstract void shoot(); +} + +class Green_Enemy extends Enemy { + int dist = 200; + int pos = 3; + Green_Enemy() { + size = 120; + speed = 5; + max_hp = 5; + hp = 5; + xpos = width + size / 2; + ypos = dist; + } + + void update() { + if (pos == 3) { + xpos -= speed; + if (xpos <= dist) { + pos = 2; + } + } else if (pos == 2) { + ypos += speed; + if (ypos >= height - dist) { + pos = 1; + } + } else if (pos == 1) { + xpos += speed; + if (xpos >= width - dist) { + pos = 0; + } + } else { + ypos -= speed; + if (ypos <= dist) { + pos = 3; + } + } + + if ((time - appear_time) % 30 == 0) { + shoot(); + } + } + + void show() { + pushMatrix(); + translate(xpos - 60 + size / 2, ypos - 60 + size / 2); + rotate(pos * PI / 2); + image(green1, - size / 2, - size / 2, size, size); + rotate(- pos * PI / 2 + calculate_angle(xpos, ypos, player.xpos, player.ypos)); + image(green2, -25, -80, 50, 100); + popMatrix(); + show_hp(); + } + + void shoot() { + float angle = calculate_angle_(xpos, ypos, player.xpos, player.ypos); + float turret_length = 80; + bullets.add(new Green_Bullet(xpos + turret_length * sin(angle), ypos + turret_length * cos(angle))); + } +} + +class Red_Enemy extends Enemy { + float xspeed, yspeed; + Red_Enemy() { + size = 120; + speed = 3; + max_hp = 4; + hp = 4; + xpos = random(size / 2, height - size / 2); + ypos = int(random(2)) * width; + } + + void update() { + float x_dist = player.xpos - xpos; + float y_dist = player.ypos - ypos; + xspeed = speed * x_dist / dist(xpos, ypos, player.xpos, player.ypos); + yspeed = speed * y_dist / dist(xpos, ypos, player.xpos, player.ypos); + xpos += xspeed; + ypos += yspeed; + + if ((time - appear_time) % 60 == 0) { + shoot(); + } + } + + void show() { + pushMatrix(); + translate(xpos - 60 + size / 2, ypos - 60 + size / 2); + rotate(calculate_angle(xpos, ypos, player.xpos, player.ypos)); + image(red, - size / 2, - size / 2, size, size); + popMatrix(); + show_hp(); + } + + void shoot() { + float angle = calculate_angle_(xpos, ypos, player.xpos, player.ypos); + float turret_length = 60; + bullets.add(new Red_Bullet(xpos + turret_length * sin(angle), ypos + turret_length * cos(angle))); + } +} + +class Blue_Enemy extends Enemy { + float xtarget, ytarget, xspeed, yspeed; + Blue_Enemy() { + size = 135; + speed = 2; + max_hp = 7; + hp = 7; + xtarget = random(300, 900); + ytarget = random(300, 900); + xpos = int(random(2)) * height; + ypos = random(size / 2, width - size / 2); + float x_dist = xtarget - xpos; + float y_dist = ytarget - ypos; + xspeed = speed * x_dist / dist(xpos, ypos, xtarget, ytarget); + yspeed = speed * y_dist / dist(xpos, ypos, xtarget, ytarget); + } + + void update() { + if (abs(xpos - xtarget) > 1) { + xpos += xspeed; + ypos += yspeed; + } + + if ((time - appear_time) % 100 == 0) { + shoot(); + } + } + + void show() { + pushMatrix(); + translate(xpos - 75 + size / 2, ypos - 60 + size / 2); + float angle = calculate_angle(xpos, ypos, xtarget, ytarget); + rotate(angle); + image(blue1, - size / 2, - size / 2, size, size); + rotate(- angle + calculate_angle(xpos, ypos, player.xpos, player.ypos)); + image(blue2, -30, -100, 60, 120); + popMatrix(); + show_hp(); + } + + void shoot() { + float angle = calculate_angle_(xpos, ypos, player.xpos, player.ypos); + float turret_length = 100; + bullets.add(new Blue_Bullet(xpos + turret_length * sin(angle), ypos + turret_length * cos(angle))); + } +} + +class Life_Icon { + int size = 60; + float xpos = random(size / 2, width - size / 2); + float ypos = random(size / 2, height - size / 2); + + void show() { + image(heart2, xpos, ypos, size, size); + } + + boolean check_collision() { + if (dist(xpos, ypos, player.xpos, player.ypos) < (size + player.size) / 2) { + if (hp < MAX_HP) { + hp ++; + } + return true; + } + return false; + } +} + +class Bullet_Icon { + int size = 65; + float xpos = random(size / 2, width - size / 2); + float ypos = random(size / 2, height - size / 2); + + void show() { + image(bullet2, xpos, ypos, size, size); + } + + boolean