I. Analysis of Data
KULKUNYA PRAYARACH, PH.D.
Multiple Regression Analysis
II. Hypothesis Testing III. Dummy Variable IV. Research & Group Work
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I. Analysis of Data
KULKUNYA PRAYARACH, PH.D.
Multiple Regression Analysis
II. Hypothesis Testing III. Dummy Variable IV. Research & Group Work
OUTLINE
Analysis of Data and Model
Hypothesis Testing
Dummy Variables
Research in Finance
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I. Analysis of Data
KULKUNYA PRAYARACH, PH.D.
Multiple Regression Analysis
II. Hypothesis Testing III. Dummy Variable IV. Research & Group Work
Trend
Seasonal Variation
Cyclical Variation
Irregular Variation
Time Series data Cross-Sectional data
1-dimensional Data set
Observing many subjects
(size, company, counties,
etc) at the same time
Panel data
Multi-dimensional data set
Time-Series + Cross-
Sectional Data
MULTIPLE REGRESSION
ANALYSIS: Types of Data
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I. Analysis of Data
KULKUNYA PRAYARACH, PH.D.
Multiple Regression Analysis
II. Hypothesis Testing III. Dummy Variable IV. Research & Group Work
Least Square Estimator Maximum Likelihood Estimator
𝑌𝑖 = 𝛽1 + 𝛽2𝑋1𝑖 + 𝛽3𝑋2𝑖 + 𝑢𝑖
ANALYSIS: Type of Estimator
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I. Analysis of Data
KULKUNYA PRAYARACH, PH.D.
Multiple Regression Analysis
II. Hypothesis Testing III. Dummy Variable IV. Research & Group Work
Linear model Non Linear Model
ANALYSIS: Type of Model
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I. Analysis of Data
KULKUNYA PRAYARACH, PH.D.
Multiple Regression Analysis
II. Hypothesis Testing III. Dummy Variable IV. Research & Group Work
Y = a + b x
Time series Panel Model
Pooled or Panel Model
Fixed-Effect Model
Random-Effect Model
Time-Series with Condition
ARCH/GARCH Multiple Regression ARMA/ ARIMA
X ~ regressor
independent variable
explanatory variable
predictor Variable
Y ~ regressand var
response var
dependent var
observed var
ANALYSIS: Fitted Regression on Model
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I. Analysis of Data
KULKUNYA PRAYARACH, PH.D.
Multiple Regression Analysis
II. Hypothesis Testing III. Dummy Variable IV. Research & Group Work
Y = a + b x
Logit Model Probit ModelY is discrete
ANALYSIS: Fitted Regression on Model
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I. Analysis of Data
KULKUNYA PRAYARACH, PH.D.
Multiple Regression Analysis
II. Hypothesis Testing III. Dummy Variable IV. Research & Group Work
Y = a + b x
Vector Auto Regression
(VAR)
Error Correction
Model (ECM)
Y and X are Dynamic
ANALYSIS: Fitted Regression on Model
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I. Analysis of Data
KULKUNYA PRAYARACH, PH.D.
Multiple Regression Analysis
II. Hypothesis Testing III. Dummy Variable IV. Research & Group Work
FITTED REGRESSION MODEL
Y = a + b x
ANALYSIS: Expansion from Simple Regression to Multiple Regression
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I. Analysis of Data
KULKUNYA PRAYARACH, PH.D.
Multiple Regression Analysis
II. Hypothesis Testing III. Dummy Variable IV. Research & Group Work
• F-Test is of interest to test more than one
coefficient simultaneously.
F-Test
Conditional to Reject H0:
Significant if p-value < 0.05
TESTING MULTIPLE HYPOTHESIS: F-test
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I. Analysis of Data
KULKUNYA PRAYARACH, PH.D.
Multiple Regression Analysis
II. Hypothesis Testing III. Dummy Variable IV. Research & Group Work
• t-Test is of interest to test ONLY one coefficient
t-Test
Conditional to Reject H0:
Significant if p-value < 0.05
Oh my gosh!!!! It fails to reject H0, what does it mean?
What I should do? Cut it or leave it?
TESTING MULTIPLE HYPOTHESIS: t-test
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I. Analysis of Data
KULKUNYA PRAYARACH, PH.D.
Multiple Regression Analysis
II. Hypothesis Testing III. Dummy Variable IV. Research & Group Work
TMB
RP1BBLNPLFRNJASDJ
NIKKEI
1990M01 2011 M12
Example I: Stock Asset Price Regression
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I. Analysis of Data
KULKUNYA PRAYARACH, PH.D.
Multiple Regression Analysis
II. Hypothesis Testing III. Dummy Variable IV. Research & Group Work
Dependent Variable : Y ~ Rental Values DefinitionsExample II: Hedonic Pricing Model
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I. Analysis of Data
KULKUNYA PRAYARACH, PH.D.
