In MULTIPLE linear regression, is it still true that the regression sum of squares is equal to ∑ (Y_i hat -Y bar)^2 ???
My textbook defines regression SS in the chapters for simple linear regression as ∑ (Y_i hat -Y bar)^2, and then in the chapters for multiple linear regression, the regression SS is defined in MATRIX form, and it did not say anywhere whether it is still equal to ∑ (Y_i hat -Y bar)^2 or not, so I am confused...
If it is still equal to ∑ (Y_i hat -Y bar)^2 in MULTIPLE linear regression (this is such a simple formula), what is the whole point of expressing the regression SS in terms of matrices in mutliple linear regression? I don't see any point of doing so when the formula ∑ (Y_i hat -Y bar)^2 is already so simple. There is no need to develop additional headaches...
Thanks for explaining!
[also under discussion in Talk Stats forum]