We use the Haynes et al. [1978] data of Table 11.20. The multiple correlation squared of the Framingham type A variable with all 16 of the other variables is 0.424 . Note the high correlations for variables $2,3,14,15$, and 17 .
$$
R_{1(2,3,14,15,17)}^2=0.352
$$
(a) Is there a statistically significant ( $p<0.05$ ) gain in $R^2$ by adding the remainder of the variables?
(b) Find the partial correlation of variables 1 and 2 after adjusting for variable 15. That is, what is the correlation of the Framingham type A index and emotional lability if adjustment is made for the amount of tension?
Stoudt et al. [1970] report on the relationship between certain body size measurements and anthropometric indices. As one would expect, there is considerable correlation among such measurements. The details of the measurements are reported in the reference above. The correlation for women are given in Table 11.21.