demand estimation

demand estimation - Transcript

PowerPoint Slides Prepared by Robert F Brooker Ph D

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1

PowerPoint Slides Prepared by Robert F Brooker Ph D

Copyright 2007 by Oxford University Press Inc

Slide 2

Marketing Research Approaches to Demand Estimation
Consumer Surveys
data from survey questions

Observational Research
data from observed behavior

Consumer Clinics
data from laboratory experiments

Market Experiments
data from real market tests
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Slide 4

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Slide 5

Regression Analysis
Year 1 2 3 4 5 6 7 8 9 10 X 10 9 11 12 11 12 13 13 14 15 Y 44 40 42 46 48 52 54 58 56 60
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Slide 6

Scatter Diagram

PowerPoint Slides Prepared by Robert F Brooker Ph D

PowerPoint Slides Prepared by Robert F Brooker Ph D

Copyright 2007 by Oxford University Press Inc

Slide 7

Regression Analysis
Regression Line Line of Best Fit Regression Line Minimizes the sum of the squared vertical deviations et of each point from the regression line Ordinary Least Squares OLS Method
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Slide 8

PowerPoint Slides Prepared by Robert F Brooker Ph D

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Slide 9

Ordinary Least Squares OLS
Model
Yt a bX t et Yt a bX t et Yt Yt

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Slide 10

Ordinary Least Squares OLS
Objective Determine the slope and intercept that minimize the sum of the squared errors
et2 Yt Yt 2 Yt a bX t 2
t 1 t 1 t 1 n n n

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Slide 11

Ordinary Least Squares OLS
Estimation Procedure
n

b

X
t 1 n t 1

t

X Yt Y

X t X 2

a Y bX

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Slide 12

Ordinary Least Squares OLS
Estimation Example
Time
1 2 3 4 5 6 7 8 9 10
n

Xt
10 9 11 12 11 12 13 13 14 15 120

Yt
44 40 42 46 48 52 54 58 56 60 500

Xt X
2 3 1 0 1 0 1 1 2 3
n

Yt Y
6 10 8 4 2 2 4 8 6 10

X t X Yt Y
12 30 8 0 2 0 4 8 12 30 106

X t X 2
4 9 1 0 1 0 1 1 4 9 30

n 10 X
t 1 n

X t 120
t 1

Yt 500
t 1

n

X
t 1 n

t

X 2 30 X Yt Y 106

106 3 533 b 30 a 50 3 533 12 7 60

X t 120 12 n 10

Y

Yt 500 50 10 t 1 n

n

X
t 1

t

PowerPoint Slides Prepared by Robert F Brooker Ph D

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Slide 13

Ordinary Least Squares OLS
Estimation Example
n 10
X
t 1 n n

X t 120 12 n 10

X
t 1
n t 1 n

n

t

120
2

Y
t 1

n

t

500

Y

Yt 500 50 10 t 1 n

X X
t 1

t

X 30 X Yt Y 106

106 3 533 b 30

t

a 50 3 533 12 7 60
Copyright 2007 by Oxford University Press Inc
Slide 14

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Tests of Significance
Standard Error of the Slope Estimate
2 Yt Y

sb

n k X t X

2



e n k X
2 t

t

X 2

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Slide 15

Tests of Significance
Example Calculation
Time
1 2 3 4 5 6 7 8 9 10

Xt
10 9 11 12 11 12 13 13 14 15

Yt
44 40 42 46 48 52 54 58 56 60

Yt
42 90 39 37 46 43 49 96 46 43 49 96 53 49 53 49 57 02 60 55

et Yt Yt
1 10 0 63 4 43 3 96 1 57 2 04 0 51 4 51 1 02 0 55

et2 Yt Yt 2
1 2100 0 3969 19 6249 15 6816 2 4649 4 1616 0 2601 20 3401 1 0404 0 3025 65 4830

X t X 2
4 9 1 0 1 0 1 1 4 9 30

e Yt Y 2 65 4830 t
t 1 2 t t 1

n

n

X
t 1

n

t

X 30
2

sb

Y Y n k X X
2 t t

2



65 4830 0 52 10 2 30
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PowerPoint Slides Prepared by Robert F Brooker Ph D

Copyright 2007 by Oxford University Press Inc

Tests of Significance
Example Calculation
et2 Yt Yt 2 65 4830
t 1 t 1 n n

X t X 2 30
t 1

n

65 4830 sb 0 52 2 n k X t X 10 2 30
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2 Yt Y

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Slide 17

Tests of Significance
Calculation of the t Statistic
b 3 53 t 6 79 sb 0 52

Degrees of Freedom n k 10 2 8 Critical Value at 5 level 2 306
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Slide 18

Tests of Significance
Decomposition of Sum of Squares
Total Variation Explained Variation Unexplained Variation

Y 2 Y Y 2 Yt Y Y t t
2

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Slide 19

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Slide 20

Tests of Significance
Coefficient of Determination
R2 Explained Variation Total Variation Y Y 2

Yt Y 2

373 84 R 0 85 440 00
2

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Slide 21

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Slide 22

Tests of Significance
Coefficient of Correlation
r R 2 with the sign of b

1 r 1
r 0 85 0 92

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Slide 23

Multiple Regression Analysis

Model

Y a b1 X 1 b2 X 2 L bk X k

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Slide 26

Multiple Regression Analysis
Adjusted Coefficient of Determination
n 1 n k

R 2 1 1 R 2

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Slide 27

Multiple Regression Analysis
Analysis of Variance and F Statistic
F Explained Variation k 1 Unexplained Variation n k

R 2 k 1 F 1 R 2 n k

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Slide 28

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
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Slide 29

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Slide 30

Durbin Watson Statistic
Test for Autocorrelation
et et 1 2
t 2 n

d

et2
t 1

n

If d 2 autocorrelation is absent

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Slide 31

Steps in Demand Estimation
Model Specification Identify Variables Collect Data Specify Functional Form Estimate Function Test the Results

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Slide 32

Functional Form Specifications
Linear Function
QX a0 a1PX a2 I a3 N a4 PY L e

Power Function
b QX a PX1 PYb2

Estimation Format
ln QX ln a b1 ln PX b2 ln PY

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Copyright 2007 by Oxford University Press Inc

Slide 33

Chapter 4 Appendix

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PowerPoint Slides Prepared by Robert F Brooker Ph D

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PowerPoint Slides Prepared by Robert F Brooker Ph D

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Slide 37

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 AddIns When the Add Ins dialog appears select Analysis ToolPak and then click OK
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Slide 38

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Slide 39

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
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Slide 40

Example Data

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Slide 41

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
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PowerPoint Slides Prepared by Robert F Brooker Ph D

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Slide 44

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
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Slide 45

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Slide 46

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
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Slide 47

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Slide 48

Regression Output

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Slide 49

Multiple Regression Data

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Slide 50

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Slide 51

Regression Output

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Slide 52