# Regression SS in multiple linear regression

#### kingwinner

##### New Member
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!

#### kingwinner

##### New Member
I did, and that's the first thing I do before I post this thread.
But I am not sure whether the first formula holds for mutliple linear regression or not...

#### Rounds

##### New Member
It holds for multipe regression. Matrix multiplications are relatively simple operations for a computer and to instruct a computer to do. Also the matrix forms are useful for proving theoretical results.