The provost at a major university would like to develop a model to examine the r
ID: 3315020 • Letter: T
Question
The provost at a major university would like to develop a model to examine the relationship between thesalaries of full-time associate professors at the institution (the dependent variable) and the following independent variables (explanatory variables): an associate professor’s performance rating on a scale of 1 to 20, his or her gender, student approval rating on a scale of 0 to 100%, the associate professors age, years of teaching experience, and the college (arts, sciences, or business) the associate professor teaches. The provost has collected these data from a random sample of associate professors, which can be found in the Excel fileFaculty Salaries (the data may be found in the content area).
Simple Linear Regression
Run a simple linear regression of faculty salaries as a function of years of experience.
Is the regression coefficient on years of experience significant at the 2.5% level? Explain.
Provide a forecast of the mean faculty salary given 25 years of experience.
Construct a 95% confidence prediction interval for the predicted salary in part c.
Report and interpret the R2 for this regression equation.
Multiple Linear Regression
Construct and run a regression model using all the independent/explanatory variables.
Check for the presence of multi-collinearity between the independent/explanatory variables. If multi-collinearity is suspected explain why and then eliminate that variable(s) which you determine to be multi-collinear.
Run a regression of this new linear model after deleting the collinear variables.
Using the results from this regression model interpret each regression coefficient.
Test the significance of each of the estimated coefficients using a level of significance, , of 10% (ie. .10).
Interpret the coefficient of determination, R2.
Test the significance of the R2 using a level of significance, , of 5% (ie. .05).
Remove those explanatory variables from this model that were not significant at the 10% level.
Run an additional regression for this linear regression model after removing the insignificant coefficients.
Using the p-value approach again test the significance of the estimated coefficients using a level of significance, , at the .05 level.
Perform a Regression with Faculty Salary as the dependent variable and Years of Teaching Experience, Performance Score, Student Approval Rating, the Gender Dummy Variable and the College Dummy Variable as the explanatory variables. Then answer p and q.
Predict the salary of a female associate professor in the business college who is 41 years old with 11 years of teaching experience, a performance score of 17, and a student approval rating of 88.3%.
Predict this salary of a male associate professor in the business college who is 41 years old with 11 years of teaching experience, a performance score of 17, and a student approval rating of 88.3%.
Data:
(Salary ($)) (Performance) (College) (Age) (Student Approval) (Experience Gender)
110714 14 Arts & Science 45 89.2 19 Male
103756 13 Business 53 81.8 22 Female
105764 16 Business 50 85.7 19 Female
106118 18 Business 48 82.8 22 Male
100266 16 Business 36 69.7 11 Female
60705 14 Arts & Science 55 89.2 29 Female
104843 16 Business 45 77.7 23 Female
100705 13 Business 54 85.6 23 Male
78195 15 Arts & Science 44 79.8 14 Female
92867 14 Business 38 79.6 10 Female
76675 17 Arts & Science 48 85.6 20 Male
73309 20 Business 31 78.9 6 Male
114377 14 Business 49 86.6 23 Male
73952 14 Business 33 97.2 6 Female
