Multiple Regression Analysis I. Analysis of Data III. Dummy Variable II. Hypothesis Testing IV. Research & Group Work 1 KULKUNYA PRAYARACH, PH.D.
Multiple Regression Analysis I. Analysis of Data III. Dummy Variable II. Hypothesis Testing IV. Research & Group Work OUTLINE Analysis of Data and Model Hypothesis Testing Dummy Variables Research in Finance 2 KULKUNYA PRAYARACH, PH.D.
Multiple Regression Analysis I. Analysis of Data III. Dummy Variable II. Hypothesis Testing IV. Research & Group Work ANALYSIS: Types of Data Panel data Cross-Sectional data Time Series data T rend 1- dimensional Data set Multi- dimensional data set S easonal Variation Observing many subjects Time-Series + Cross- C yclical Variation (size, company, counties, Sectional Data I rregular Variation etc) at the same time MULTIPLE REGRESSION 3 KULKUNYA PRAYARACH, PH.D.
Multiple Regression Analysis I. Analysis of Data III. Dummy Variable II. Hypothesis Testing IV. Research & Group Work ANALYSIS: Type of Estimator Least Square Estimator Maximum Likelihood Estimator 𝑍 𝑗 = 𝛾 1 + 𝛾 2 𝑌 1 𝑗 + 𝛾 3 𝑌 2 𝑗 + 𝑣 𝑗 4 KULKUNYA PRAYARACH, PH.D.
Multiple Regression Analysis I. Analysis of Data III. Dummy Variable II. Hypothesis Testing IV. Research & Group Work ANALYSIS: Type of Model Non Linear Model Linear model 5 KULKUNYA PRAYARACH, PH.D.
Multiple Regression Analysis I. Analysis of Data III. Dummy Variable II. Hypothesis Testing IV. Research & Group Work ANALYSIS: Fitted Regression on Model Y = a + b x X ~ regressor Y ~ regressand var independent variable response var explanatory variable dependent var predictor Variable observed var Panel Model Time series Time-Series with Condition Pooled or Panel Model ARCH/GARCH Multiple Regression Fixed-Effect Model ARMA/ ARIMA Random-Effect Model 6 KULKUNYA PRAYARACH, PH.D.
Multiple Regression Analysis I. Analysis of Data III. Dummy Variable II. Hypothesis Testing IV. Research & Group Work ANALYSIS: Fitted Regression on Model Y = a + b x Y is discrete Logit Model Probit Model 7 KULKUNYA PRAYARACH, PH.D.
Multiple Regression Analysis I. Analysis of Data III. Dummy Variable II. Hypothesis Testing IV. Research & Group Work ANALYSIS: Fitted Regression on Model Y = a + b x Y and X are Dynamic Error Vector Auto Correction Regression Model (ECM) (VAR) 8 KULKUNYA PRAYARACH, PH.D.
Multiple Regression Analysis I. Analysis of Data III. Dummy Variable II. Hypothesis Testing IV. Research & Group Work ANALYSIS: Expansion from Simple Regression to Multiple Regression FITTED REGRESSION MODEL Y = a + b x 9 KULKUNYA PRAYARACH, PH.D.
Multiple Regression Analysis I. Analysis of Data III. Dummy Variable II. Hypothesis Testing IV. Research & Group Work TESTING MULTIPLE HYPOTHESIS: F-test • F-Test is of interest to test more than one coefficient simultaneously. F-Test Conditional to Reject H 0 : Significant if p-value < 0.05 10 KULKUNYA PRAYARACH, PH.D.
Multiple Regression Analysis I. Analysis of Data III. Dummy Variable II. Hypothesis Testing IV. Research & Group Work TESTING MULTIPLE HYPOTHESIS: t-test • t-Test is of interest to test ONLY one coefficient t-Test Conditional to Reject H 0 : Significant if p-value < 0.05 Oh my gosh!!!! It fails to reject H 0 , what does it mean? What I should do? Cut it or leave it? 11 KULKUNYA PRAYARACH, PH.D.
