Mike Wilde is president of the teachers’ union for Otsego School District. In pr
ID: 3175181 • Letter: M
Question
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:
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) $__________________
Conduct a global test to determine if any of the regression coefficients are not equal to zero at the 0.01 level of significance (show all steps of the hypothesis test, along with your concluding statement).
Interpret the values generated by Excel for R Square and Standard Error. Is the overall estimated regression model a good one? Explain with reference to the values for R Square and Standard Error.
Should you delete any of the independent variables at the 0.01 significance level? Explain your answer by considering only the p-values generated by Excel.
If your decision is to delete one or more independent variables, run the regression analysis again without those variables. Copy and paste your Excel output into the space below. Write out the estimated regression equation when all remaining independent variables are significant.
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Compare the values for both R Square and Adjusted R Square before and after deleting the insignificant independent variable(s). Why did they increase or decrease? (think about what we would expect to happen to these variables if we had started out with a regression that did not include the insignificant independent variable(s) and then added it to our regression)
Salary ($K) Yrs. Experience Princ. Rating Masters Degree 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
Following is the output of regression analysis :
The estimated regression equation is
salary = 19.915 + 0.899 Yrs-exp + 0.154 Princ.rating - 0.667 MasterDegeree
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) $__________________
salary = 19.915 + 0.899*5 + 0.154*60 - 0.667 *0 = 33.65
So requried salary is $33.65 ($K).
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Conduct a global test to determine if any of the regression coefficients are not equal to zero at the 0.01 level of significance (show all steps of the hypothesis test, along with your concluding statement).
F test statistics: 52.72
P-value of the test: 0.0000
Since p-value is less than 0.01 so model is siginificant. That is coefficient is different from zero.
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R-sqaure: 0.9081
It shows that 90.81% of variation is dependent variable is exaplined by regression model.
Standrad error:
Standard error: 2.39
It represents the distance between the data values and regression line. It should be small.
Yes it seems it is a good model.
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The p-value of MasterDegree is 0.5901.
Since it is greater than 0.01 so it is not significant to the model. That is we can delete it.
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Following is the new regression analysis output:
The new regression equation is
salary = 20.116 + 0.893 Yrs.Experience + 0.1464 Princ.Rating
SUMMARY OUTPUT Regression Statistics Multiple R 0.952959718 R Square 0.908132225 Adjusted R Square 0.890907017 Standard Error 2.389667843 Observations 20 ANOVA df SS MS F Significance F Regression 3 903.1938016 301.0646005 52.72111845 1.62312E-08 Residual 16 91.36819837 5.710512398 Total 19 994.562 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 19.91519148 1.916260316 10.39273804 1.60294E-08 15.85290111 23.97748185 Yrs.Experience 0.899379367 0.087678764 10.25766477 1.92579E-08 0.713508692 1.085250042 Princ.Rating 0.153916002 0.031440644 4.895446882 0.000161689 0.087264815 0.220567189 MastersDegree -0.66730799 1.213932825 -0.54970751 0.590111376 -3.240730601 1.906114621