Multiple Regression Analysis - Kasetsart Universityfin.bus.ku.ac.th/01131591 Financial Research/Lecture Slides/W3... · Multiple Regression Analysis II. Hypothesis Testing III. Dummy

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




OUTLINE

Analysis of Data and Model

Hypothesis Testing

Dummy Variables

Research in Finance

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I. Analysis of Data




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




Least Square Estimator Maximum Likelihood Estimator

𝑌𝑖 = 𝛽1 + 𝛽2𝑋1𝑖 + 𝛽3𝑋2𝑖 + 𝑢𝑖

ANALYSIS: Type of Estimator

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I. Analysis of Data




Linear model Non Linear Model

ANALYSIS: Type of Model

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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




Y = a + b x

Logit Model Probit ModelY is discrete


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I. Analysis of Data




Y = a + b x

Vector Auto Regression

(VAR)

Error Correction

Model (ECM)

Y and X are Dynamic


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I. Analysis of Data




FITTED REGRESSION MODEL

Y = a + b x

ANALYSIS: Expansion from Simple Regression to Multiple Regression

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I. Analysis of Data




• 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




• 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




TMB

RP1BBLNPLFRNJASDJ

NIKKEI

1990M01 2011 M12

Example I: Stock Asset Price Regression

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I. Analysis of Data




Dependent Variable : Y ~ Rental Values DefinitionsExample II: Hedonic Pricing Model

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I. Analysis of Data




• 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




• 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




• 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




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




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




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




• Three Factor Model (Fama and French (1992))

Kenneth R. FrenchEugene Fama

RESEARCH PAPER: THREE FACTOR MODEL

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WORK SHOP

#1

I. Analysis of Data




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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Multiple Regression Analysis - Kasetsart Universityfin.bus.ku.ac.th/01131591 Financial Research/Lecture Slides/W3... · Multiple Regression Analysis II. Hypothesis Testing III. Dummy