The correlation coefficient r measures the strength of a linear relationship between ordered pairs (xi,yi). Suppose you are testing the strength of a non-linear relationship. How would you modify the formula for the calculation of r?

To save you time, here is one representation of the formula for r:

r = [ SUM(xi - xbar)(yi - ybar) ] / [ SQRT(SUM(xi - xbar)^2) * SQRT(SUM(yi - ybar)^2) ].

Or is there an entirely different way to measure this?

Thank you.

HANK

Linear regression based on assumption of linearity!

HANK

gogosean

Yes, linear regression assume linearity, but people model non linnear relationships every day in OLS. Force a linear transformation for the predictor variable against the independant variabe. What I am about to show you is one of an infinite ways to approach this problem. For example, use a quadratic formula lke x+x^2+x^3 etc... to represent the non linearity. If you feel it is quadratic, take each predictor and raise it to a power of 2,3,4,5,6. The carrot "^" means "to the power of". First put in X, then put in X^2 and go on up the ladder until P<.10 or .05 for the newest predictor, depending on your preferences for Null hypothesis significance testing. Open your mind, you don't need a new R, just transformations. Thousands upon thousands of possible transformations exist. You can find some answers in books like "Data preparation for data mining." Good Luck.