Hi On Fri, 26 Mar 2004, David Jones wrote:
> jim clark wrote: > > No, the two ways of computing r^2 should agree, no matter how > > many predictors you have. > > Unfortunately/importantly, this is not true. They only agree if the > predictor is of a specific form: > Y2 = a + b*Y3 > where Y3 is another predictor, and a and b are effectively fitted by > least squares (possibly at the same time Y3 is fitted). If the form of > the predictor Y2 is not such as to have the "free" parameters a and b > of this type, then Pearson's r^2 will give a different answer because > it essentially does allow for these extra free parameters (because it > is the correlation). > > If you do use Pearson's r^2 as a measure of "fit" you are > effectively allowing for further adjustment of your predictor, beyond > what you originally fitted ... thus this r^2 (correlation) will be at > least as large as R^2 (calculated from the errors). Below is what I wrote in its entirety. I would really like to see an example where the correlation between the original y and the predicted y does NOT equal the multiple R defined as sqrt(SSpred/SStotal). ----------------------------------------------------------- No, the two ways of computing r^2 should agree, no matter how many predictors you have. Just to be clear, if y^ = b0 + b1*x1 + b2*x2 .... , where one or more xs could be polynomial predictors, then R^2 = SSy^ / SSy (just another variation of your formula) will equal r(yy^)^2 ----------------------------------------------------------- Best wishes Jim ============================================================================ James M. Clark (204) 786-9757 Department of Psychology (204) 774-4134 Fax University of Winnipeg 4L05D Winnipeg, Manitoba R3B 2E9 [EMAIL PROTECTED] CANADA http://www.uwinnipeg.ca/~clark ============================================================================ . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
