Question

how do we get error sum of squares in a multiple linear regression with two independent variables x1 and x2

Answer 1

I will show you how to calculate error sum of squares in case of multiple linear regression using matrices.

Let there be n observations of y, x1 and x2.

Let be a vector of order n X 1 containing the values of x1, be a vector of order n X 1 containing the values of x2, be a vector of order n X 1 containing the values of y and, lastly, be a vector containing "n" number of 1's and, as a result, of order n X 1 (required for the intercept term).

Now, the design matrix is given as: , which is order n X 3.

The 3 parameters (2 regression coefficients and 1 intercept), represented by , are estimated in the following way: .

The SSE is now calculated as: .