The question might be silly, but I wondered if is correct to use linear regressions when you want to assess how a numerical variable
A and a categorical variable
B affects the linear relationship between
I ask that because I am not interested in assessing if
Y. Instead, I am interested in assessing if the relationship (linear) between
X is affected by
A a discrete numerical variable and
B a categorical one.
I think the common way of evaluating this would be a linear regression of the next form:
Y = b0 + b1.X + b2.A + b3.B + E
Is it mathematically right?