check_collision() { + if (dist(xpos, ypos, player.xpos, player.ypos) < (size + player.size) / 2) { + bullet_num = constrain(bullet_num + 10, 0, MAX_BULLET); + return true; + } + return false; + } +} + +float calculate_angle(float this_xpos, float this_ypos, float target_xpos, float target_ypos) { + PVector reference = new PVector(0, -1); + PVector actual = new PVector(target_xpos - this_xpos, target_ypos - this_ypos); + if (this_xpos < target_xpos) { + return PVector.angleBetween(reference, actual); + } else { + return -PVector.angleBetween(reference, actual); + } +} + +float calculate_angle_(float this_xpos, float this_ypos, float target_xpos, float target_ypos) { + PVector reference = new PVector(0, 1); + PVector actual = new PVector(target_xpos - this_xpos, target_ypos - this_ypos); + if (this_xpos < target_xpos) { + return PVector.angleBetween(reference, actual); + } else { + return -PVector.angleBetween(reference, actual); + } +} + +void setup() { + size(1200, 1200); + heart1 = loadImage("heart1.png"); + heart2 = loadImage("heart2.png"); + bullet1 = loadImage("bullet1.png"); + bullet2 = loadImage("bullet2.png"); + background = loadImage("background.png"); + green1 = loadImage("green1.png"); + green2 = loadImage("green2.png"); + red = loadImage("red.png"); + blue1 = loadImage("blue1.png"); + blue2 = loadImage("blue2.png"); + player1 = loadImage("player1.png"); + player2 = loadImage("player2.png"); + player = new Player(); + life = new Life_Icon(); + bul = new Bullet_Icon(); +} + +void draw() { + background(background); + player.update(); + player.show(); + life.show(); + if (life.check_collision()) { + life = new Life_Icon(); + } + bul.show(); + if (bul.check_collision()) { + bul = new Bullet_Icon(); + } + boolean next_enemy = false; + if (enemies.isEmpty()) { + next_enemy = true; + } + if (time < 3000) { + if ((time - last_time) % 1000 == 0) { + next_enemy = true; + } + } else { + if ((time - last_time) % 500 == 0) { + next_enemy = true; + } + } + if (next_enemy) { + float rand = random(1); + if (rand < 0.4) { + enemies.add(new Green_Enemy()); + } else if (rand < 0.8) { + enemies.add(new Red_Enemy()); + } else { + enemies.add(new Blue_Enemy()); + } + enemy_count ++; + last_time = time; + } + Iterator itr = bullets.iterator(); + while (itr.hasNext()) { + Bullet b = (Bullet)itr.next(); + if (b.update()) { + itr.remove(); + } else { + b.show(); + if (b.check_collision()) { + itr.remove(); + if (hp <= 0) { + hp = 0; + exit(); + } + } + } + } + itr = enemies.iterator(); + while (itr.hasNext()) { + Enemy e = (Enemy)itr.next(); + e.update(); + e.show(); + } + itr = my_bullets.iterator(); + while (itr.hasNext()) { + My_Bullet b = (My_Bullet)itr.next(); + if (b.update()) { + total ++; + itr.remove(); + } else { + b.show(); + if (b.check_hit()) { + total ++; + itr.remove(); + } + } + } + show_status(); + score ++; + time ++; +} + +void show_status() { + fill(255); + stroke(0); + strokeWeight(3); + rect(80, 28, 145, 27, 5); + image(heart1, 20, 19, 45, 45); + fill(255, 0, 0); + noStroke(); + rect(82, 30, 142 * hp / MAX_HP, 24, 3); + fill(0); + strokeWeight(5); + textSize(24); + text(hp + " / 6", 125, 50); + if (hp <= 2) { + fill(255, 0, 0); + textSize(42); + text("!", 240, 55); + } + + fill(255); + stroke(0); + strokeWeight(3); + rect(80, 83, 145, 27, 5); + image(bullet1, 15, 70, 55, 55); + fill(60, 60, 255); + noStroke(); + rect(82, 85, 142 * bullet_num / MAX_BULLET, 24, 3); + fill(0); + strokeWeight(5); + textSize(24); + text(bullet_num + " / 60", 110, 105); + if (bullet_num <= 20) { + fill(0, 0, 255); + textSize(42); + text("!", 240, 111); + } + + fill(0); + textSize(42); + text("Score: " + score, 900, 100); + textSize(25); + text("Enemies Destroyed: " + enemies_destroyed, 900, 155); + int accuracy = 0; + if (total > 0) { + accuracy = 100 * hit / total; + } + text("Accuracy: " + accuracy + "%", 900, 200); +} + +void mousePressed() { + player.shoot(); +} +``` + +Here's the result: + +![](images/image1.png) + + + +## Part VII: Adding Obstacles + +With the shapes replaced by the images, the program already looks like a real game now, but there're still numerous features that could be added to spice up the game. Depending on your theme, you may also want to consider adding some obstacles for the player to hide behind. + +For example, I decided to add [this obstacle](https://github.com/Bowen1Zhu/Bullet-Dodging-Game/blob/master/data/obstacle.png) at the bottom of my arena. After loading the image with `PImage obstacle;` and then `obstacle = loadImage("obstacle.png");` as usual, I called `image(obstacle, 500, 700, 200, 200);` right after the `background()` function. + +Next, to keep the player from moving into the obstacle, add the following two conditions in `update()` in the Player class to constrain the player's horizontal and vertical conditions around the obstacle: + +``` +if (ypos > 710 - size / 3 && ypos < 890 + size / 3) { + if (xpos < width / 2) { + xpos = constrain(xpos, 50, 500 - size / 3); + } else { + xpos = constrain(xpos, 700 + size / 3, width - 50); + } +} +if (xpos > 500 - size / 3 && xpos < 700 + size / 3) { + if (ypos < 850) { + ypos = constrain(ypos, 50, 700 - size / 3); + } else { + ypos = constrain(ypos, 900 + size / 3, height - 50); + } +} +``` + +Similarly, add a `check_obstacle()` function in the Bullet class and a `constrain_position()` function in the Enemy class to prevent them from going into the obstacle as well. + +``` +boolean check_obstacle() { + if (xpos > 500 - size / 2 && xpos < 700 + size / 2 && ypos > 700 - size / 2 && ypos < 900 + size / 2) { + return true; + } + return false; +} +``` + +``` +void constrain_position() { + if (ypos > 710 - size / 2 && ypos < 890 + size / 2) { + if (xpos < width / 2) { + xpos = constrain(xpos, 50, 500 - size / 2); + } else { + xpos = constrain(xpos, 700 + size / 2, width - 50); + } + } + if (xpos > 500 - size / 2 && xpos < 700 + size / 2) { + if (ypos < 850) { + ypos = constrain(ypos, 50, 700 - size / 2); + } else { + ypos = constrain(ypos, 900 + size / 2, height - 50); + } + } +} +``` + +Then, simply call `check_obstacle()` whenever `check_collision()` and `check_hit()` are called in `draw()`, and add `constrain_position()` in the `update()` methods in the subclasses of the Enemy class. + +The bouncing bullet, however, deserves a bit more attention since it should now bounce from the obstacle as well. Therefore, let's add an extra OR condition in its `update()` method to check if the bouncing bullet has hit the obstacle and should bounce back: + +``` +boolean update() { + xpos += xspeed; + ypos += yspeed; + //reappear on the top if it moves below the bottom + if (xpos <= size / 2 || xpos >= width - size / 2 || + (ypos > 700 - size / 2 && ypos < 900 + size / 2 && (abs(xpos - 500) < size / 2 || abs(xpos - 700) < size / 2))) { + if (bounced == false) { + bounced = true; + xspeed = - xspeed; + xpos += 2.5 * xspeed; + } else { + return true; + } + } else if (ypos <= size / 2 || ypos >= height - size / 2 || + (xpos > 500 - size / 2 && xpos < 700 + size / 2 && (abs(ypos - 700) < size / 2 || abs(ypos - 900) < size / 2))) { + if (bounced == false) { + bounced = true; + yspeed = - yspeed; + ypos += 2.5 * yspeed; + } else { + return true; + } + } + return false; +} +``` + +Another small modification to our code is to prevent the heart icon from appearing within the obstacle. Otherwise, the player won't be able to collect it and a new icon will not appear elsewhere without the first one being touched first. + +The solution to the problem is to reinitialize the position of the icon until it is generated outside the obstacle: + +``` +Life_Icon() { + while(xpos > 500 && xpos < 700 && ypos > 700 && ypos < 900) { + xpos = random(size / 2, width - size / 2); + ypos = random(size / 2, height - size / 2); + } +} +``` + +Now we have created an obstacle that the player can hide behind at the bottom of the field: + +![](./images/image2.png) + + + +## Part VIII: Pausing and Restarting the Game + +Congrats! We have completed all