Multiple Regression Analysis I. Analysis of Data III. Dummy Variable II. Hypothesis Testing IV. Research & Group Work Example I: Stock Asset Price Regression TMB 1990M01 2011 M12 RP1 BBL NPL FRN JAS DJ NIKKEI 12 KULKUNYA PRAYARACH, PH.D.
Multiple Regression Analysis I. Analysis of Data III. Dummy Variable II. Hypothesis Testing IV. Research & Group Work Example II: Hedonic Pricing Model Definitions Dependent Variable : Y ~ Rental Values 13 KULKUNYA PRAYARACH, PH.D.
Multiple Regression Analysis I. Analysis of Data III. Dummy Variable II. Hypothesis Testing IV. Research & Group Work TESTING MULTIPLE HYPOTHESIS: Goodness of Fit Testing R 2 • R 2 is desirable to answer how well regression model actually fits the data • In other words, R 2 is desirable to answer how well does the model containing the explanatory variables 0 ≤ R 2 ≤ 1 R 2 = 1 0 < R 2 < 1 14 KULKUNYA PRAYARACH, PH.D.
Multiple Regression Analysis I. Analysis of Data III. Dummy Variable II. Hypothesis Testing IV. Research & Group Work TESTING MULTIPLE HYPOTHESIS: Problem with using R 2 Cannot compare R 2 of two models with same X but change Y • R 2 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 15 KULKUNYA PRAYARACH, PH.D.
Multiple Regression Analysis I. Analysis of Data III. Dummy Variable II. Hypothesis Testing IV. Research & Group Work TESTING MULTIPLE HYPOTHESIS: Adjusted R 2 • 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 16 KULKUNYA PRAYARACH, PH.D.
Multiple Regression Analysis I. Analysis of Data III. Dummy Variable II. Hypothesis Testing IV. Research & Group Work DUMMY VARIABLE: How to Create Dummy 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 17 KULKUNYA PRAYARACH, PH.D.
Multiple Regression Analysis I. Analysis of Data III. Dummy Variable II. Hypothesis Testing IV. Research & Group Work DUMMY VARIABLE: 2 Type of Dummy Variables II. Different Slope I. Different Intercept D is dummy = 1 if Safe Area JAN is dummy = 1 if January = 0 Otherwise = 0 otherwise RENT Regression for Safe Area Regression for JAN Y Slop = Β 3 + β 4 D β 4 Regression for Criminal Regression for Other Area months α α α + β 4 X DISTANT 18 KULKUNYA PRAYARACH, PH.D.
Multiple Regression Analysis I. Analysis of Data III. Dummy Variable II. Hypothesis Testing 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 R 2 19 KULKUNYA PRAYARACH, PH.D.
Multiple Regression Analysis I. Analysis of Data III. Dummy Variable II. Hypothesis Testing IV. Research & Group Work RESEARCH PAPER: THREE FACTOR MODEL • Three Factor Model (Fama and French (1992)) Eugene Fama Kenneth R. French 20 KULKUNYA PRAYARACH, PH.D.
Multiple Regression Analysis I. Analysis of Data III. Dummy Variable II. Hypothesis Testing IV. Research & Group Work 21 KULKUNYA PRAYARACH, PH.D.
Multiple Regression Analysis I. Analysis of Data III. Dummy Variable II. Hypothesis Testing IV. Research & Group Work 22 KULKUNYA PRAYARACH, PH.D.
Multiple Regression Analysis I. Analysis of Data III. Dummy Variable II. Hypothesis Testing IV. Research & Group Work WORK SHOP #1 23 KULKUNYA PRAYARACH, PH.D.
Multiple Regression Analysis I. Analysis of Data III. Dummy Variable II. Hypothesis Testing 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 R 2 (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 24 KULKUNYA PRAYARACH, PH.D.
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