On 3 Sep 2003 01:42:07 -0700, [EMAIL PROTECTED] (Bastian) wrote: > I wonder if the coefficient of determination, which usually ranges > from -1 to +1, can achieve other values for nonlinear relations. I > read something like that in an artikel which said that this is shown > in GREENE, W. H., Econometric analysis (1997), p. 318. > > Unfortunately I can't get the book the next weeks, so I'd be glad > about any comments on the topic or some hints to other literature > sources.
W.H. Green, Econometric analysis (1997) does not say anything about coefficient of determination on page 318. Or about anything that I see as relevant. The C of D is listed in the index for page 85 and page 252. On p. 252, Greene writes, "The coefficient of determination is denoted R2. As we have shown, it must be between 0 and 1, and it measures the proportion of the total variation in y that is accounted for by variation in the regressors." So, I don't see the support in Greene that you mentioned. On the other hand -- I've seen R2 that is, in a sense, legitimately outside the range, though I hesitate to call those "coefficient of variation." - If you define your total variation as the mean-corrected variation, that's one thing. Or, if you don't use the mean at all, sometimes the Total is defined as the raw Sum of squares. That's a complication that people get into with "no-intercept" regression, even though it is linear. If your regression does not account for the mean, then the residual can have a larger Sum of squares than the (mean-adjusted) Total sum. That is one way that you can come up with funny numbers, either directly or by subtraction. -- Rich Ulrich, [EMAIL PROTECTED] http://www.pitt.edu/~wpilib/index.html "Taxes are the price we pay for civilization." . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
