In a study designed to examine the effects of adding cats to the typical American diet, Individuals were randomly divided into two different groups. Twice a day, the first group substituted oats for other foods containing carbohydrates. The members of the second group did not make any changes to their diet. One outcome of interest is the serum cholesterol level of each individual eight weeks after the start of the study. Explanatory variables that might be associated with this response include diet group, serum cholesterol level at the start of the study, body mass index (measured in kg/m), and sex. The estimated coefficients and standard errors from a multiple linear regression model constructed based on a sample of size 76 and containing these four explanatory variables are displayed below [286].

(a) Conduct tests of the null hypotheses that each of the four coefficients in the population regression equation is equal to 0.

At the 0.

05 level of significance, which of the explanatory variables are associated with serum cholesterol level eight weeks after the start of the study, adjusting for the others?

(b) What is the probability distribution of each of the test statistics calculated in part (a)?

(c) If an Individual's body mass index were to Increase by 1 kg/m while the values of all other explanatory variables remained constant, what would happen to his or her serum cholesterol level?

(d) If an individual's body mass index were to increase by 10 kg/m while the values of all other explanatory variables remained constant, what would happen to his or her serum cholesterol level?

(e) The Indicator variable sex is coded so that 1 represents a male and 0 a female. Who Is more likely to have a higher serum cholesterol level eight weeks after the start of the study, a male or a female? How much higher would it be, on average?

Variable Coefficient Standard Error Diet group -11.25 4.33 Baseline cholesterol 0.85 0.07 Body mass index 0.23 0.65 Sex -3.02 4.42