An example I used to assign in an intermediate course, though not for this purpose: data were from a textbook (Cochran, I think), being dry weights of chick embryos at ages 6 to 16 days, at 1-day intervals. Very nicely fitted an exponential growth curve (R^2 = 97% or so). But to fit the curve y = a*e^(b*x) one took logarithms of the response variable: log(y) = log(a) + b*x. Here the R^2 based on the obvious ANOVA is the square of the correlation between <log(y)> and <predicted value of log(y)>. If you take the regression results and back-transform (using antilogs = exponentials) to get actual predicted values of y, you can then correlate those with the original (or observed) y. But these are now two different variables. Related to those in the ANOVA R^2, but related nonlinearly; so the square of that correlation would not be expected to be identical to (SSpred/SStotal). (In this case the two values of R^2 are necessarily quite close, because they're so close to 1. Haven't investigated data with a less compelling fit, so don't know what to expect in general.)
[If you want the data to play with, ask. I've got it somewhere around here, but it will take a little time to find it.] Cheers! -- Don. On Fri, 26 Mar 2004, jim clark wrote in part: > 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). ------------------------------------------------------------ Donald F. Burrill [EMAIL PROTECTED] 56 Sebbins Pond Drive, Bedford, NH 03110 (603) 626-0816 . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