70750 14 Business 33 93.5 8 Female
101661 19 Business 48 75.3 20 Female
113276 18 Business 49 94.5 23 Male
76831 14 Business 40 78.4 14 Female
97251 17 Business 41 83.6 12 Female
105763 18 Business 34 99.4 6 Female
88489 17 Business 42 78.1 18 Female
95185 16 Business 42 84 15 Male
88430 15 Business 34 83.2 8 Male
66569 15 Arts & Science 55 76.6 29 Female
68104 16 Arts & Science 34 84.7 6 Female
60023 15 Business 39 82.5 10 Female
82395 15 Arts & Science 59 82.3 26 Female
107532 20 Business 56 98.9 24 Female
90208 15 Business 42 88.2 18 Female
71750 12 Arts & Science 46 89.5 22 Female
80801 17 Business 45 71.3 15 Male
73038 14 Arts & Science 42 96.1 13 Male
58753 14 Arts & Science 38 73.4 14 Male
83084 14 Business 49 88.6 20 Male
58163 14 Arts & Science 36 76 11 Female
82375 16 Business 36 83.5 12 Male
78510 18 Business 34 84.1 9 Male
103295 13 Business 48 90.9 24 Male
102911 18 Arts & Science 44 91.7 20 Male
74561 19 Arts & Science 49 95.1 18 Male
75975 13 Arts & Science 44 75.3 20 Male
89213 19 Arts & Science 40 89.6 13 Male
78566 13 Business 38 97 10 Female
70206 14 Arts & Science 35 88.5 7 Female
63864 16 Arts & Science 59 75.2 26 Male
74535 13 Arts & Science 43 77.7 14 Male
99667 17 Business 40 97.9 11 Female
65824 15 Arts & Science 50 83.8 19 Male
89298 15 Business 43 90.5 16 Female
72244 13 Business 32 86 5 Male
81216 15 Business 48 82.2 20 Female
65317 17 Arts & Science 61 81.4 29 Male
55357 15 Arts & Science 35 87.5 11 Female
65681 12 Arts & Science 50 79.1 19 Male
87191 15 Business 32 91.4 5 Male
108409 20 Business 41 88.9 14 Female
63459 17 Arts & Science 55 82 25 Female
62931 12 Arts & Science 53 77.8 22 Male
111807 15 Business 45 90.8 17 Male
95754 15 Arts & Science 48 86 20 Male
74162 16 Arts & Science 40 87.8 14 Female
68311 14 Arts & Science 36 80.9 10 Female
111610 17 Business 48 78.9 20 Female
72434 14 Arts & Science 41 86.9 17 Female
75522 13 Arts & Science 37 93.8 9 Female
125407 17 Business 58 88.6 30 Male
58986 13 Arts & Science 40 81.3 15 Male
69668 15 Arts & Science 41 75.8 14 Female
81318 16 Business 45 81.1 17 Male
94079 17 Business 38 95.7 12 Female
80252 19 Arts & Science 56 97.5 24 Male
120263 18 Business 48 78.8 18 Male
74511 19 Arts & Science 40 74.2 17 Female
68715 17 Arts & Science 36 85.8 10 Female
66271 15 Arts & Science 48 82.2 20 Male
87741 20 Arts & Science 47 71.3 23 Male
94076 18 Business 58 78.7 26 Female
58908 13 Arts & Science 33 83.5 8 Female
79548 13 Business 34 91.9 6 Male
94613 12 Business 44 82.7 16 Male
56345 12 Arts & Science 30 88 5 Female
74608 16 Arts & Science 43 80.3 17 Female
60040 13 Arts & Science 36 87.3 10 Female
70647 15 Business 38 92.9 14 Female
76272 12 Business 30 85.3 4 Male
Explanation / Answer
LINEAR REGRESSION
> model=lm(Salary~Experience)
> summary(model)
Call:
lm(formula = Salary ~ Experience)
Residuals:
Min 1Q Median 3Q Max
-31677 -10308 -2373 14011 35849
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 71374.9 4778.9 14.935 <2e-16 ***
Experience 724.4 276.2 2.623 0.0104 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 16710 on 83 degrees of freedom
Multiple R-squared: 0.07655, Adjusted R-squared: 0.06542
F-statistic: 6.88 on 1 and 83 DF, p-value: 0.01037
Yes, the slope is significant at 2.5% level since the p-value < 0.025.
Predicted salary = 71374.9 + 724.4*25 = $89,484.88
> newdata=data.frame(Experience = 25)
> predict(model,newdata,interval="predict")
fit lwr upr
1 89484.88 55692.33 123277.4 #95%Prediction interval
R2 = 0.07655 means that 7.655% of the total variation is explained by the fitted regression model.
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