1. Guide to Using Minitab 14 For Basic Statistical Applications
To Accompany
Business Statistics: A Decision Making Approach, 6th Ed.
Chapter 15:
Multiple Regression and Model Building By
Groebner, Shannon, Fry, & Smith
Prentice-Hall Publishing Company
Copyright, 2008

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

3. Chapter 15 Minitab Examples (cont’d)
Second Order Model
Ashley Investment Services
Standard Stepwise Regression
Lomgmont Corporation
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. Multiple Regression – First City Real Estate
Open File First City.MTW

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

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

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

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

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

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

12. Multiple Regression – First City Real Estate
The regression coefficients, R2, S, and sum of squares are all generated by the regression command.

13. Multiple Regression – Variance Inflation Factor First City Real Estate
Issue: 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

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

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

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

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

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

19. Multiple Regression – Dummy Variable First City Real Estate
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

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

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

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

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

24. 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

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

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

27. Curvilinear Relationships – Ashley Investment Services
Select Simple

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

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

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

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

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

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

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

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

36. Second Order Model - 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

37. Second Order Model – Ashley Investment Services
Open File Ashley-2.MTW

38. Second Order Model – Ashley Investment Services
To simplify the next few steps, modify the names of Columns C2 and C3, adding X1 and X2

39. Second Order Model – 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

40. Second Order Model – Ashley Investment Services
Click on Stat then Regression and then Regression.

41. Second Order Model – Ashley Investment Services
Identify the columns containing the X and Y variables. Then click OK.

42. Second Order Model – Ashley Investment Services
Regression Coefficients

43. Standard Stepwise - Longmont Corporation
Issue: The Longmont Corporation wishes to develop a regression model to help explain the monthly dollar loss due to shoplifting
Objective: Use Minitab to perform a standard stepwise regression analysis using Shoplifting losses as the dependent variable.
Data file is Longmont.MTW

44. Standard Stepwise – Longmont
Open file Longmont.MTW

45. Standard Stepwise – Longmont
To develop the correlation matrix use Stat – Basic Statistics - Correlation

46. Standard Stepwise – Longmont
Specify the variables to be included in the correlation matrix

47. Standard Stepwise – Longmont
Correlation Results

48. Standard Stepwise – Longmont
To develop a stepwise model, first click on Stat, then Regression and then on Stepwise.

49. Standard Stepwise – Longmont
Identify columns containing the y variable and the x variables – then select Methods

50. Standard Stepwise – Longmont
Select Forward selection – specify Alpha to enter (0.05 in this case) and F to enter

51. Standard Stepwise – Longmont
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.

52. Residual Analysis - First City Real Estate
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

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

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

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

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

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

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

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

60. Residual Analysis – First City Real Estate