1. Guide to Using Minitab For Basic Statistical Applications To Accompany Business Statistics: A Decision Making Approach, 6th Ed. Chapter 14: Multiple Regression Analysis and Model Building By Groebner, Shannon, Fry, & Smith Prentice-Hall Publishing Company Copyright, 2005

2. Chapter 14 Minitab Examples  Multiple Regression Multiple Regression First City Real Estate  Multiple Regression – Variance Inflation Factor Multiple Regression – Variance Inflation Factor First City Real Estate  Multiple Regression – Dummy Variable Multiple Regression – Dummy Variable First City Real Estate  Curvilinear Regression Prediction Curvilinear Regression Prediction Ashley Investment Services  Interaction Effects Interaction Effects Ashley Investment Services More Examples

3. Chapter 14 Minitab Examples  Standard Stepwise Regression Standard Stepwise Regression Motor Fan Magazine  Best Subsets Regression Best Subsets Regression Fortune 50 Companies  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 O.K. Multiple Regression – First City Real Estate

8. The Minitab output shows the correlation and p-value 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 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 identify any multicollinearity that exists in the predictor variables. First City managers wish to identify any multicollinearity that exists in the predictor variables.Objective: Use Minitab to calculate the variance inflation factors (VIF). Data file is First City.mtw Multiple Regression – Variance Inflation Factor First City Real Estate Multiple Regression – Variance Inflation Factor First City Real Estate

14. Open file First City.mtw. Multiple Regression – VIF - First City

15. Click on Stat then Regression and then Regression. Multiple Regression – VIF - First City

16. Define the columns containing the Response and Predictor Variables then select Options to use the VIF. Multiple Regression – VIF - First City

17. Click to determine the Variance Inflation Factors Multiple Regression – VIF - First City

18. The output shows the variance inflation factors. All VIFs are below 5. Multicollinearity is not evident. Multiple Regression – VIF - First City

19. Issue: First City managers wish to improve the model by adding a location variable. 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

20. Open file First City.mtw. Move to column on the worksheet containing the Area data. Multiple Regression – Dummy Variable - First City

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

22. Define the columns containing the Response and Predictor Variables then select Options to use the VIF. Multiple Regression – Dummy Variable - First City

23. Click to determine the Variance Inflation Factors Multiple Regression – Dummy Variable - First City

24. The output shows an improved regression model. Multiple Regression – Dummy Variable - First City

25. 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

26. Open File Ashley.mtw File contains values for 20 Investment Advisors. Curvilinear Relationships – Ashley Investment Services

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

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

29. The scatter plot shows a relationship that could be either linear or nonlinear. Curvilinear Relationships – Ashley Investment Services

30. To find the linear model, return to the data sheet, click on Stat, then Regression and finally Regression again. Curvilinear Relationships – Ashley Investment Services

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

32. The output shows the R Square value and the Regression Coefficients. Curvilinear Relationships – Ashley Investment Services

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

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

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

36. 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

37. Interaction Effects - Ashley Investment Services Interaction Effects - Ashley Investment Services Issue: The director of personnel is trying to determine whether the model can be improved by separating observations between those taken from men and women. Objective: Use Minitab to determine whether the relationship between the measures can be improved. Data file is Ashley-2.mtw

38. Open File Ashley-2.mtw Interaction Effects – Ashley Investment Services

39. Click on the Graph button then select Plot Interaction Effects – Ashley Investment Services

40. Identify the columns containing the X and Y variables, and the column identifying the gender groups. Interaction Effects – Ashley Investment Services

41. The data plot shows a different pattern for males and females. Interaction Effects – Ashley Investment Services

42. To further analyze the data we will sort it by gender. Click on the Manip and then Sort. Interaction Effects – Ashley Investment Services

43. Identify the columns to be sorted and the values to control the sort. Interaction Effects – Ashley Investment Services

44. The data are now sorted into groups. Interaction Effects – Ashley Investment Services

45. The Burnout and Socialization values for males and females are pasted into separate columns. Interaction Effects – Ashley Investment Services

46. A Fitted Line Plot will be constructed for both Males and Females. Click on Stat, then Regression and then Fitted Line Plot. Interaction Effects – Ashley Investment Services

47. The columns containing the X and Y values for females are identified. The same will be done for males. Interaction Effects – Ashley Investment Services

48. This is the quadratic regression model for females. Interaction Effects – Ashley Investment Services

49. This is the quadratic model for males. Interaction Effects – Ashley Investment Services

50. Issue: The magazine staff is performing a descriptive analysis to determine which vehicle characteristics explain the variation in highway mileage. Objective: Use Minitab to perform a standard stepwise regression analysis using highway mileage as the dependent variable. Data file is Automobiles.mtw Use Minitab to perform a standard stepwise regression analysis using highway mileage as the dependent variable. Data file is Automobiles.mtw Standard Stepwise - Motor Fan Magazine Standard Stepwise - Motor Fan Magazine

51. Open file Automobiles.mtw Standard Stepwise – Motor Fan Magazine

52. First click on Stat, then Regression and then on Stepwise. Standard Stepwise – Motor Fan Magazine

53. Identify columns containing the x and y Variables and Minitab will default on a F to enter and remove of 4.0. You can change if desired. Standard Stepwise – Motor Fan Magazine

54. This is the final step in the output. Two variables have entered the model. The last column shows the regression coefficients, their t values and R- Square. Standard Stepwise – Motor Fan Magazine

55. Issue: We want to understand the variables that lead to profits for large companies. We want to understand the variables that lead to profits for large companies.Objective: Use Minitab develop a best subsets regression model to explain the variation in total profit. Data file is Fortune 50.mtw Use Minitab develop a best subsets regression model to explain the variation in total profit. Data file is Fortune 50.mtw Best Subsets Regression - Fortune 50 Companies

56. Open file Fortune 50.mtw Best Subsets Regression – Fortune 50 Companies

57. First click on Stat, then Regression and then on Best Subsets. Best Subsets Regression – Fortune 50 Companies

58. Identify the columns containing the X and Y Variables. Best Subsets Regression – Fortune 50 Companies

59. The best model is the one with C- p closest to variables + 1. Best Subsets Regression – Fortune 50 Companies

60. Return to the Regression options. Best Subsets Regression – Fortune 50 Companies

61. The Best Subsets model is is formed using these variables identified by the C-p value. Best Subsets Regression – Fortune 50 Companies

62. This is the output for the Best Subsets model. Best Subsets Regression – Fortune 50 Companies

63. 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 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

64. Open file First City-3.mtw Residual Analysis – First City Real Estate

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

66. Identify the x and y variables. Minitab residual options are found using either Graphs or Results. Residual Analysis – First City Real Estate

67. These are the options using the Graphs button. Residual Analysis – First City Real Estate

68. These are the options available using Results. Residual Analysis – First City Real Estate

69. This plot shows the residuals become more disperse with later observations. This might be worth investigation. Residual Analysis – First City Real Estate

70. The residuals seem to be approximately normally distributed. Residual Analysis – First City Real Estate

71. This is the output if the Normal Probability Plot option is selected. Residual Analysis – First City Real Estate

72. Minitab will provide both Residual and Standardized Residual values. Residual Analysis – First City Real Estate