A question I've been pondering recently is the derivation of the correlation coefficient for nonlinear regression. I'm more interested in the LA approach so I thought I'd ask here.

I just looked at this paper and noted the formula for r. (Second panel down on the left.) Is it really this simple a formula? If so what is the geometric meaning of it? I've never seen that form when talking about linear regression (just the form with all the sums and no geometric explanation.)

-Dan

PS For those who don't want to look up the page

$\displaystyle r = \sqrt{1 - \frac{ \sum_{i = 1}^n ( y_i - yf_i )^2 }{ \sum_{i = 1}^n (y_i - \bar{y} )^2 }}$

where yf_i are the "fitted" values.