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

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

Chapter 15 Minitab Examples (cont’d) Second Order Model Ashley Investment Services Standard Stepwise Regression Lomgmont Corporation 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

Multiple Regression – First City Real Estate 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 = -0.073) 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, R2, S, and sum of squares are all generated by the regression command.

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

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

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

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 – 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

Multiple Regression – Dummy Variable - First City 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.

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

Curvilinear Relationships – Ashley Investment Services 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.

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

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

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

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

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

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

Second Order Model – Ashley Investment Services Regression Coefficients

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

Standard Stepwise – Longmont Open file Longmont.MTW

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

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

Standard Stepwise – Longmont Correlation Results

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

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

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

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.

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

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