Based on the model you obtained in the previous section, determine the adjusted SBP means for smokers and nonsmokers.

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

1. HW3Q01.sas7bdat gives the systolic blood pressure (SBP), body size (QUET), dichotomized age (AGE_BINARY =1 if age >=60; AGE_BINARY =0 if Age <60), and smoking history (SMK = 0 if a nonsmoker, SMK = 1 if a current or previous smoker) for a hypothetical sample of 32 white males over 40 years old from the town of Angina.

a. State the appropriate regression model to use for comparing the mean blood pressure between the two smoking status (smokers versus non-smokers), controlling both AGE_BINARY and QUET (hint: check the 1st order and 2nd order interaction terms and determine which interaction term(s) should be included in the final regression model)

b. Based on the model you obtained in the previous section, determine the adjusted SBP means for smokers and nonsmokers.

Hint: First, find the overall sample mean of QUET and the mode of AGE_BINARY. You can use SAS Proc Freq to get the mode of AGE_BINARY. Remember mode is defined as the level of AGE_BINARY with the highest frequency.

Proc Freq data=HW3Q01; table AGE_BINARY;

run;

Then, report the adjusted SBP means for smokers and non-smokers at the mean value of QUET and mode of AGE.

c. Test whether the true adjusted mean SBP- QUET relationship is the parallel between the two age groups within each smoking status.

2. HW3Q02.sas7bdat presents the starting annual salaries (SAL) of a group of 30 college graduates who have recently entered the job market, along with their cumulative grade-point averages (CGPA). For the simple linear regression model of SAL (Y) on CGPA (X),

a. Examine a plot of the jackknife residuals versus the predicted values. Are any regression assumption violations apparent? If so, suggest possible remedies.

b. Examine whether the normality assumption violated. If violated, suggest possible remedies.

c. Examine outlier diagnostics, including leverage, jackknife residuals, and Cook’s distance, and identify any potential outliers.

d. Find the least-square estimated equations for a quadratic model of SAL (Y) on CGPA (X).

e. Is there a collinearity problem for the model in part (d) based on VIF? If yes, remove the collinearity and find the estimated equations for the quadratic model.

f. Test for the significance of the addition of the X2 term to the model in part (e).

g. Can we use lack-of-fit test to check the adequacy of fit of the quadratic model? If yes, perform the lack-of-fit test; if not, explain why.

Attachments:

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