1. Guide to Using Minitab 14 For Basic Statistical Applications To Accompany Business Statistics: A Decision Making Approach, 8th Ed. Chapter 15: Multiple Regression and Model Building By Groebner, Shannon, Fry, & Smith Prentice-Hall Publishing Company Copyright, 2011

2. Chapter 15 Minitab Examples Multiple Regression Multiple Regression Multiple Regression Multiple Regression First City Real Estate Multiple Regression – Variance Inflation Factor Multiple Regression – Variance Inflation Factor Multiple Regression – Variance Inflation Factor Multiple Regression – Variance Inflation Factor First City Real Estate Multiple Regression – Dummy Variable Multiple Regression – Dummy Variable Multiple Regression – Dummy Variable Multiple Regression – Dummy Variable First City Real Estate Curvilinear Regression Prediction Curvilinear Regression Prediction Curvilinear Regression Prediction Curvilinear Regression Prediction Ashley Investment Services More Examples

3. Chapter 15 Minitab Examples (cont’d) Second Order Model Second Order Model Second Order Model Second Order Model Ashley Investment Services Standard Stepwise Regression Standard Stepwise Regression Standard Stepwise Regression Standard Stepwise Regression Lomgmont Corporation Residual Analysis Residual Analysis Residual Analysis Residual Analysis First City Real Estate

4. Multiple Regression First City Real Estate Issue: First City management wishes to build a model that can be used to predict sales prices for residential property. Objective: Use Minitab to build a multiple regression model relating sales price to a set of measurable variables. Data file is First City.MTW

5. Open File First City.MTW Multiple Regression – First City Real Estate

6. First click on Stat, then Basic Statistics and finally on Correlation. Multiple Regression – First City Real Estate

7. Identify columns for Variables. Click on OK Multiple Regression – First City Real Estate

8. The Minitab output shows the correlation (r = -0.073) between Age and Square Feet. Multiple Regression – First City Real Estate

9. The correlation between each predictor and Price is highly significant. Thus, each predictor will be inserted into the regression model. Multiple Regression – First City Real Estate

10. Click on Stat, then Regression and then Regression again. Multiple Regression – First City Real Estate

11. Define the columns containing the Response (Price) and Predictor Variables Multiple Regression – First City Real Estate

12. The regression coefficients, R 2, S, and sum of squares are all generated by the regression command. Multiple Regression – First City Real Estate

13. Issue: First City managers wish to improve the model by adding a location variable. Objective: Use Minitab to improve a regression model by adding a dummy variable. Data file is First City.MTW Multiple Regression – Dummy Variable First City Real Estate Multiple Regression – Dummy Variable First City Real Estate

14. Open file First City.MTW. Multiple Regression – Dummy Variable - First City

15. Click on Stat then Regression and then Regression again. Multiple Regression – Dummy Variable - First City

16. Select the columns containing the Response and Predictor Variables. Multiple Regression – Dummy Variable - First City

17. The output shows an improved regression model with the variable, Area, included. Multiple Regression – Dummy Variable - First City

18. Curvilinear Relationships - Ashley Investment Services Issue: The director of personnel is trying to determine whether there is a relationship between employee burnout and time spent socializing with co-workers. Objective: Use Minitab to determine whether the relationship between the two measures is statistically significant. Data file is Ashley.MTW

19. Open File Ashley.MTW File contains values for 20 Investment Advisors. Curvilinear Relationships – Ashley Investment Services

20. To develop the scatter plot first click on Graph button then select Scatterplot Curvilinear Relationships – Ashley Investment Services

21. Select Simple Curvilinear Relationships – Ashley Investment Services

22. Identify the columns containing the variables to be graphed. Curvilinear Relationships – Ashley Investment Services

23. Relationship may be curvilinear – next, fit linear to see model results Curvilinear Relationships – Ashley Investment Services

24. Click on Stat then Regression and then Regression. Curvilinear Relationships – Ashley Investment Services

25. Identify the columns containing the X and Y variables. Then click OK. Curvilinear Relationships – Ashley Investment Services

26. To find a nonlinear model, click on Stat then Regression and select Fitted Line Plot. Curvilinear Relationships – Ashley Investment Services

27. Minitab gives the choice of three models, select Quadratic. Curvilinear Relationships – Ashley Investment Services

28. This gives the Quadratic Regression Line. The Regression Equation and R- Square value are given. Curvilinear Relationships – Ashley Investment Services

29. This gives Regression Equation and R- square value. The R-Square value is larger than that for the linear model. Curvilinear Relationships – Ashley Investment Services

30. Interactive Effects - Ashley Investment Services Issue: The director of personnel is trying to determine whether there are interactive effects in the relationship between employee burnout and time spent socializing with co-workers. Objective: Use Minitab to determine whether interactive effects between the two measures are statistically significant. Data file is Ashley-2.MTW

31. Interactive Effects – Ashley Investment Services Open File Ashley- 2.MTW

32. Interactive Effects – Ashley Investment Services To simplify the next few steps, modify the names of Columns C2 and C3, adding X1 and X2

33. Interactive Effects – Ashley Investment Services Using the Calculator tab, set up columns C4, C5 and C6 as: Column C4 – Expression C2 * C2 Column C5 – Expression C2 * C1 Column C6 – Expression C4 * C3 Identify the column headings

34. Interactive Effects – Ashley Investment Services Click on Stat then Regression and then Regression.

35. Identify the columns containing the X and Y variables. Then click OK. Interactive Effects – Ashley Investment Services

36. Regression Coefficients

37. Issue: The company is interested in analyzing the residuals of the regression model to determine whether the assumptions are satisfied. Objective: Use Minitab to analyze residuals from a regression model. Data file is First City-3.MTW Residual Analysis - First City Real Estate Residual Analysis - First City Real Estate

38. Open file First City-3.MTW Residual Analysis – First City Real Estate

39. Click on Stat, then Regression and then Regression again. Residual Analysis – First City Real Estate

40. Identify the x and y variables. Residual Analysis – First City Real Estate

41. R-square = 96.9% Residual Analysis – First City Real Estate

42. These are the options using the Graphs button – Select Residuals versus fits. Residual Analysis – First City Real Estate

43. Residual Plot versus fitted y values. Residual Analysis – First City Real Estate

44. Select Histogram of residuals Residual Analysis – First City Real Estate