Linear Regression Algorithm in Practice

Regression analysis is a process of predicting a response variable given an explanatory variable. The response variable is also called a dependent variable and an explanatory variable is known as an independent variable. Given a problem statement, when there are multiple explanatory variables and one response variable, then the process is known as Multiple Linear Regression. On contrary, if a problem statement contains only one explanatory variable and one response variable, it is known as Simple Linear Regression.

Introduction

Regression analysis is a process of predicting a response variable given an explanatory variable. The response variable is also called a dependent variable and an explanatory variable is known as an independent variable. Given a problem statement, when there are multiple explanatory variables and one response variable, then the process is known as Multiple Linear Regression. On contrary, if a problem statement contains only one explanatory variable and one response variable, it is known as Simple Linear Regression.

*Note *— For implementing regression analysis, there needs to be a strong relationship between the explanatory variable and the response variable.

Unlike predicting the class label (in classification task), here we predict the real value (continuous value) for the new unseen data.

Mathematical Model

Let’s denote the response variable as `y` and the explanatory variable as `X`. Here `X`, can take either a single feature or multiple features.

In the case of `X` having one feature, the model would be -

In the case of `X` having multiple features, the model would be -

The mathematical model (1) is used for simple linear regression tasks, whereas (2) for multiple linear regression tasks. In both cases, the response variable `y^` is the target feature.

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