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Copyright 2007 by Oxford University Press, Inc.PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 1 1
Copyright 2007 by Oxford University Press, Inc.PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 2
Multiple Regression Analysis
Model: 1 1 2 2 ' 'k kY a b X b X b X
Copyright 2007 by Oxford University Press, Inc.PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 3
Copyright 2007 by Oxford University Press, Inc.PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 4
Copyright 2007 by Oxford University Press, Inc.PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 5
Multiple Regression Analysis
Adjusted Coefficient of Determination
2 2 ( 1)1 (1 )
( )
nR R
n k
Copyright 2007 by Oxford University Press, Inc.PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 6
Multiple Regression Analysis
Analysis of Variance and F Statistic
/( 1)
/( )
ExplainedVariation kF
UnexplainedVariation n k
2
2
/( 1)
(1 ) /( )
R kF
R n k
Copyright 2007 by Oxford University Press, Inc.PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 7
Problems in Regression Analysis
• Multicollinearity: Two or more explanatory variables are highly correlated.
• Heteroskedasticity: Variance of error term is not independent of the Y variable.
• Autocorrelation: Consecutive error terms are correlated.
Copyright 2007 by Oxford University Press, Inc.PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 8
Copyright 2007 by Oxford University Press, Inc.PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 9
Durbin-Watson Statistic
Test for Autocorrelation
21
2
2
1
( )n
t tt
n
tt
e ed
e
If d = 2, autocorrelation is absent.
Copyright 2007 by Oxford University Press, Inc.PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 10
Steps in Demand Estimation
• Model Specification: Identify Variables
• Collect Data
• Specify Functional Form
• Estimate Function
• Test the Results
Copyright 2007 by Oxford University Press, Inc.PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 11
Functional Form Specifications
Linear Function:
Power Function:
0 1 2 3 4X X YQ a a P a I a N a P e
1 2( )( )b bX X YQ a P P
Estimation Format:
1 2ln ln ln lnX X YQ a b P b P
Copyright 2007 by Oxford University Press, Inc.PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 12
Copyright 2007 by Oxford University Press, Inc.PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 13
Copyright 2007 by Oxford University Press, Inc.PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 14
Copyright 2007 by Oxford University Press, Inc.PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 15
Chapter 4 Appendix
Copyright 2007 by Oxford University Press, Inc.PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 16
Copyright 2007 by Oxford University Press, Inc.PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 17
Copyright 2007 by Oxford University Press, Inc.PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 18
Copyright 2007 by Oxford University Press, Inc.PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 19
Getting Started
• Install the Analysis ToolPak add-in from the Excel installation media if it has not already been installed
• Attach the Analysis ToolPak add-in– From the menu, select Tools and then
Add-Ins...– When the Add-Ins dialog appears, select
Analysis ToolPak and then click OK.
Copyright 2007 by Oxford University Press, Inc.PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 20
Copyright 2007 by Oxford University Press, Inc.PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 21
Entering Data
• Data on each variable must be entered in a separate column
• Label the top of each column with a symbol or brief description to identify the variable
• Multiple regression analysis requires that all data on independent variables be in adjacent columns
Copyright 2007 by Oxford University Press, Inc.PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 22
Example Data
Copyright 2007 by Oxford University Press, Inc.PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 23
Running the Regression
• Select the Regression tool from the Analysis ToolPak dialog– From the menu, select Tools and then
Data Analysis...– On the Data Analysis dialog, scroll down
the list of Analysis Tools, select Regression, and then click OK
– The Regression tool dialog will then be displayed
Copyright 2007 by Oxford University Press, Inc.PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 24
Copyright 2007 by Oxford University Press, Inc.PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 25
Copyright 2007 by Oxford University Press, Inc.PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 26
Select the Data Ranges
• Type in the data range for the Y variable or select the range on the worksheet
• Type in the data range for the X variable(s) or select the range on the worksheet
• If your ranges include the data labels (recommended) then check the labels option
Copyright 2007 by Oxford University Press, Inc.PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 27
Copyright 2007 by Oxford University Press, Inc.PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 28
Select an Output Option
• Output to a selected range– Selection is the upper left corner of the
output range
• Output to a new worksheet– Optionally enter a name for the worksheet
• Output to a new workbook
• And then click OK
Copyright 2007 by Oxford University Press, Inc.PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 29
Copyright 2007 by Oxford University Press, Inc.PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 30
Regression Output
Copyright 2007 by Oxford University Press, Inc.PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 31
Multiple Regression Data
Copyright 2007 by Oxford University Press, Inc.PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 32
Copyright 2007 by Oxford University Press, Inc.PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Slide 33
Regression Output
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