Mike is president of the teachers\' union for Lakeview School District. In prepa
ID: 3066397 • Letter: M
Question
Mike is president of the teachers' union for Lakeview School District. In preparing for upcoming negotiations, he would like to investigate the salary structure of teachers in the district. He believes there are three factors that influence a teacher's salary: years of experience, a rating of teaching effectiveness given by the principal, and whether or not the teacher has a master's degree. A random sample of 20 teachers resulted in the data given below (note that salary is in thousands of dollars per year)
a) Check for multicollinearity by analyzing the correlation matrix. Copy/paste (screenshot) the correlation matrix from Excel below. Does it appear that multicollinearity is a problem? Explain.
b)Compute the variance inflation factor for each independent variable. Show your calculations for the VIF’s below. Based on these VIF’s, does multicollinearity appear to be a problem? Explain
c) Copy and paste( screenshot) the Excel regression output table that gives values for the estimated regression coefficients below. Write out the least squares regression equation_________.
d) What is the estimated mean yearly salary for a teacher with 5 years' experience, a rating by the principal of 60, and no master's degree?(show your work)
Yearly Salary ($1,000's) Years Rating *Masters *Yes = 1, No = 0 31.1 8 35 0 33.6 5 43 0 29.3 2 51 1 43.0 15 60 1 38.6 11 73 0 45.0 14 80 1 42.0 9 76 0 36.8 7 54 1 48.6 22 55 1 31.7 3 90 1 25.7 1 30 0 30.6 5 44 0 51.8 23 84 1 46.7 17 76 0 38.4 12 68 1 33.6 14 25 0 41.8 8 90 1 30.7 4 62 0 32.8 2 80 1 42.8 8 72 0Explanation / Answer
Result:
a) Check for multicollinearity by analyzing the correlation matrix. Copy/paste (screenshot) the correlation matrix from Excel below. Does it appear that multicollinearity is a problem? Explain.
Correlation Matrix
Yearly Salary ($1,000's)
Years
Rating
Masters
Yearly Salary ($1,000's)
1.000
Years
.868
1.000
Rating
.547
.187
1.000
Masters
.311
.208
.458
1.000
20
sample size
Since all the correlations between independent variables are small, it appears that there is no multicollinearity.
b)Compute the variance inflation factor for each independent variable. Show your calculations for the VIF’s below. Based on these VIF’s, does multicollinearity appear to be a problem? Explain
Years and all other X
Regression Statistics
Multiple R
0.2318
R Square
0.0537
Adjusted R Square
-0.0576
Standard Error
6.6103
Observations
20
VIF
1.0568
Rating and all other X
Regression Statistics
Multiple R
0.4673
R Square
0.2184
Adjusted R Square
0.1264
Standard Error
18.4341
Observations
20
VIF
1.2794
Masters and all other X
Regression Statistics
Multiple R
0.4743
R Square
0.2250
Adjusted R Square
0.1338
Standard Error
0.4774
Observations
20
VIF
1.2903
Since all the VIF’s are < 10 , there is no problem of multicollinearity
c) Copy and paste( screenshot) the Excel regression output table that gives values for the estimated regression coefficients below. Write out the least squares regression equation_________.
Yearly Salary ($1,000's) = 19.9152+0.8994* Years +0.1539* Rating -0.6673* Masters
d) What is the estimated mean yearly salary for a teacher with 5 years' experience, a rating by the principal of 60, and no master's degree?(show your work)
estimated Yearly Salary ($1,000's) = 19.9152+0.8994* 5 +0.1539* 60 -0.6673* 0
=33.6462
Regression Analysis
R²
0.908
Adjusted R²
0.891
n
20
R
0.953
k
3
Std. Error
2.390
Dep. Var.
Yearly Salary ($1,000's)
ANOVA table
Source
SS
df
MS
F
p-value
Regression
903.1938
3
301.0646
52.72
1.62E-08
Residual
91.3682
16
5.7105
Total
994.5620
19
Regression output
confidence interval
variables
coefficients
std. error
t (df=16)
p-value
95% lower
95% upper
VIF
Intercept
19.9152
1.9163
10.393
1.60E-08
15.8529
23.9775
Years
0.8994
0.0877
10.258
1.93E-08
0.7135
1.0853
1.057
Rating
0.1539
0.0314
4.895
.0002
0.0873
0.2206
1.279
Masters
-0.6673
1.2139
-0.550
.5901
-3.2407
1.9061
1.290
1.209
Predicted values for: Yearly Salary ($1,000's)
95% Confidence Interval
95% Prediction Interval
Years
Rating
Masters
Predicted
lower
upper
lower
upper
5
60
0
33.6470
31.8706
35.4235
28.2787
39.0153
Correlation Matrix
Yearly Salary ($1,000's)
Years
Rating
Masters
Yearly Salary ($1,000's)
1.000
Years
.868
1.000
Rating
.547
.187
1.000
Masters
.311
.208
.458
1.000
20
sample size