Supplemental Worksheet: Computing correlation coefficients

The formula for calculating R² given in Should We Risk It? only applies when you’ve fit the curve using least squares. When this hasn’t been done, the symmetry TSS = ESS + RSS doesn’t hold. Instead, use r, or the correlation coefficient.

 

 

 

To calculate correlation coefficient

 

r =                                 covariance (predicted, observed)                      .

standard deviation (predicted) ´ standard deviation (observed)

Recall that

and

The significance of r can be tested using the Student’s t (n-2 degrees of freedom)

 

 

Alternate formula for r:

 

 

(substitute x_oi for x and x_pi for y)

 

Copyright 2003 David M. Hassenzahl