[PPT] - 1 KULKUNYA PRAYARACH, PH.D. Multiple Regression Analysis I. PowerPoint Presentation

SLIDE 1

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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SLIDE 2

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 2

SLIDE 3

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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SLIDE 4

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

𝑍

𝑗 = 𝛾1 + 𝛾2𝑌1𝑗 + 𝛾3𝑌2𝑗 + 𝑣𝑗

ANALYSIS: Type of Estimator

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SLIDE 5

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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SLIDE 6

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

bserved var

ANALYSIS: Fitted Regression on Model

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SLIDE 7

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 Model Y is discrete

ANALYSIS: Fitted Regression on Model

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SLIDE 8

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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SLIDE 9

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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SLIDE 10

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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SLIDE 11

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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SLIDE 12

I. Analysis of Data

KULKUNYA PRAYARACH, PH.D.

Multiple Regression Analysis

II. Hypothesis Testing
III. Dummy Variable
IV. Research & Group Work

TMB

RP1 BBL NPL FRN JAS DJ NIKKEI 1990M01 2011 M12

Example I: Stock Asset Price Regression

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SLIDE 13

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

Definitions Example II: Hedonic Pricing Model

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SLIDE 14

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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SLIDE 15

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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SLIDE 16

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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SLIDE 17

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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SLIDE 18

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

β4 Regression 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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SLIDE 19

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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SLIDE 20

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. French Eugene Fama

RESEARCH PAPER: THREE FACTOR MODEL

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SLIDE 21

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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SLIDE 22

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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SLIDE 23

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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WORK SHOP #1

SLIDE 24

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

Monthly Data : (1) Window Dressing in June and (2)

End-Year Effect.

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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