Question: You want to estimate the relationship between body fat and various physical characteristics of men. Download the file with data on “Body fat”. The file contains a sample of the data that have been collected by a major American hospital for a specific year. The following variables are included:

PCBF_i : The percent of body fat in the weight of the i-th person;

WEIT_i : The weight of the i-th person in pounds;

HEIT_i : The height of the i-th person in inches;

WAIS_i : The circumference of the waist of the i-th person in inches

You think that the following theoretical model would be appropriate for your study on body fat:

PCBF_i = β₀ + β₁*WEIT_i + β₂*HEIT_i + β₃* WAIS_i + ε_i

a. Briefly hypothesize the signs of the coefficients. (2 points)

b. Run the regression shown above and report your results in full reporting mode. (3 points)

c. Without actually running the specific tests, evaluate the significance of the coefficients taken individually (signs and sizes), and collectively (F-ratio) (3 points)

d. Evaluate the coefficient of determination. (2 points)

e. Do you think that there is a problem with this model and why? (3 points)

f. Suppose that you suspect that the model suffers from multicollinearity. Run a correlation test to measure the correlation coefficients of the regressors taken by two. What do you conclude? (2 points)

g. Calculate the VIF coefficients for all three regressors and comment on them. (4 points)

h. What can you do to cure multicollinearity? Would you drop one of the two collinear variables? (3 pts)

i. Assuming that you think that, in spite of the multicollinearity, all variables are needed. You decide to create another variable that is a ratio of inches of Waist per inch of Height. Run the Percent of Body Fat against Weight and the ratio variable and report your results. (3 points)

j. Run a correlation test of the new variables. What do you conclude? (2 points)

k. Which regression you prefer? The one in (b) or the one in (i)? (3 points)