Linear Regression is a statistical technique used to find the linear relationship between dependent and one or more independent variables. This technique is applicable for Supervised learning Regression problems where we try to predict a continuous variable. Linear Regression can be classified into two types – Simple and Multiple Linear Regression. Simple Linear Regression is the simplest form of Linear Regression where we fit a straight line to the data.
Simple Linear Regression
Simple Linear Regression (or SLR) is the simplest model in machine learning. It models the linear relationship between the independent and dependent variables. Suppose there is an independent variable denoted by X. Similarly, there is one dependent or output variable denoted by y. We want to build a linear relationship between these variables. A mathematical equation that can model this form of the linear relationship is given by:-
Y = β0 + β1*X — (1)
In this equation, X and Y are called independent and dependent variables, respectively, β1 is the coefficient for the independent variable, and β0 is the constant term. β0 and β1 are called parameters of the model.
For simplicity, we can compare the above equation with the basic line equation of the form:-
y = ax + b — (2)
Multiple Linear Regression
We know how to build a model with one X (feature variable) and Y (response variable). But what if we have three feature variables or more than that. Building a separate model for each of them, combining them, and then understanding them will be very difficult. By using multiple linear regression, we can build models between a response variable and many feature variables. Also known as “multivariate linear regression”, the multivariable form of the hypothesis function is thus given as:
Y = β0 + β1X1 + β2X2 + β3X3 + … + βnXn
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