Time for action - calculating the correlation coefficient

Let us try to calculate the correlation coefficient for the fit of the leaf length for tree A. We just need to follow Equation (7.9):

octave:21> denom = (length(yA) - 1)*var(yA);
octave:22> rcor = 1 sA.normr^2/denom
rcor = 0.96801

This gives an indication that the fit is good as we expected.

What just happened?

In Command 21, we calculated the denominator in Equation (7.9). Notice that instead of calculating the square of the standard deviation, we simply use the variance found with var. From Equation (7.9), we see that the 2-norm of the residuals enters the nominator. This is already calculated in polyfit and stored in the structure field normr, so we use this in the evaluation of the correlation coefficient.

Residual plot

If there is a systematic deviation between the fit and the data, the model may have to be rejected. These deviations can be sufficiently small and are therefore not captured by the correlation coefficient. They...