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# 16 Mike Wilde is president of the teachers' union for Otsego School District.

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14.16  Mike Wilde is president of the teachers' union for Otsego School District. In preparing for upcoming negotiations, he would like to investigate the salary structure of classroom teachers in the district. He believes there are three factors that affect a teacher's salary: years of experience, a rating of teaching effectiveness given by the principal, and whether the teacher has a master's degree. A random sample of 20 teachers resulted in the following data.
(see chart in attached file)
a. Develop a correlation matrix. Which independent variable has the strongest correlation with the dependent variable? Does it appear there will be any problems with multicollinearity?
b. Determine the regression equation. What salary would you estimate for a teacher with five years' experience, a rating by the principal of 60, and no master's degree?
c. Conduct a global test of hypothesis to determine whether any of the net regression coefficients differ from zero. Use the .05 significance level.
d. Conduct a test of hypothesis for the individual regression coefficients. Would you consider deleting any of the independent variables? Use the .05 significance level.
e. If your conclusion in part (d) was to delete one or more independent variables, run the analysis again without those variables.
f. Determine the residuals for the equation of part (e). Use a stem-and-leaf chart or a histogram to verify that the distribution of the residuals is approximately normal.
g. Plot the residuals computed in part (f) in a scatter diagram with the residuals on the Y-axis and the Y' values on the X-axis. Does the plot reveal any violations of the assumptions of regression?

14.16 Mike Wilde is president of the teachers' union for Otsego School
District. In preparing for upcoming negotiations, he would like to
investigate the salary structure of classroom teachers in the district.
He believes there are three factors that affect a teacher's salary:
years of experience, a rating of teaching effectiveness given by the
principal, and whether the teacher has a master's degree. A random
sample of 20 teachers resulted in the following data.
Salary (\$ thousands), Y
Years of Experience, X1
Principal's Rating, X2
Master's Degree,*X3
21.1 8 35 0
23.6 5 43 0
19.3 2 51 1
33.0 15 60 1
28.6 11 73 0
35.0 14 80 1
32.0 9 76 0
26.8 7 54 1
38.6 22 55 1
21.7 3 90 1
15.7 1 30 0
20.6 5 44 0
41.8 23 84 1
36.7 17 76 0
28.4 12 68 1
23.6 14 25 0
31.8 8 90 0
20.7 4 62 0
22.8 2 80 1
32.8 8 72 0
a. Develop a correlation matrix. Which independent variable has the
strongest correlation with the dependent variable? Does it appear there
will be any problems with multicollinearity?
b. Determine the regression equation. What salary would you estimate for
a teacher with five years' experience, a rating by the principal of 60,
and no master's degree?
c. Conduct a global test of hypothesis to determine whether any of the
net regression coefficients differ from zero. Use the .05 significance
level.
d. Conduct a test of hypothesis for the individual regression
coefficients. Would you consider deleting any of the independent
variables? Use the .05 significance level.
e. If your conclusion in part (d) was to delete one or more independent
variables, run the analysis again without those variables.
f. Determine the residuals for the equation of part (e). Use a
stem-and-leaf chart or a histogram to verify that the distribution of
the residuals is approximately normal.
g. Plot the residuals computed in part (f) in a scatter diagram with the
residuals on the Y-axis and the Y' values on the X-axis. Does the plot
reveal any violations of the assumptions of regression?

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