Discuss the below:
Q: The provost at Aluacha Balaclava College wants to look at the faculty salary data in some other ways. She has collected data on salary, years of service, rank, school, gender, and tenure. A sample of the data is shown below:
|
Salary
($)
|
Years of Service
|
Rank
|
Schools
|
Gender
M/F
|
Tenure
Y/N
|
|
53,316
|
22
|
ASST
|
BUSINESS
|
F
|
Y
|
|
64,375
|
11
|
PROF
|
BUSINESS
|
M
|
Y
|
|
63,501
|
7
|
ASSO
|
BUSINESS
|
M
|
Y
|
|
59,426
|
6
|
ASSO
|
BUSINESS
|
M
|
N
|
|
49,058
|
20
|
ASSO
|
BUSINESS
|
M
|
Y
|
|
94,969
|
4
|
PROF
|
BUSINESS
|
M
|
N
|
|
54,762
|
21
|
ASST
|
BUSINESS
|
M
|
Y
|
|
55,516
|
9
|
ASSO
|
BUSINESS
|
M
|
Y
|
a). Make scatter plots (using excel) of salary versus years of service for the entire faculty. Do you think that there is a linear relationship between the two variables? Why or why not?
b). Find the simple linear regression model with salary as the dependent variable and years of service as the independent variable.
c). At the 0.05 level, is there a significant linear relationship between salary and years of service?
d). What is the value of R² for this model? What does it mean?
e). Separate the data by rank and create scatter plots (using excel) of salary versus years of service for each rank. How do these plots compare to the one for all of the faculty?
f). Find a simple linear regression model for salary versus years of service for each rank. How do the regression coefficients for each rank compare to each other? How do they compare to the overall model for all of the faculty?
g). At the 0.05 level of significance, are any of the models significant?
h). What are the R² values for each of the models?
i). Calculate the residuals for all significant models. Create a plot (using excel) of residuals versus predicted values for each model. Is the simple linear model appropriate for these data? Why or why not?
j). For each significant model, investigate the assumption of normality. Do you think the assumption is valid for these data? Why or why not?
k). Are there any data values that might be exerting a strong influence on the model? If so, which ones? Drop any unusual values from the data and rerun the models. How does this change the results?
l). Perform any additional analyses that you feel would be helpful to determine whether or not the simple linear model is an appropriate one for these data. Write a short report with your conclusions.