Sum of squares explained by X and explained by X after Z

We again emphasise that these two sums of squares can be different. Adding the variable X to the model with no variables usually explains more variability than adding it to a model that already contains Z.

The higher the correlation between X and Z, the greater the difference between these sums of squares.


Leafing-out time of maples

The diagram below shows an index of the leafing-out time of batches of maple seedlings grown in Wooster, Ohio. The explanatory variables are the latitude (X° North) and mean July temperature (Z° F) of the place of origin of the seeds. A relationship would prove that there is a genetic difference between seeds from the different locations.

Use the Component pop-up menu to display the component explained by X, and the component explained by X after Z. Observe that the sum of squares explained by X if much lower when Z is already in the model. (The sums of squares tables at the bottom are a concise way to describe this.)

Use the Sum of sqrs for: pop-up menu to see the same effect for the variable Z.