understanding Linear regression model equation after simplifying.

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I have run Linear regression on 2 independent variables (b,c) and one dependent variable(a) as shown below.
the model equation is simple as ==> y = intercept + x1*b + x2*c
However, When I simplyfy the model using step as shown below
I could'nt be able to understand the model equation. ==> y~ 1+ x1*x2.
how would I make the equation?
Any help would be appreciated.
Thanking you in anticipation.

Accepted Answer

Jeff Miller
Jeff Miller on 17 Nov 2021
I think the notation y~ 1+ x1*x2 is shorthand for y~ 1*b0+ b1*x1 + b2*x2 + b3*x1*x2. The four b values are the four estimates in the table. The notation is a bit confusing because the interaction term x1:x2 is the numerical product x1*x2. In the model notation, x1*x2 refers to all of the possible combinations of the terms separated by *'s, i.e. x1, x2, and x1:x2.

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