Reference no: EM132400267

Assignment -

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 until successful rehabilitation. Patient records in the rehabilitation center were examined, and 29 female 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.

Prior Physical Fitness Status
Below Average		Average		Above Average
Recovery Days	Age (years)	Recovery Days	Age (years)	Recovery Days	Age (years)
29	18.3	30	20.8	26	22.7
42	30.0	35	25.2	32	28.7
38	26.5	39	29.2	21	18.9
40	28.1	28	20.0	20	18.0
43	29.7	33	21.5	23	21.7
40	27.8	31	22.1	22	20.0
30	19.8	29	19.7	26	26.5
42	29.3	35	24.7	28	26.1
36	24.2	29	20.2
33	21.1	33	22.9
		36	27.0

The prior physical fitness status (Below average, Average, Above average), number of days required for successful completion of physical therapy, and the patient age for each patient are given in the table above. Note that there are 10 patients in the below average group, 11 in the average group, and 8 in the above average group, where the two values in a row are the recovery days and age for one female.

The researcher anticipates that patients in worse prior physical condition and older patients will tend to take longer to recover from knee surgery. It is also of interest to examine whether the effect of prior physical fitness status on recovery time depends on the age of the patient. Finally, the researcher would like to identify any patients who have unusually short or long recovery times relative to the fitness status and age.

(a) Create a scatterplot of recovery time vs. patient age with separate plotting symbols for each prior fitness status. Describe the relationship between these three variables in a few complete sentences.

(b) Write the linear model you intend to fit to these data in matrix form, clearly defining all variables used.

(c) Analyze these data addressing the four matters of interest indicated above. Write a summary of statistical findings, including any relevant output to support your findings (your report should be 1-2 pages in length, including graphs/tables, but no more). Your summary should include both exploratory analysis and statistical analysis directed toward the research interests stated above.

These data can be found in the MatLab data file rehab.mat on the course webpage. The data appear as 3 columns in the data structure rehab, with the first column being the recovery times rehab.time, the second column being the prior physical fitness status rehab.group, and the third column being the patient age rehab.age.