Week Three Homework Assignment Linear Regression Complete Solution
Week Three Homework Assignment - Linear Regression
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, years of service and relevant certifications. 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 |
Number of Relevant Certifications |
---|---|---|---|---|
1 |
48.2 |
2.18 |
9 |
6 |
2 |
55.3 |
3.31 |
20 |
6 |
3 |
53.7 |
3.18 |
18 |
7 |
4 |
61.8 |
3.62 |
33 |
7 |
5 |
56.4 |
2.62 |
31 |
8 |
6 |
52.5 |
3.75 |
13 |
6 |
7 |
54.0 |
4.25 |
25 |
6 |
8 |
55.7 |
3.43 |
30 |
4 |
9 |
45.1 |
1.93 |
5 |
6 |
10 |
67.9 |
4.5 |
47 |
8 |
11 |
53.2 |
2.81 |
25 |
5 |
12 |
46.8 |
3.06 |
11 |
6 |
13 |
58.3 |
5 |
23 |
8 |
14 |
59.1 |
4.06 |
35 |
7 |
15 |
57.8 |
4.12 |
39 |
5 |
16 |
48.6 |
2.31 |
21 |
4 |
17 |
49.2 |
3.87 |
7 |
6 |
18 |
63.0 |
4.37 |
40 |
7 |
19 |
53.0 |
2.5 |
35 |
6 |
20 |
50.9 |
2.81 |
23 |
4 |
21 |
55.4 |
3.68 |
33 |
5 |
22 |
51.8 |
3.5 |
27 |
4 |
23 |
60.2 |
3 |
34 |
8 |
24 |
50.1 |
2.43 |
15 |
5 |
The personnel director is interested in creating a linear regression model that can be used to estimate the annual salary an employee might expect to receive based upon his or her past performance, years of service and/or number of relevant certifications. The regression model will be used as a basis for determining whether or not there is any validity to the employees’ complaints regarding salary inequities.
Perform each of the following seven regression analyses using a 95% confidence level.
Hint: Refer to the handouts posted on Blackboard pertaining to interpreting regression statistics in order to determine if a given regression model is acceptable.This same handout also provides guidance regarding how to select a preferred regression model from amongst multiple acceptable regression models, including models with differing numbers of independent variables.
Hint: For the purposes of this homework assignment, the minimum difference between the R2 or Adjusted R2 values for two acceptable models with differing numbers of independent variables that would favor selecting the model with the larger number of independent variables is 0.03. Please ensure that you fully understand the process for selecting a preferred model before attempting to apply this criterion.
Hint: Question 19 is intended to have you demonstrate that you understand how to determine which univariate models are acceptable, and then select a preferred univariate model from amongst the acceptable univariate models. Question 20 is intended to have you demonstrate that you understand how to determine which bivariate models are acceptable, and then select a preferred bivariate model from amongst the acceptable bivariate models. Question 21 is intended to have you demonstrate that you understand how to select a preferred model from amongst multiple acceptable models that have differing numbers of independent variables. Question 22 is intended to have you demonstrate that you understand how to determine if the trivariate model is acceptable, and then select a preferred model from amongst multiple acceptable models.
Hint: For questions 24 and 25, you need to use the regression equation associated with the preferred model selected for question 22 in order to calculate the predicted salary for each of the 24 employees. In order to answer questions 24 and 25 you need to keep in mind that the predicted salary value for each employee is only a point estimate (this concept was discussed in week one relative to the mean). While a point estimate is a precise value, it is not necessarily an accurate value since the standard error value tells us there is some potential degree of error associated with using the preferred regression model to predict salary values. In order to answer questions 24 and 25 you will need to create an interval estimate (this concept was also discussed during week one relative to the mean) for the predicted salary for each of the 24 employees. To calculate the interval estimate for each employee, simply multiply the standard error value for the preferred regression model by 1.5 and then subtract this value from the predicted point estimate salary value to define the lower limit of the interval estimate and add this value to the predicted point estimate salary value to define the upper limit for the interval estimate. Once you have created an interval estimate for each employee, you will then need to compare each employee's current salary to their corresponding interval estimate in order to determine if each employee's current salary falls within their predicted interval estimate.
Use the results for the univariate regression analysis for annual salary vs. average performance rating for the past 3 years in order to answer questions 1 through 14.
Perform a correlation analysis between the dependent variable and each of the three independent variables. Use the results of the correlation analysis to answer questions 15 and 16.
Perform a correlation analysis between each of the three pairs of independent variables. Use the results of the correlation analyses to answer question 17.
Use the regression statistics pertaining to all seven regression analyses in order to answer questions 15 through 23.
The personnel is interested in comparing each employee’s actual salary to their predicted salary in order to determine if there are any prevailing salary inequities. Suppose the personnel director considers an employee’s current salary to be fair and reasonable if it is within plus or minus 1.5 standard errors of the value estimated by the regression model selected in response to question 22. For each individual employee, calculate his or her estimated salary using the regression model selected in response to question 22, as well calculate his or her upper and lower limits for a fair reasonable salary, in order to answer questions 24 and 25.
Week Three Homework Assignment - Linear Regression Complete Solution
Perform each of the following seven regression analyses using a 95% confidence level.
• Annual salary vs. average performance rating for the past 3 years
• Annual salary vs. years of service
• Annual salary vs. number of relevant certifications
• Annual salary vs. average performance rating for the past 3 years and years of service
• Annual salary vs. average performance rating for the past 3 years and number of relevant certifications
• Annual salary vs. years of service and number of relevant certifications
• &nb...
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