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.

Linear regression based on assumption of linearity!

HANK :eek:

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.
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 independent 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.