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

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

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

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

Open File First City.mtw Multiple Regression – First City Real Estate

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

Identify columns for Variables. Click on O.K. Multiple Regression – First City Real Estate

The Minitab output shows the correlation and p-value between Age and Square Feet. 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. Multiple Regression – First City Real Estate

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

Define the columns containing the Response and Predictor Variables Multiple Regression – First City Real Estate

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Open file Automobiles.mtw Standard Stepwise – Motor Fan Magazine

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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