Calculations for the unstandardized coefficients for a multiple regression analysis

#1
I am looking to write a spreadsheet of the calculations for the unstandardized coefficients for a multiple regression analysis (the B values). Trouble is I can't find a good explanation of how to do this by hand, as all the books I have consulted say something like "Use Miniitab or Excel ... to do this step" (!)

Can anyone point me in the direction of a book or article that will give me information about the detailed steps of the calculation please?

And yes I know I can just run 'Regression' in Excel - this is fine for getting results out quicky, but not actually what I need to know.

Many thanks in advance for any help,
Baggies
 

Dragan

Super Moderator
#2
Can anyone point me in the direction of a book or article that will give me information about the detailed steps of the calculation please?


Many thanks in advance for any help,
Baggies
The OLS unstandardized regression weights (B) are easiest to express and caclulate using matrix algebra as:


B = (X^T * X)^(-1)*X^T *Y

where is B kx1, (X^T * X)^(-1) is kxk, X^T is kxN, and Y is Nx1.
 
#3
Just in case you need an actual reference, I believe the Neter, Kutner, Wachtsheim books have that formula, and if I remember correctly, not in linear algebra terms.

Their books are "Applied Linear Regression Models" and "Applied Linear Statistical Models" (which contains ANOVA too).

Every edition of the book they switch around the authors, even adding or dropping someone, but any edition should have the formulas. Just search the author names on Amazon or Google books and you should find them pretty easily.

Karen