When fitting a line into a data set the V_r2 represent the correlation coefficient right?, If this is true when you force the best fit line to pass through the origin (0,0) the V_r2 seem to improve, and I don’t think that is right.... What is the best to get a true V_r2 value if the line is forced through 0,0
I don't think r-squared (or "coefficient of determination") is valid when you force the fit through the origin. But I agree that it seems like doing that would make the value *larger*, not smaller. Here is a response I sent to someone who saw r-squared values *larger than one*:
I am using the definition of r^2 given under "As explained variance". My feeling is that in the context of curve fitting, the "explained variance" interpretation is good to have. In the cases where you hold the constant term and get a V_r2 larger than 1, it is telling you that you have actually increased the variance compared to the data. Probably a good thing to know.
You will also note from that article section "As squared correlation coefficient" that the r^2 = (correlation coefficient)^2 holds only for the y = a + bx model. When you hold either a or b you are not fitting that model.
It's possible that my documentation should be expanded, with the risk of getting more complaints about the size of Igor's manuals. There is a strong inverse relationship between the length of the documentation and the probability that customers actually read it :)
John Weeks
WaveMetrics, Inc.
support@wavemetrics.com
February 1, 2012 at 09:08 am - Permalink