1. Consider the Rehabilitation Therapy data of Problem 16.9 on p.476, and continued in Problem 22.11 on p.553. Patients were classified into three groups according to prior physical fitness (Below average, Average, and Above average). The response variable is the time (days) required in physical therapy until successful rehabilitation. Since age of patient may affect rehabilitation time, it was decided to use it as covariate.

1. (a)Use PROC GLM to conduct an Analysis of Covariance test for significant dif- ferences in mean therapy time between the three groups with adjustment for covariate age.
2. (b)Does adjusting for age make theF-test for mean differences more significant or less significant? Is the change inFcaused more by a change in the numerator or denominator?
3. (c)Using PROC GLM, estimate the mean rehabilitation time for the three groups
4. i. unadjusted for age ii. adjusted for age
5. (d)Calculate by hand theF-test statistic in (a) for significant difference between group means adjusted for age. (You may use PROC REG to calculate SSE for full and reduced models.)
6. (e)Calculate by hand the mean rehabilitation time for the Below Average group adjusted for age.

The data set is

Subject Days Fitness Age 1 29.0 Below 18.3 2 42.0 Below 30.0 3 38.0 Below 26.5 4 40.0 Below 28.1 5 43.0 Below 29.7 6 40.0 Below 27.8 7 30.0 Below 19.8 8 42.0 Below 29.3 9 30.0 Average 20.8 10 35.0 Average 25.2 11 39.0 Average 29.2 12 28.0 Average 20.0 13 31.0 Average 21.5 14 31.0 Average 22.1 15 29.0 Average 19.7 16 35.0 Average 24.7 17 29.0 Average 20.2 18 33.0 Average 22.9 19 26.0 Above 22.7 20 32.0 Above 28.7 21 21.0 Above 18.9 22 20.0 Above 18.0 23 23.0 Above 21.7 24 22.0 Above 20.0