Guide to Using Minitab 14 For Basic Statistical Applications

Guide to Using Minitab 14 For Basic Statistical Applications

To AccompanyTo AccompanyBusiness Statistics: A Decision Making

Approach, 6th Ed.Chapter 15:Chapter 15:

Multiple Regression and Model BuildingMultiple Regression and Model BuildingByBy

Groebner, Shannon, Fry, & SmithGroebner, Shannon, Fry, & SmithPrenticePrentice--Hall Publishing CompanyHall Publishing Company

Copyright, 2008Copyright, 2008

Chapter 15 Minitab Chapter 15 Minitab ExamplesExamples

Multiple Regression Multiple Regression First City Real EstateFirst City Real Estate

Multiple Regression Multiple Regression –– Variance Inflation Factor Variance Inflation Factor First City Real EstateFirst City Real Estate

Multiple Regression Multiple Regression –– Dummy Variable Dummy Variable First City Real EstateFirst City Real Estate

Curvilinear Regression Prediction Curvilinear Regression Prediction Ashley Investment ServicesAshley Investment Services

More Examples

Chapter 15 Minitab Chapter 15 Minitab Examples (contExamples (cont’’d)d)

Second Order Model Second Order Model Ashley Investment ServicesAshley Investment Services

Standard Stepwise Regression Standard Stepwise Regression LomgmontLomgmont CorporationCorporation

Residual Analysis Residual Analysis First City Real EstateFirst City Real Estate

Multiple RegressionMultiple Regression First City Real EstateFirst City Real Estate

Issue: Issue: First City management wishes to build a First City management wishes to build a model that can be used to predict sales prices model that can be used to predict sales prices for residential property. for residential property.

Objective: Use Minitab to build a multiple Objective: Use Minitab to build a multiple regression model relating sales price to a set of regression model relating sales price to a set of measurable variables. measurable variables.

Data file is Data file is First First City.MTWCity.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 = -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 – First City Real Estate

Issue: Issue: First City managers wish to identify any First City managers wish to identify any multicollinearity that exists in the predictor multicollinearity that exists in the predictor variables. variables.

Objective: Use Minitab to calculate the variance Objective: Use Minitab to calculate the variance inflation factors (VIF). inflation factors (VIF).

Data file is Data file is First First City.MTWCity.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 – 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 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: Issue: First City managers wish to improve the First City managers wish to improve the model by adding a location variable. model by adding a location variable.

Objective: Use Minitab to improve a regression Objective: Use Minitab to improve a regression model by adding a dummy variable. model by adding a dummy variable.

Data file is Data file is First First City.MTWCity.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 Curvilinear Relationships - Ashley Investment Services

Issue: Issue: The director of personnel is trying to determine The director of personnel is trying to determine whether there is a relationship between employee whether there is a relationship between employee burnout and time spent socializing with coburnout and time spent socializing with co--workers. workers.

Objective: Use Minitab to determine whether the Objective: Use Minitab to determine whether the relationship between the two measures is statistically relationship between the two measures is statistically significant. significant.

Data file is Data file is AshleyAshley.MTW.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

Second Order Model - Ashley Investment Services Second Order Model - Ashley Investment Services

Issue: Issue: The director of personnel is trying to determine The director of personnel is trying to determine whether there are interactive effects in the relationship whether there are interactive effects in the relationship between employee burnout and time spent socializing between employee burnout and time spent socializing with cowith co--workers. workers.

Objective: Use Minitab to determine whether interactive Objective: Use Minitab to determine whether interactive effects between the two measures are statistically effects between the two measures are statistically significant. significant.

Data file is Data file is AshleyAshley--22.MTW.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.

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

Second Order Model – Ashley Investment Services

Second Order Model – Ashley Investment Services

Regression Coefficients

Issue: Issue: The Longmont Corporation wishes to develop a The Longmont Corporation wishes to develop a regression model to help explain the monthly dollar regression model to help explain the monthly dollar loss due to shoplifting loss due to shoplifting

Objective: Use Minitab to Objective: Use Minitab to perform a standard stepwise perform a standard stepwise regression analysis using Shoplifting losses as the regression analysis using Shoplifting losses as the dependent variable. dependent variable.

Data file is Data file is LongmontLongmont.MTW.MTW

Standard Stepwise -Longmont Corporation

Standard Stepwise -Longmont Corporation

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

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.

Issue: Issue: The company is interested in analyzing the The company is interested in analyzing the residuals of the regression model to determine whether residuals of the regression model to determine whether the assumptions are satisfied. the assumptions are satisfied.

Objective: Use Minitab to analyze residuals from a Objective: Use Minitab to analyze residuals from a regression model.regression model.

Data file is Data file is First CityFirst City--33.MTW.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

Residual Analysis – First City Real Estate