Explain simple linear regression model

The goal of a simple linear regression is to find the relationship between a single feature (explanatory variable x) and the outcome. The equation of a linear model with one explanatory variable is defined as follows:

Y=w0 +w1x

Here, the weight w0 represents the y axis intercepts and w1 is the coefficient of the attributes or the independent variable. We need to learn the weights of the linear equation to describe the relationship between the features and the target variable, which is then used to predict the responses of new explanatory variables that were not part of the training dataset.

Based on the linear equation that we defined previously, linear regression can be understood as finding the best-fitting straight line through the sample points, as shown in the following figure:

This best-fitting line is also called the regression line, and the vertical lines from the regression line to the sample points are the so-called residuals which are nothing but the errors of our prediction.

The special case of one feature is also called simple linear regression, but of course we can also generalize the linear regression model to multiple features. Hence, this process is called multiple linear regression.

Y=w0x0 +w1x1 + ………+ wmxm = wTx

Where w0 is the intercept of y-axis when x0=1