Mike is president of the teachers\' union for Lakeview School District. In prepa
ID: 353702 • 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 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 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)
e) Conduct a global test to determine whether any of the population regression coefficients are not equal to zero at the 0.01 level of significance. You are not required to compute the observed value of F, but use the value given by Excel. Is the overall model a good one? Does the p-value given in the Excel output support your conclusion? Explain.
f) Should you delete any of the independent variables at the 0.01 significance level? To make your decision, do not conduct a hypothesis test, but instead explain with reference to the p-values in the Excel output.
g) 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 below. (Write out the new least squares regression equation).
h) Does it appear that there exists a linear relationship between each remaining independent variable and salary? Generate scatter plots using Excel to answer this. Copy and paste the scatter plots into the space below.
i)Plot the residuals against the predicted values of salary in a scatter diagram. To do this, you need to check off “Residuals” in Data Analysis, Regression. This will give you the predicted values of Y along with the residuals in two columns. Then use the “Insert Scatter Chart” tool in Excel to generate a scatter plot of the residuals against the predicted Y’s. Copy and paste your scatter plot below. Does it appear that any of the multiple regression assumptions concerning linearity, equal error variance or independent error terms are violated? Explain.
j)Use Excel to generate a histogram of the residuals and a normal probability plot. To create a histogram, use Data Analysis, Histogram. The “Input Range” is the column of residuals from part (i). To create the normal probability plot, check off “Normal Probability Plots” in Data Analysis, Regression. Based on the histogram of residuals and the normal probability plot, do the residuals appear to be normally distributed?Explain. Copy and paste both the histogram and normal probability plot below.
k)Suppose we started out with the regression equation in part (g) i.e. the equation without the insignificant variable(s). Then we added the insignificant variable(s) to this regression to get the equation in part (c). Compare the R Square and R Square Adjusted values for both regressions. Does R Square increase or decrease after adding the insignificant independent variable(s)? Does Adjusted R Square increase or decrease after adding the insignificant independent variable(s)? Explain why we would expect these to happen. Show the values of R Square and R Square Adjusted before and after adding the insignificant independent variables in the space below, along with your explanations.
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
1
early Salary ($1,000's) Years Rating *Masters *Yes = 1, No = 0 31.1 8 35 01
33.6 5 43 0 0 29.3 2 51 1 0 43.0 15 60 1 1 38.6 11 73 0 1 45.0 14 80 1 0 42.0 9 76 0 0 36.8 7 54 1 0 48.6 22 55 1 1 31.7 3 90 1 1 25.7 1 30 0 0 30.6 5 44 0 1 51.8 23 84 1 1 46.7 17 76 0 0 38.4 12 68 1 0 33.6 14 25 0 0 41.8 8 90 1 1 30.7 4 62 0 1 32.8 2 80 1 0 42.8 8 72