Perform a simple linear regression analysis to predict

Question

The personnel director for a local manufacturing firm has received complaints from the employees in a certain shop regarding what they perceive to be inequities in the annual salary for employees who have similar performance ratings, years of service and relevant certifications.  The personnel director believes that an employee's pay in this particular shop should be positively correlated to their prior performance rating and years of service.  The personnel director has collected the data shown in the following table pertaining to the employees within the shop. 

Employee	Current Annual Salary (Thousands)	Average Performance Rating for Past 3 Years (5 point scale)	Years of Service
1	48.2	2.18	9
2	55.3	3.31	20
3	53.7	3.18	18
4	61.8	3.62	33
5	56.4	2.62	31
6	52.5	3.75	13
7	54.0	4.25	25
8	55.7	3.43	30
9	45.1	1.93	5
10	67.9	4.50	47
11	53.2	2.81	25
12	46.8	3.06	11
13	58.3	5.00	23
14	59.1	4.06	35
15	57.8	4.12	39
16	48.6	2.31	21
17	49.2	3.87	7
18	63.0	4.37	40
19	53.0	2.50	35
20	50.9	2.81	23
21	55.4	3.68	33
22	51.8	3.50	27
23	60.2	3.00	34
24	50.1	2.43	15

1. Perform a simple linear regression analysis to predict an employee's annual salary based upon his or her average performance rating for the past 3 years using a 95% level of confidence.
   1. Does the regression model confirm a positive correlation between the dependent variable and the independent variable as hypothesized?
   2. Is the statistical significance of the model as a whole acceptable for a 95% level of confidence?
   3. Is the statistical significance of the linear relationship between the dependent and independent variable acceptable for a 95% level of confidence?
   4. What is the regression equation for the model?
   5. What is the predicted annual salary for employee number 13 based upon his or her average performance rating for the past 3 years, and what does the predicted salary value suggest regarding his or her current annual salary?
2. Perform a simple linear regression analysis to predict an employee's annual salary based upon his or her years of service using a 95% level of confidence.
   1. Does the regression model confirm a positive correlation between the dependent variable and the independent variable as hypothesized?
   2. Is the statistical significance of the model as a whole acceptable for a 95% level of confidence?
   3. Is the statistical significance of the linear relationship between the dependent and independent variable acceptable for a 95% level of confidence?
   4. What is the regression equation for the model?
   5. What is the predicted annual salary for employee number 13 based upon his or her years of service, and what does the predicted salary value suggest regarding his or her current annual salary?
3. Perform a multiple linear regression analysis to predict an employee's annual salary based upon his or her average performance rating for the past 3 years and his or her years of service using a 95% level of confidence.
   1. Is the statistical significance of the model as a whole acceptable for a 95% level of confidence?
   2. Is the statistical significance of the linear relationship between the dependent variable and each of the independent variables acceptable for a 95% level of confidence?
   3. What is the regression equation for the model?
   4. What is the predicted annual salary for employee number 13 based upon his or her average performance rating for the past 3 years and years of service, and what does the predicted salary value suggest regarding his or her current annual salary?
4. Which of the two simple linear regression models is the preferred model, and why?
5. Is the multiple regression model preferable to the preferred simple regression model, and why?

Hint: For the purposes of this homework assignment, the minimum difference between the R² or Adjusted R² values for two acceptable regression models that would favor selecting a model with a larger number of independent variables is 0.05.