I've generated these plots:
The upper two scatter plots show linear regressions of two different combinations of three variables ($W2$, $K$ and $R$), both against $log(z)$, with their
r values in the legend. The bottom two plots show the residuals of each of the upper plots. My question is about the relationship between the correlation coefficients and the range of the residuals:
r-value | range of resids |-----------|----------------- W2/R | 0.629395 | 0.188974 K/W2 | -0.644147 | 0.344847
Why does the ratio K/W2 show a higher correlation coefficient, but the residuals have a lower spread?
I would have expected that a high
r means a low spread of residuals. Why is this not the case?