jim clark wrote: > Hi > > On 25 Mar 2004, Bin Zhou wrote: > >> Hello, all, >> >> In linear regression, Y1 is dependent variable, Y2 is predicted >> value. R is Pearson's r for Y1 and Y2, so I can get R square. >> I can also get R square by the following formula. >> R square = 1 - SSE/CSS >> WHERE >> SSE = the sum of squares for error >> CSS = CORRECTED TOTAL SUM OF SQUARES FOR THE DEPENDENT VARIABLE. >> >> I found the two values are different. So I think I can only use the >> second formula for nolinear regrssion, in linear regression, I can >> only calculate pearson's r. Is it right? > > 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). David Jones . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
