Hi- My mom is taking a correspondence course in Simple Linear Regression and Correlation Analysis and we've been arguing about the relationship between the correlation -rxy and standard estimate of error-Sy.x. I took statistics last year in high school and I remember something about the Sy.x being proportionate to the r. Are they inversely related, directly related, not related, or can only range from 0 to 1.00? Her book doesn't say very much and I believe they are inversely related. She says they're directly related. Do you have more information because I haven't been able to find very much information and I have a Happy Meal riding on this. Thanks for your help with this question.

Hi,

The standard error of estimate, Sy.x is the square root of S2y.x. The quantity S2y.x is also called the mean square error and designated MSE. The relationship between Sy.x and rxy is

Sy.x = Sqrt[1 - r2] SSY/n - 2 where SSY is the sum of the squares of the Y's. In other words Sy.x = Sqrt[1 - r2] S2y( n - 1/n - 2) where S2y is the variance of the Y's. (notice that if n is large then  n - 1/n - 2 is close to 1.)

Thus if r is large (close to plus or minus 1), Sy.x is small (close to zero) and if r is small (close to zero), Sy.x is large (close to the variance in the Y's).

Cheers,
Chris and Penny
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