Multiple Linear Regression; Terms in X

I would like to ask why in the carsmall example X has the extra term x1.*x2, like this:

X = [ones(size(x1)) x1 x2 x1.*x2];

Running b = regress(y,X) returns

b = 4×1

60.7104

-0.0102

-0.1882

0.0000

which means that eitherway the last term plays no role.

Thanks :)

https://www.mathworks.com/help/stats/regress.html#mw_9aa001d2-583e-41ab-92bb-9cc24c78c457

Answer 1

[Benjamin Thompson]

It is a bilinear fit so the regression is attempting to find the optimal b vector that fits a two-input function F of X and Y:

YFIT = b(1) + b(2)*X1FIT + b(3)*X2FIT + b(4)*X1FIT.*X2FIT;

Hence, the ones in the first column of X in your example since that is the constant. This technique can also be used to fit to polynomial functions and other nonlinear functions as long as the problem is linear in the coefficients you solve for.

[Theo Pap]

So it is just an extra term for polynomial fit. That's why the yfitted mesh is curved and not a straight plane. Ok, it make sense. Initially it just seemed to me a totally random thing to do. Thanks.