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