Given a curved regression, the correlation index is defined by r_c congruent s_(yy^^)/(s_y s_(y^^)), where s_y and s_(y^^) are the standard deviations of the data points y and the estimates y^^ given by the regression line. Unfortunately, the quantity s_(yy^^) appears not to be defined by Kenney and Keeping. Then r_c^2 | = | s_(y^^)^2/s_y^2 | = | 1 - s_(e y)^2/s_y^2, where s_(e y)^2 is the variance of the observed ys about the best-fitting curved line.

correlation coefficient | regression