Assume that one has two input variables (X1, X2) and one output variable (Y). One can approach regression in two ways:
One can first run a univariate regression between X1 and X2, have a residual vector (e.g. lets call it X1v2-res), and then run a univariate regression between X1v2-res and the Y variable.
Alternatively - one can first run a univariate regression between X1 and Y, have a residual vector (lets call it X1vY-res) and then run a univariate regression between X1vY-res and the Y variable.
Am i right that the first approach gives us the multivariate regression coefficients (e.g. one can switch around X1 and X2 to get each of their coefficients), whereas the second approach is maybe somewhaat akin a forward selection regression, but doesnt give us the standard multivariate regression coefficients?
Please let me know in case i am wrong - many thanks; W