Multiple Regression Analysis
II. Hypothesis Testing III. Dummy Variable IV. Research & Group Work
• R2 is desirable to answer how well regression model
actually fits the data
• In other words, R2 is desirable to answer how well does
the model containing the explanatory variables
R2 = 1 0 < R2 < 1
0 ≤ R2 ≤ 1
TESTING MULTIPLE HYPOTHESIS: Goodness of Fit Testing R2
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I. Analysis of Data
KULKUNYA PRAYARACH, PH.D.
Multiple Regression Analysis
II. Hypothesis Testing III. Dummy Variable IV. Research & Group Work
• Cannot compare R2 of two models with same X but change Y
• R2 never falls if more regressors are added to the regression
• R2 can take values of 0.9 or higher for time series regressions,
and hence it is not good at discrimanating between models
TESTING MULTIPLE HYPOTHESIS: Problem with using R2
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I. Analysis of Data
KULKUNYA PRAYARACH, PH.D.
Multiple Regression Analysis
II. Hypothesis Testing III. Dummy Variable IV. Research & Group Work
• If an extra regressor is added to the model, k increases
and unless R2 increases by a more than off-setting
amount, will actually fall.
• If model contains a lot of significant and insignificant
variables, can be negative
TESTING MULTIPLE HYPOTHESIS: Adjusted R2
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I. Analysis of Data
KULKUNYA PRAYARACH, PH.D.
Multiple Regression Analysis
II. Hypothesis Testing III. Dummy Variable IV. Research & Group Work
Dummy is variables that assume such 0 and 1 values
If a model contains M categories, then only M-1 dummy
variables should be created. Otherwise, multicollinearity
Problem
Category for which no dummy variable is assigned is
known as base, benchmark
2 types of dummy variables: Intercept vs. slope change
dummy
DUMMY VARIABLE: How to Create Dummy
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I. Analysis of Data
KULKUNYA PRAYARACH, PH.D.
Multiple Regression Analysis
II. Hypothesis Testing III. Dummy Variable IV. Research & Group Work
Slop = Β3 + β4D
I. Different Intercept
JAN is dummy = 1 if January
= 0 otherwise
II. Different Slope
X
Y
α
β4Regression for Other months
Regression for JAN
α+β4
D is dummy = 1 if Safe Area
= 0 Otherwise
DISTANT
RENT
Regression for Criminal Area
Regression for Safe Area
α
DUMMY VARIABLE: 2 Type of Dummy Variables
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I. Analysis of Data
KULKUNYA PRAYARACH, PH.D.
Multiple Regression Analysis
II. Hypothesis Testing III. Dummy Variable IV. Research & Group Work
STEP BY STEP
Quantitative Analysis (Multiple Regression)
1. Conceptual Framework
2. Choose Type of regression (Linear vs. Non Linear)
3. Group Variables
4. Analyze Data (Take logarithm or not)
5. Look at the sign of estimated parameters.
6. Test Hypothesis
7. Take a look at Adjust R2
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I. Analysis of Data
KULKUNYA PRAYARACH, PH.D.
Multiple Regression Analysis
II. Hypothesis Testing III. Dummy Variable IV. Research & Group Work
• Three Factor Model (Fama and French (1992))
Kenneth R. FrenchEugene Fama
RESEARCH PAPER: THREE FACTOR MODEL
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I. Analysis of Data
KULKUNYA PRAYARACH, PH.D.
Multiple Regression Analysis
II. Hypothesis Testing III. Dummy Variable IV. Research & Group Work
21
I. Analysis of Data
KULKUNYA PRAYARACH, PH.D.
Multiple Regression Analysis
II. Hypothesis Testing III. Dummy Variable IV. Research & Group Work
22
I. Analysis of Data
KULKUNYA PRAYARACH, PH.D.
Multiple Regression Analysis
II. Hypothesis Testing III. Dummy Variable IV. Research & Group Work
23
WORK SHOP
#1
I. Analysis of Data
KULKUNYA PRAYARACH, PH.D.
Multiple Regression Analysis
II. Hypothesis Testing III. Dummy Variable IV. Research & Group Work
WORK ORDERS : Multiple Regression
(1) Using Three Factor Model to regress Multiple Regression on your group assignment
(2) Interpret F-test, and T-Test.(3) Explain Adjusted R2
(4) Create Dummy variables o Monthly Data : (1) Window Dressing in June and (2)
End-Year Effect. o Annual Data : (1) Asian Crisis during 1997-1999,
(2) Subprime Crisis during 2008-2010, (3) Europe Debt crisis during 2008-2012.
(5) Redo Work Orders (1) – (4) with new model
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