ch. 4-demand-estimation(2)
DESCRIPTION
Microeconomics-SalvatoreTRANSCRIPT
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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 1
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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 2
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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 3
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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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 4
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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 5
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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 6
Scatter Diagram
Regression Analysis
Year X Y
1 10 44
2 9 40
3 11 42
4 12 46
5 11 48
6 12 52
7 13 54
8 13 58
9 14 56
10 15 60
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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 7
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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 8
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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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 9
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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 10
Ordinary Least Squares (OLS)
Model: t t tY a bX e
ˆˆ ˆt tY a bX
ˆt t te Y Y
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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 11
Ordinary Least Squares (OLS)
Objective: Determine the slope and intercept that minimize the sum of the squared errors.
2 2 2
1 1 1
ˆˆ ˆ( ) ( )n n n
t t t t tt t t
e Y Y Y a bX
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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 12
Ordinary Least Squares (OLS)
Estimation Procedure
1
2
1
( )( )ˆ
( )
n
t tt
n
tt
X X Y Yb
X X
ˆa Y bX
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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 13
Ordinary Least Squares (OLS)
Estimation Example
1 10 44 -2 -6 122 9 40 -3 -10 303 11 42 -1 -8 84 12 46 0 -4 05 11 48 -1 -2 26 12 52 0 2 07 13 54 1 4 48 13 58 1 8 89 14 56 2 6 12
10 15 60 3 10 30120 500 106
4910101149
30
Time tX tY tX X tY Y ( )( )t tX X Y Y 2( )tX X
10n
1
12012
10
nt
t
XX
n
1
50050
10
nt
t
YY
n
1
120n
tt
X
1
500n
tt
Y
2
1
( ) 30n
tt
X X
1
( )( ) 106n
t tt
X X Y Y
106ˆ 3.53330
b
ˆ 50 (3.533)(12) 7.60a
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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 14
Ordinary Least Squares (OLS)Estimation Example
10n1
12012
10
nt
t
XX
n
1
50050
10
nt
t
YY
n
1
120n
tt
X
1
500n
tt
Y
2
1
( ) 30n
tt
X X
1
( )( ) 106n
t tt
X X Y Y
106ˆ 3.53330
b
ˆ 50 (3.533)(12) 7.60a
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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 15
Tests of Significance
Standard Error of the Slope Estimate
2 2
ˆ 2 2
ˆ( )
( ) ( ) ( ) ( )t t
bt t
Y Y es
n k X X n k X X
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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 16
Tests of Significance
Example Calculation
2 2
1 1
ˆ( ) 65.4830n n
t t tt t
e Y Y
2
1
( ) 30n
tt
X X
2
ˆ 2
ˆ( ) 65.48300.52
( ) ( ) (10 2)(30)t
bt
Y Ys
n k X X
1 10 44 42.90
2 9 40 39.37
3 11 42 46.43
4 12 46 49.96
5 11 48 46.43
6 12 52 49.96
7 13 54 53.49
8 13 58 53.49
9 14 56 57.02
10 15 60 60.55
1.10 1.2100 4
0.63 0.3969 9
-4.43 19.6249 1
-3.96 15.6816 0
1.57 2.4649 1
2.04 4.1616 0
0.51 0.2601 1
4.51 20.3401 1
-1.02 1.0404 4
-0.55 0.3025 9
65.4830 30
Time tX tY tY ˆt t te Y Y 2 2ˆ( )t t te Y Y 2( )tX X
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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 17
Tests of Significance
Example Calculation
2
ˆ 2
ˆ( ) 65.48300.52
( ) ( ) (10 2)(30)t
bt
Y Ys
n k X X
2
1
( ) 30n
tt
X X
2 2
1 1
ˆ( ) 65.4830n n
t t tt t
e Y Y
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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 18
Tests of Significance
Calculation of the t Statistic
ˆ
ˆ 3.536.79
0.52b
bts
Degrees of Freedom = (n-k) = (10-2) = 8
Critical Value at 5% level =2.306
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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 19
Tests of Significance
Decomposition of Sum of Squares
2 2 2ˆ ˆ( ) ( ) ( )t t tY Y Y Y Y Y
Total Variation = Explained Variation + Unexplained Variation
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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 20
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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 21
Tests of Significance
Coefficient of Determination
22
2
ˆ( )
( )t
Y YExplainedVariationR
TotalVariation Y Y
2 373.840.85
440.00R
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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 22
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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 23
Tests of Significance
Coefficient of Correlation
2 ˆr R with the signof b
0.85 0.92r
1 1r
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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 24
Multiple Regression Analysis
Model: 1 1 2 2 ' 'k kY a b X b X b X
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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 25
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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 26
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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 27
Multiple Regression Analysis
Adjusted Coefficient of Determination
2 2 ( 1)1 (1 )
( )
nR R
n k
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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 28
Multiple Regression Analysis
Analysis of Variance and F Statistic
/( 1)
/( )
ExplainedVariation kF
UnexplainedVariation n k
2
2
/( 1)
(1 ) /( )
R kF
R n k
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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 29
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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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 30
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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 31
Durbin-Watson Statistic
Test for Autocorrelation
21
2
2
1
( )n
t tt
n
tt
e ed
e
If d = 2, autocorrelation is absent.
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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 32
Steps in Demand Estimation
• Model Specification: Identify Variables• Collect Data• Specify Functional Form• Estimate Function• Test the Results
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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 33
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
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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 34
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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 35
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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 36
Chapter 4 Appendix
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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 37
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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 38
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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 39
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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 40
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.
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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 41
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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 42
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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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 43
Example Data
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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 44
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. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 45
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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 46
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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 47
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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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 48
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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 49
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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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 50
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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 51
Regression Output
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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 52
Multiple Regression Data
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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 53
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PowerPoint Slides Prepared by Robert F. Brooker, Ph.D. Copyright 2007 by Oxford University Press, Inc. (Adapted by OUP India, 2008) Slide 54
Regression Output