Please use SAS to solve these questions and provide the codes:

Scientists examined subjects with chronic, nonspecific low back pain. In this study, 20 of the subjects completed a survey questionnaire assessing physical functioning (Y) at baseline, and after 1, 3, and 6 months (time). Subjects also received two types of treatment (treat). Higher physical functioning values indicate better physical functioning.

1. a. We first want to assess if there is a difference in treatments across time. Therefore, model physical functioning as a function of time (as a continuous variable), drug, time, and drug interaction, and adjust for age. You may use the compound symmetry correlation/covariance structure. Identify, test, and interpret the interaction term for time and drug.

2. b. We now want to look at time as a categorical variable (baseline as the referent group). Rerun the model with time, drug, and age as the predictors but with NO interactions. Which correlation/covariance structure is best?

2. c. Using the best correlation/covariance structure from part b), identify and test the hypothesis needed to determine if there is a difference in treatment, interpret your result. (Perform hypothesis testing and interpret).

ID 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 treat 6 6 6 6 7 7 7 7 8 8 8 8 9 9 9 9 10 10 10 10 11 11 11 11 12 12 12 12 13 13 13 13 14 14 14 14 15 15 15 15 16 16 16 16 17 17 17 17 18 18 18 18 19 19 19 19 20 20 20 20 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N age 2 2 2 2 2 2 2 1 1 1 1 2 2 2 2 2 2 1 1 1 1 2 2 2 2 2 2 45 45 45 45 35 35 35 35 25 25 25 25 22 22 22 22 21 21 21 21 55 55 55 55 56 56 56 56 60 60 60 60 63 63 63 63 49 49 49 49 43 43 43 43 35 35 35 35 36 36 36 36 52 52 52 52 38 38 38 38 27 27 27 27 20 20 20 20 56 56 Time Y 1 2 3 4 1 56 56 26 26 26 26 48 48 48 48 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 233 234 4 1 4 1 80 60 95 100 95 90 95 95 65 55 50 45 50 45 70 70 60 75 80 85 70 70 75 70 80 80 85 80 70 60 75 65 80 80 70 65 65 30 45 60 60 70 95 80 50 50 70 60 50 65 80 65 85 45 85 80 50 65 90 70 15 30 20 25 10 15 55 75 80 85 90 70 15 20 30 45 50 55 70 75