Take home problems for Exam 5

 1) The baseball researcher from Exam 2 is back and now believes that a player’s age is more related to their salary than their team.

Below are the data of players from five positions for each of five teams:

Team position salary(M) age
Yankees SS 16.7 38
Yankees 3B 29.0 36
Yankees RF 6.5 38
Yankees C 0.5 26
Phillies SS 11.0 33
Phillies 3B 18.3 35
Phillies RF .75 26
Phillies C 5.0 33
Twins SS .5 25
Twins 3B .5 26
Twins RF .5 25
Twins C 23.0 29
Mariners SS 3.25 30
Mariners 3B .5 24
Mariners RF .5 25
Mariners C 1.5 32
Rangers SS 5.0 23
Rangers 3B 16.0 33
Rangers RF 10.3 31
Rangers C 7.5 35

Perform an analysis of covariance to test for the effect of position on salary after adjusting for age.

Calculate adjusted means and standard errors for each position, calculate the efficiency of the covariate, and produce residual plots to check model assumptions.

Test for equal slopes. Write a few sentences summarizing your results.

2) A researcher is investigating the effect on salary of a person’s highest educational level,

being a college graduate versus being a high school graduate.

Age is also thought to be a factor, so age was collected from each subject in the data below:

level age income(K)
HighSchool 47 25
HighSchool 63 37
HighSchool 53 20
HighSchool 37 22
HighSchool 66 35
HighSchool 56 15
HighSchool 49 10
HighSchool 62 24
HighSchool 40 21
HighSchool 54 20
HighSchool 55 41
HighSchool 57 34
College 33 35
College 50 55
College 62 60
College 43 58
College 24 43
College 35 48
College 50 67

Perform an analysis of covariance to test for the effect of educational level on salary after adjusting for age.

 Calculate adjusted means and standard errors for the two levels, calculate the efficiency of the covariate, and produce residual plots to check model assumptions.

Test for equal slopes. Write a few sentences summarizing your results.

3) It was mentioned that for ANCOVA to be appropriate, the range of x values between groups should have some overlap.

Briefly discuss why having no overlap between x values in different groups can invalidate ANCOVA. Give a hypothetical example of why this is inappropriate.