11.28. For a group of 100 children of ages varying from 3 to 15, the correlation between vocabulary score on an achievement test and height of child is 0.65.

The correlation between vocabulary score and age for this sample is 0.85, and the correlation between height and age is 0.75.

(a) Show that the partial correlation between vocabulary and height, controlling for age, is 0.036. Interpret.

(b) Test whether this partial correlation is significantly nonzero. Interpret.

(c) Is it plausible that the relationship between height and vocabulary is spurious, in the sense that it is due to theirjoint dependence on age?

Explain.