Regression

from data.gov.in

The dataset contains the information about the taxation in the west zone of Surat for some chosen wards from the year 2004 to 2015.

Problem Statement-

For the given dataset our framed regression problem is to predict the total recovery which is dependent on demand. We have observed that ward no and year attribute are not related to Total recovery so we took- Independent attribute: Demand Dependent attribute: Total Recovery. Both the terms are highly correlated that can be seen in the following correlation matrix. The values for the attributes are in crores.

Library	Function	Usage
Pandas	read_csv	to read the dataset
NumPy	Sqrt	to calculate square root
Seaborn	heatmap, distmap	to visualize relationship b/w dependent & independent variable
sklearn.model_selection	train_test_split	to partition the dataset
sklearn.metrics	mean_absolute_error, mean_squared_error	to find mean squared error, mean absolute error and root mean squared error
sklearn.linear_model	LinearRegression	to fit linear regression on dataset
matplotlib	Pyplot	to visualize regression results and obtain relationship b/w dependent & independent variable

Result and Interpretation-

The actual and predicted values are quite similar to each other, as observed from the above graph.

From the above graph we can see that the linear model fits the data quite well. Mean Absolute Error: 0.8357969545192269 Mean Squared Error: 2.0625294895366375 Root Mean Squared Error: 1.4361509285366345 R2 value: 0.9601400116543154

We defined the R-squared value, as the fraction by which the variance of the errors is less than the variance of the dependent variable. Since the R-squared value is nearly 1, this implies a very low standard deviation, we can say that the model is a good fit for the data.