Advanced Data Analysis, II

36-402  Homework 1  Spring, 1996

Homework due — In class, Tuesday February 6.

The following problems are taken from the book “Applied Linear Statistical Models” by Neter, Wasserman, and Kutner. The data are available in the directory /afs/andrew/hss/stat/data/402.

1. Productivity improvement. An economist compiled data on productivity improvements fro a sample of firms producing electronic computing equipment. The firms were classified according to the level of their average expenditures for research and development in the past three years (low, moderate, high). The results of the study follow (productivity improvement is measured on a scale from 0 to 100). The data are in the file product.dat.

1 2  3 4 5 6 7 8 9 10 11 12
Low  7.6 8.2 6.8 5.8 6.9 6.6 6.3 7.7 6.0
Moderate 6.7 8.1 9.4 8.6 7.8 7.7 8.9 7.9 8.3 8.7 7.1 8.4
High  8.5 9.7 10.1 7.8 9.6 9.5

(a) Analyze the data, looking at fitted values, residuals, the ANOVA table, and assumptions

(b) Test for a difference between the “High” level and the others. Is it significant? Are there any other important contrasts? What about the multiple comparisons problem.

(c) Summarize the relationship (if any) between research and development expenditures and productivity improvement.

2. Rehabilitation therapy. 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 24 male 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 the physical therapy and the prior physical fitness status (below average, average, above average) for each patient follow, and are in rehab.dat.

1 2 3 4 5 6 7 8 9 10
Below average 29 42 38 40 43 40 30 42
Average  30 35 39 28 31 31 29 35 29 33
Above average 26 32 21 20 23 22

(a) Analyze the data, looking at fitted values, residuals, the ANOVA table, and assumptions.

(b) Are there any important differences between the factor levels? How did you decide which differences to test?

(c) Summarize the relationship between the factor levels and the response.

3. Soft Drinks. A soft drink manufacturer uses five agents (1,2,3,4,5) to handle the distribution of its various products. The marketing director desired to study the timeliness with which the products are distributed. Twenty transactions for each agent were selected at random, and the time lapse (in days) for handling each transaction was determined. The results are available in premium.dat. The first column is the time lag, the second column is the agent number. This is a random effects model, because of the random sample of times for each agent.

(a) Analyze the data, looking at fitted values, residuals, the ANOVA table, and assumptions.

(b) Are there any important differences between the agents? How did you decide which differences to test?

(c) Summarize the relationship between the agents and the response. If you had to select one agent to represent your product, which would you choose, or would you even care?

Let me know how things are going!