Need help in Managerial Economics
chukkarocks
Ch05Presentation4537.ppt
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
Regression Analysis
Scatter Diagram
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
Ordinary Least Squares (OLS)
Model:
Ordinary Least Squares (OLS)
Objective: Determine the slope and intercept that minimize the sum of the squared errors.
Ordinary Least Squares (OLS)
Estimation Procedure
Ordinary Least Squares (OLS)
Estimation Example
Ordinary Least Squares (OLS)
Estimation Example
Tests of Significance
Standard Error of the Slope Estimate
Tests of Significance
Example Calculation
Tests of Significance
Example Calculation
Tests of Significance
Calculation of the t Statistic
Degrees of Freedom = (n-k) = (10-2) = 8
Critical Value at 5% level =2.306
Tests of Significance
Decomposition of Sum of Squares
Total Variation = Explained Variation + Unexplained Variation
Tests of Significance
Coefficient of Determination
Tests of Significance
Coefficient of Correlation
Multiple Regression Analysis
Model:
Multiple Regression Analysis
Adjusted Coefficient of Determination
Multiple Regression Analysis
Analysis of Variance and F Statistic
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
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:
Estimation Format:
Chapter 5 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
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
ttt
YabXe
=++
ˆ
ˆ
ˆ
tt
YabX
=+
ˆ
ttt
eYY
=-
222
111
ˆ
ˆ
ˆ
()()
nnn
ttttt
ttt
eYYYabX
===
=-=--
ååå
1
2
1
()()
ˆ
()
n
tt
t
n
t
t
XXYY
b
XX
=
=
--
=
-
å
å
ˆ
ˆ
aYbX
=-
10
n
=
1
120
12
10
n
t
t
X
X
n
=
===
å
1
500
50
10
n
t
t
Y
Y
n
=
===
å
1
120
n
t
t
X
=
=
å
1
500
n
t
t
Y
=
=
å
2
1
()30
n
t
t
XX
=
-=
å
1
()()106
n
tt
t
XXYY
=
--=
å
106
ˆ
3.533
30
b
==
ˆ
50(3.533)(12)7.60
a
=-=
Time
t
X
t
Y
t
XX
-
t
YY
-
()()
tt
XXYY
--
2
()
t
XX
-
1
10
44
-2
-6
12
2
9
40
-3
-10
30
3
11
42
-1
-8
8
4
12
46
0
-4
0
5
11
48
-1
-2
2
6
12
52
0
2
0
7
13
54
1
4
4
8
13
58
1
8
8
9
14
56
2
6
12
10
15
60
3
10
30
120
500
106
4
9
1
0
1
0
1
1
4
9
30
22
ˆ
22
ˆ
()
()()()()
tt
b
tt
YYe
s
nkXXnkXX
-
==
----
åå
åå
22
11
ˆ
()65.4830
nn
ttt
tt
eYY
==
=-=
åå
2
ˆ
2
ˆ
()
65.4830
0.52
()()(102)(30)
t
b
t
YY
s
nkXX
-
===
---
å
å
Time
t
X
t
Y
ˆ
t
Y
ˆ
ttt
eYY
=-
22
ˆ
()
ttt
eYY
=-
2
()
t
XX
-
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
ˆ
ˆ
3.53
6.79
0.52
b
b
t
s
===
222
ˆˆ
()()()
ttt
YYYYYY
-=-+-
ååå
2
2
2
ˆ
()
()
t
YY
ExplainedVariation
R
TotalVariationYY
-
==
-
å
å
2
373.84
0.85
440.00
R
==
2
ˆ
rRwiththesignofb
=
0.850.92
r
==
11
r
-££
1122''
kk
YabXbXbX
=++++
L
22
(1)
1(1)
()
n
RR
nk
-
=--
-
/(1)
/()
ExplainedVariationk
F
UnexplainedVariationnk
-
=
-
2
2
/(1)
(1)/()
Rk
F
Rnk
-
=
--
2
1
2
2
1
()
n
tt
t
n
t
t
ee
d
e
-
=
=
-
=
å
å
01234
XXY
QaaPaIaNaPe
=++++++
L
12
()()
bb
XXY
QaPP
=
12
lnlnlnln
XXY
QabPbP
=++
