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The personnel director for a local manufacturing firm has received complaints
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%u2019s 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%u2019 complaints regarding salary inequities.
Perform each of the following seven regression analyses using a 95% confidence level.
%u2022 Annual salary vs. average performance rating for the past 3 years
%u2022 Annual salary vs. years of service
%u2022 Annual salary vs. number of relevant certifications
%u2022 Annual salary vs. average performance rating for the past 3 years and years of service
%u2022 Annual salary vs. average performance rating for the past 3 years and number of relevant certifications
%u2022 Annual salary vs. years of service and number of relevant certifications
%u2022 Annual salary vs. average performance rating for the past 3 years years of service and number of relevant certifications
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 8.
1. What is the degree of correlation between the dependent variable and the independent variable?
o 0.8198
o 0.6672
o 0.7862
o 0.6523
2. Is the statistical significance of the model as a whole less than the desired statistical significance for the regression model?
o Yes
o No
3. Is the statistical significance of the linear relationship between the dependent and independent variables less than the desired statistical significance
for the regression model?
o Yes
o No
4. What percentage of the observed variation between the actual values of the dependent variable and the mean value of the dependent variable in the sample
data set is explained by the regression model?
o 44.51%
o 66.72%
o 41.99%
o 76.24%
5. What is the amount by which we will be off on average when predicting values for the dependent variable using the regression model?
o $12287
o $32966
o $4169
o $25896
6. What is the coefficient for the y-intercept for the regression model?
o 39.38
o 19.94
o 12.29
o 2.96
7. What is the coefficient for the independent variable for the regression model?
o 63.08
o 4.52
o 12.29
o 2.96
8. What is the point estimate for the predicted salary for an employee with an average performance rating of 3.9?
o $71562
o $57006
o $41299
o $50896
9. Which independent variables evidence a positive correlation with the dependent variable?
o Average performance rating for the past 3 years
o Years of service
o Number of relevant certifications
o All of the above
o None of the above
10. Which of the three pairs of independent variable evidences a degree of collinearity that should be cause for concern when performing multivariate linear
regression (i.e. evidences a degree of correlation in excess of 0.5)?
o Average performance rating for the past 3 years vs. years of service
o Average performance rating for the past 3 years vs. number of relevant certifications
o Years of service vs. number of relevant certifications
o All of the above
o None of the above
Use the regression statistics pertaining to all seven regression analyses in order to answer questions 11 through 13.
11. If you were to consider only the three regression models that are based upon a single independent variable which of the following models would be your
preferred model?
o Annual salary vs. average performance rating for the past 3 years
o Annual salary vs. years of service
o Annual salary vs. number of relevant certifications
12. If you were to consider only the three regression models that are based upon two independent variables which of the following models would be your
preferred model?
o Annual salary vs. average performance rating for the past 3 years and years of service
o Annual salary vs. average performance rating for the past 3 years and number of relevant certifications
o Annual salary vs. years of service and number of relevant certifications
13. When you consider all seven regression models which is the overall preferred regression model?
o Annual salary vs. average performance rating for the past 3 years
o Annual salary vs. years of service
o Annual salary vs. number of relevant certifications
o Annual salary vs. average performance rating for the past 3 years and years of service
o Annual salary vs. average performance rating for the past 3 years and number of relevant certifications
o Annual salary vs. years of service and number of relevant certifications
o Annual salary vs. average performance rating for the past 3 years years of service and number of relevant certifications
14. The personnel director considers an employee%u2019s current salary to be fair and reasonable if it is within plus or minus 1.5 standard errors of the value
estimated using the preferred regression model. Of the 24 employees how many employees%u2019 current salary is outside the range of what the personnel
director considers fair and reasonable?
o 0
o 1
o 2
o 3
o 4
o 5
