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

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

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

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 OK Multiple Regression – First City Real Estate

The Minitab output shows the correlation (r = ) 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 (Price) 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 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. Multiple Regression – Dummy Variable - First City

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

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

The output shows an improved regression model with the variable, Area, included. 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 Scatterplot Curvilinear Relationships – Ashley Investment Services

Select Simple Curvilinear Relationships – Ashley Investment Services

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

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

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

Identify the columns containing the X and Y variables. Then click OK. 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 are 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

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

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

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

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

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

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

Regression Coefficients

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

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. Residual Analysis – First City Real Estate

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

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

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

Select Histogram of residuals Residual Analysis – First City Real Estate