Question

In multiple regression why do we include the intercept? What is the intercept's importance?

Answer 1

A multiple regression is of the form :

Y = a0 + a1X1 +a2X2 + a3X3 + .............

Where Y - Dependent variable

X1,X2,X3 ... : Independent variable / Explanatory variables

a0 = intercept

The intercept in a multiple regression model is the mean for the response when all of the explanatory variables take on the value 0.

thats is , X 1 = X2 = X3 = 0

Y = a0

We include the intercept in the multiple regression as it is an important part of the regression equation.

The intercept (often labeled as constant) is the point where the function crosses the y-axis. In some analysis, the regression model only becomes significant when we remove the intercept.A regression without a intercept means that the regression line goes through the origin wherein the dependent variable and the independent variable is equal to zero.On removing the intercept  almost all the variables become significant which shall not be the case this why it is important to include intercept in multiple regression