3. A rehabilitation center researcher was interested in examining the relationship between physical fitness prior to surgery of persons undergoing corrective knee surgery and time required in physical therapy 5 until successful rehabilitation. Patient records in the rehabilitation center were examined, and 24 males subjects ranging in age from 18 to 30 years who had undergone similar corrective knee surgery during the past year were selected for the study. The number of days required for successful completion of physical therapy and the prior physical fitness status (1 = below average, 2 = average, 3 = above average) for each patient were recorded in the file. Assume that a one-factor ANOVA model with fixed effects is appropriate to analyze these data. Suppose primary interest is in estimating the following contrasts: L1 = M1 - M2; L2 = M3 - 12. (a) We imported the data, coerced the fitness variable as a factor, and displayed its coding matrix. knees-read.csv ("knee.csv") str(knee) ## ## ## 'data.frame': $ Rehab : int $ Fitness: int 24 obs. of 2 variables: 29 42 38 40 43 40 30 42 30 35 ... 1 1 1 1 1 1 1 1 2 2 ... knee$Fitness