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## Applied Econometrics Second edition

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**Applied EconometricsSecond edition**Dimitrios Asteriou and Stephen G. Hall**MULTIPLE REGRESSION**1. The Multiple Regression Model 2. The OLS Method of Estimation 3. The R2 and the Adjusted R2 4. Hypothesis Testing 5. How to Estimate a Simple Regression in EViews**Learning Objectives**• Derive mathematically the regression coefficients of a multiple regression model. • Understand the difference between the R2 and the adjusted R2 for a multiple regression model. • Appreciate the importance of the various selection criteria for the best regression model. • Conduct hypothesis testing and test linear restrictions, omitted and redundant variables as well as the overall significance of the explanatory variables.**Learning Objectives (2)**• Obtain the output of a multiple regression estimation using econometric software. • Interpret and discuss the results of a multiple regression estimation output.**Multiple Regression Derivation of the OLS**• The three variables case (explain on board) • The k-variables case (explain on board) • Requires matrix algebra and it is quite complicated • Luckily Eviews, Mfit and Stata give results very quickly and efficiently (always correct calculations)**R2and adjusted R2**• R2measures goodness of fit as in Simple Regression • However, it cannot be used for comparing two different equations containing different • numbers of explanatory variables. • When adding more explanatory variables R2, will always be increased. • Therefore we need a different measure (the adjusted R2)**R2and adjusted R2**• R2 = ESS/TSS = 1 − RSS/TSS • Adj R2= • Similar to R2but adjusts for degrees of freedom**Criteria for Model Selection**• Akaike Information Criterion (AIC) • Finite Prediction Error (FPE) • Schwarz Bayesian Criterion (SBC) • Hannan and Quin Criterion (HQC)**Multiple Regression in EViews**• Step 1 Open EViews. • Step 2 Click File/New/Workfilein order to create a new file or File/Open to open an existing file. • Step 3 Enter the data • Step 4 Type in the EViews command line: ls y c x2 x3 . . . xk (press ‘enter’)**Hypothesis Testing**• Testing Individual Coefficients (t-tests) • Testing for Linear Restrictions (Wald Test) • Cobb Douglas Production Function • Testing for the Overall Significance (F-test) • Testing for Omitted Variables (Wald Test) • Testing for Redundant Variables (Wald Test) • Explain all the tests on board…