C opyright 2007 by Oxford University Press, Inc. PowerPoint Slides Prepared by Robert F. Brooker,...

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



Adjusted Coefficient of Determination

2 2 ( 1)1 (1 )

( )

nR R

n k



Analysis of Variance and F Statistic

/( 1)

/( )

ExplainedVariation kF

UnexplainedVariation n k

2

2

/( 1)

(1 ) /( )

R kF

R n k


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.


Durbin-Watson Statistic

Test for Autocorrelation

21

2

2

1

( )n

t tt

n

tt

e ed

e

If d = 2, autocorrelation is absent.


Steps in Demand Estimation

• Model Specification: Identify Variables

• Collect Data

• Specify Functional Form

• Estimate Function

• Test the Results


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


Chapter 4 Appendix


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.


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


Example Data


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


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


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


Regression Output


Multiple Regression Data


Regression Output

C opyright 2007 by Oxford University Press, Inc. PowerPoint Slides Prepared by Robert F. Brooker,...

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