# Residual analysis for regression

To answer the following question, please use statistical software like SPSS. Data can be found in the attached excel sheet.

3. 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 data found in the excel file under the tab Question 3. Please note that a master's degree value of 1 = yes, 0 = no.

a. Develop a correlation matrix. Which independent variable has the strongest correlation with the dependent variable?

b. Determine the regression equation. What salary would you estimate for a teacher with five years experience, a rating by the principle of 60, and no master's degree?

c. Conduct a test of hypothesis for the individual regression coefficients. Would you consider deleting any of the independent variables? Use the 0.05 significance level.

d. If your conclusion in Part C was to delete one or more independent variables, run the analysis again without those variables.

e. Determine the residuals for the equation in Part D. Use a stem-and-leaf chart or a histogram to verify that the distribution of the residuals is approximately normal.

f. Plot the residuals computed in Part E in a scatter diagram with the residuals on the Y-axis and the ? values on the X-axis. Does the plot reveal any violations of the assumptions of regression?

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#### Solution Summary

Step by step method for regression analysis is discussed here. Regression coefficients, coefficient of determination, scatter diagram and significance of regression model are explained in the solution. Residual analysis is also carried out to check the model assumptions.