A rehabilitation center researcher was interested in examining the relationship between physical fitness prior to surgery and the time in days) for successful completion of physical therapy. The fitness levels were measured as Below Average (group I), "Average" (group II), or "Above Average" (group III). Summary statistics follow: Sample mean Sample Std. Dev Sample Size 38 5.48 8 II 32 3.46 10 III 24 4.43 6 Overall 32 6.88 24 Data Source: Applied Linear Statistical Models, Kutner, Nachtsheim, Neter, & Li. 4. ANOVA (a) Write down the appropriate ANOVA model if we are interested in how each group differs from the overall mean, and specify all assumptions this model makes. (b) Estimate all values of % (gamma). (C) Interpret the estimated value of 72, where i = 2 corresponds to group II, in terms of the problem. (d) Show that the estimated values of Vi sum to zero. (e) If the ANOVA model assumptions hold, what is the distribution of i? Be as specific as you can. A rehabilitation center researcher was interested in examining the relationship between physical fitness prior to surgery and the time in days) for successful completion of physical therapy. The fitness levels were measured as Below Average (group I), "Average" (group II), or "Above Average" (group III). Summary statistics follow: Sample mean Sample Std. Dev Sample Size 38 5.48 8 II 32 3.46 10 III 24 4.43 6 Overall 32 6.88 24 Data Source: Applied Linear Statistical Models, Kutner, Nachtsheim, Neter, & Li. 4. ANOVA (a) Write down the appropriate ANOVA model if we are interested in how each group differs from the overall mean, and specify all assumptions this model makes. (b) Estimate all values of % (gamma). (C) Interpret the estimated value of 72, where i = 2 corresponds to group II, in terms of the problem. (d) Show that the estimated values of Vi sum to zero. (e) If the ANOVA model assumptions hold, what is the distribution of i? Be as specific as you can