1.In a study designed to examine the effects of adding oat bran to the typical American diet, 100 individuals were randomly divided into two different groups.Twice a day, the first group substituted oat bran for other food containing carbohydrates; the members of the second group did not make any changes to the diets.One outcome of interest was the serum cholesterol level of each individual eight weeks after the start of the study.Explanatory variables which might affect this response include diet group, serum cholesterol level at the start of the study, BMI, and gender.The estimated coefficients and standard errors are below (the intercept is not shown)

Variable Coefficient Std. Error t P

Diet group -11.25 4.33 -2.60

Baseline cholesterol 0.85 0.07 12.14

BMI 0.23 0.65 0.35

Gender -3.02 4.42 -0.68

a.At the 0.05 level of significance, how many of the four explanatory variables have an effect on serum cholesterol level eight weeks after the start of the study, adjusting for the other variables?What are they?

b.If an individual's baseline cholesterol were to increase by 20 mg/100 ml while the values of all other explanatory variables remain constant, what would happen to his or her serum cholesterol level eight weeks into the study?

c.The indicator variable diet group is coded so that a 1 represents a member of the first group and 0 designates a member of the second group.Who is more likely to have a higher serum cholesterol level?By how much?

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