Managerial Economics in a Global Economy
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Transcript Managerial Economics in a Global Economy
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Copyright 2007 by Oxford University Press, Inc.
Slide 1
1
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Slide 2
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
PowerPoint Slides Prepared by Robert F. Brooker, Ph.D.
Scatter Diagram
Copyright 2007 by Oxford University Press, Inc.
Slide 3
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Slide 4
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
PowerPoint Slides Prepared by Robert F. Brooker, Ph.D.
Copyright 2007 by Oxford University Press, Inc.
Slide 5
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Copyright 2007 by Oxford University Press, Inc.
Slide 6
Ordinary Least Squares (OLS)
Model:
Yt a bX t et
ˆ
Yˆt aˆ bX
t
et Yt Yˆt
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Copyright 2007 by Oxford University Press, Inc.
Slide 7
Ordinary Least Squares (OLS)
Objective: Determine the slope and
intercept that minimize the sum of
the squared errors.
n
n
n
t 1
t 1
t 1
2
2
ˆ )2
ˆ
ˆ
e
(
Y
Y
)
(
Y
a
bX
t t t t
t
PowerPoint Slides Prepared by Robert F. Brooker, Ph.D.
Copyright 2007 by Oxford University Press, Inc.
Slide 8
Ordinary Least Squares (OLS)
Estimation Procedure
n
bˆ
(X
t 1
t
X )(Yt Y )
n
(X
t 1
t
X)
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ˆ
aˆ Y bX
2
Copyright 2007 by Oxford University Press, Inc.
Slide 9
Ordinary Least Squares (OLS)
Estimation Example
Time
Xt
1
2
3
4
5
6
7
8
9
10
10
9
11
12
11
12
13
13
14
15
120
n 10
Yt
44
40
42
46
48
52
54
58
56
60
500
n
n
X t 120
Yt 500
t 1
n
X
t 1
X t 120
12
n
10
t 1
n
Yt 500
50
10
t 1 n
Y
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Xt X
Yt Y
-2
-3
-1
0
-1
0
1
1
2
3
-6
-10
-8
-4
-2
2
4
8
6
10
n
(X
t 1
t 1
( X t X )2
12
30
8
0
2
0
4
8
12
30
106
4
9
1
0
1
0
1
1
4
9
30
t
X )2 30
106
bˆ
3.533
30
t
X )(Yt Y ) 106
aˆ 50 (3.533)(12) 7.60
n
(X
( X t X )(Yt Y )
Copyright 2007 by Oxford University Press, Inc.
Slide 10
Ordinary Least Squares (OLS)
Estimation Example
n
X
n 10
n
X
t 1
t
n
(X
t 1
t 1
120
n
Y 500
t 1
t
n
Yt 500
50
10
t 1 n
Y
t
X ) 30
106
ˆ
b
3.533
30
t
X )(Yt Y ) 106
aˆ 50 (3.533)(12) 7.60
2
n
(X
t 1
X t 120
12
n
10
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Copyright 2007 by Oxford University Press, Inc.
Slide 11
Tests of Significance
Standard Error of the Slope Estimate
sbˆ
2
ˆ
(Yt Y )
( n k ) ( X t X )
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2
e
(n k ) ( X
Copyright 2007 by Oxford University Press, Inc.
2
t
2
X
)
t
Slide 12
Tests of Significance
Example Calculation
Yˆt
et Yt Yˆt
et2 (Yt Yˆt )2
( X t X )2
44
42.90
1.10
1.2100
4
9
40
39.37
0.63
0.3969
9
3
11
42
46.43
-4.43
19.6249
1
4
12
46
49.96
-3.96
15.6816
0
5
11
48
46.43
1.57
2.4649
1
6
12
52
49.96
2.04
4.1616
0
7
13
54
53.49
0.51
0.2601
1
8
13
58
53.49
4.51
20.3401
1
9
14
56
57.02
-1.02
1.0404
4
10
15
60
60.55
-0.55
0.3025
9
65.4830
30
Time
Xt
Yt
1
10
2
n
n
e (Yt Yˆt )2 65.4830
t 1
2
t
t 1
(X
t 1
(Y Yˆ )
( n k ) ( X X )
2
n
X ) 30
2
t
PowerPoint Slides Prepared by Robert F. Brooker, Ph.D.
sbˆ
t
2
t
Copyright 2007 by Oxford University Press, Inc.
65.4830
0.52
(10 2)(30)
Slide 13
Tests of Significance
Example Calculation
n
n
t 1
t 1
2
2
ˆ
e
(
Y
Y
)
t t t 65.4830
n
2
(
X
X
)
30
t
t 1
2
ˆ
(Yt Y )
65.4830
sbˆ
0.52
2
( n k ) ( X t X )
(10 2)(30)
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Slide 14
Tests of Significance
Calculation of the t Statistic
bˆ 3.53
t
6.79
sbˆ 0.52
Degrees of Freedom = (n-k) = (10-2) = 8
Critical Value at 5% level =2.306
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Copyright 2007 by Oxford University Press, Inc.
Slide 15
Tests of Significance
Decomposition of Sum of Squares
Total Variation = Explained Variation + Unexplained Variation
2
2
ˆ
ˆ
(Yt Y ) (Y Y ) (Yt Yt )
2
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Slide 16
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Slide 17
Tests of Significance
Coefficient of Determination
R2
Explained Variation
TotalVariation
2
ˆ
(
Y
Y
)
2
(
Y
Y
)
t
373.84
R
0.85
440.00
2
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Copyright 2007 by Oxford University Press, Inc.
Slide 18
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Copyright 2007 by Oxford University Press, Inc.
Slide 19
Tests of Significance
Coefficient of Correlation
r R2 withthe signof bˆ
1 r 1
r 0.85 0.92
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Slide 20
Chapter 4 Appendix
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Slide 21
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Slide 22
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Slide 23
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Slide 24
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.
PowerPoint Slides Prepared by Robert F. Brooker, Ph.D.
Copyright 2007 by Oxford University Press, Inc.
Slide 25
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Slide 26
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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Copyright 2007 by Oxford University Press, Inc.
Slide 27
Example Data
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Slide 28
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
PowerPoint Slides Prepared by Robert F. Brooker, Ph.D.
Copyright 2007 by Oxford University Press, Inc.
Slide 29
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Copyright 2007 by Oxford University Press, Inc.
Slide 30
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Slide 31
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 32
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Slide 33
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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Copyright 2007 by Oxford University Press, Inc.
Slide 34
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Slide 35
Regression Output
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Slide 36
Multiple Regression Data
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Slide 37
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Copyright 2007 by Oxford University Press, Inc.
Slide 38
Regression Output
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Copyright 2007 by Oxford University Press, Inc.
Slide 39