In a study designed to examine the effects of adding oats to

In a study designed to examine the effects of adding oats 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 affect this response include diet group, serum cholesterol level at the start of the study, body mass index, and gender. The estimated coefficients and standard errors from the multiple regression model containing these four explanatory variables are displayed below.

Variable ------------------------------Coefficient ---------------------Standard Error
Diet Group _________________-11.25________________ 4.33
Baseline Cholesterol_________ 0.85__________________ 0.07
Body Mass Index ___________0.23__________________ 0.65
Gender ___________________-3.02__________________ 4.42

(a) (4 marks, one for the test of each coefficient) 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 have an effect on serum cholesterol level eight weeks after the start of the study?

(b) (1 mark) If an individual’s body mass index were to increase by 1kg/m2 while the values of all other explanatory variables remained constant, what would happen to his or her serum cholesterol level?

(c) (1 mark) If an individual’s body mass index were to increase by 10 kg/m2 while the values of all other explanatory variables remained constant, what would happen to his or her serum cholesterol level?

(d) (2 marks) The indicator variable gender 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 man or a woman? How much higher would it be, on average?

Solution

(a) to test that each of the four coefficients in the population regression equation is equal to zero.

In the above table for the given four explanatory variable coefficients in the population regression equation is different from zero only last two explanatory variable and first two have different from zero. because last two variable having p- value is greater than 0.05 and remaining variable is less than 0.05.

(b) If an individuals body mass index were to increase by 1 kg/m2and other independent variable are remains same in that situations   serum cholesterol level not change because the coefficient of body mass index is insignificant in the above table.