the functions in our shooting game. One final step is to enable the user to pause and resume the game, as well as a restart function so that the player doesn't need to rerun the program every time after game over. + +To record the state of the game, we will first declare two global variables at the top--`int state = 0;` and `boolean pause = false;`. While `pause` can only be either true or false, `state` can have three possible values--0 means before the game, 1 means during the game, and 2 means after the game. + +Similar to the `mousePressed()` function, we will use `keyPressed()` to enable the player to control the state of the game by pressing the spacebar. Whenever the spacebar is pressed, we will either change `state` to 1 or flip `pause`. When we switch from state = 2 back to state = 1, we also need to restore the global variables to their initial values so that we are ready for a new game. + +``` +void keyPressed() { + if (key == 32) { // keyCode for spacebar + if (state == 0) { // start the game if it hasn't started + state = 1; + } else if (state == 2) { // after game over, reinitialize the variables if the game is to be restarted + state = 1; + hp = 6; + bullet_num = 60; + score = 0; + enemies_destroyed = 0; + hit = 0; + total = 0; + time = 0; + last_time = 0; + player = new Player(); + life = new Life_Icon(); + bul = new Bullet_Icon(); + my_bullets = new ArrayList(); + bullets = new ArrayList(); + enemies = new ArrayList(); + } else { //pause or resume the game during the game + pause = !pause; + } + } +} +``` + +In addition, we don't want the player to take advantage of shooting in the paused state, so in the `mousePressed()` function we'll only call `player.shoot()` when the game is on: + +``` +void mousePressed() { + if (state == 1 && ! pause) { + player.shoot(); + } +} +``` + +Now we can use the two state variables to control the flow of the game. Below is the structure of the code in `draw()` that gives us the ability to pause and restart the game. + +First, we check if `state == 0` (the game has not started yet). If so, we only need to call `show()` without `update()`. + +``` +if (state == 0) { // before the game starts + background(background); + image(obstacle, 500, 700, 200, 200); + player.show(); + life.show(); + bul.show(); + show_status(); + fill(0); + textSize(60); + text("Press SPACE to start/pause", 200, 400); +} +``` + +Then we check if `state == 1` (the game has started but not finished). We put our previous code in `draw()` in the following block that will run when the game is not paused. On the other hand, we simply show a line of prompt without performing any other functions when the game is paused. + +``` +else if (state == 1) { // during the game + if (!pause) { // perform all the functions when the game is not paused + // previous code in draw() + } else { // if the game is paused, stop updating any data + fill(0); + textSize(60); + text("Press SPACE to resume", 270, 400); + } +} +``` + +Also, if the game is over, we can choose to print a message to the screen. We can also record the highest score by declaring a global variable `high_score == 0` initially. + +``` +// update the highest score +if (score > high_score) { + high_score = score; +} +// dark background at the center of the screen +noStroke(); +fill(0, 80); +rect(220, 270, 800, 400, 50); +// show game over and the highest score +fill(0); +textSize(60); +text("Game Over", 450, 380); +textSize(40); +text("High score: " + high_score, 445, 470); +textSize(60); +text("Press SPACE to restart", 300, 580); +``` + +After viewing the high score, we can now restart the game after game over! + +![](images/image3.png) + + + +We have completed the ultimate version of the program that allows us to pause, resume, and restart the game in addition to all the functions we have implemented earlier. [Here](https://github.com/Bowen1Zhu/Bullet-Dodging-Game) are all the images that I have used in my shooting game. 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