13. (20 points) A researcher is interested in estimating the association between educational attainment and body mass index (BMI) in the US adult population. The researcher would like to estimate the correlation between educational attainment and BMI, but his research mentor advised him to "control" for the effects of age. The researcher is puzzled. Help him compute the correlation between education (X) and BMI (Y), and then help him compute the partial correlation between education and BMI while controlling for age (Z). The researcher's mentor got the ball rolling by estimating the correlation between education (X) and age (Z), and also calculating the means and "Total Sum of Squares" (i.e., total variation) for BMI, education, and age: BMI Education Age ( Y) (X) (Z) Mean 27.9 13.6 47.5 Variation 202.0 146.0 382.0 Cov(XY) -32.5 Cov(XZ) -153.3 Cov( YZ) -142.2 Ixy Ixz -.649 Iyz a. Estimate the Pearson's correlation coefficient for educational attainment (X) and BMI (Y). b. Interpret the Pearson's correlation coefficient between educational attainment and BMI