Applied Econometrics

Applied EconometricsSecond edition

Dimitrios Asteriou and Stephen G. Hall

Applied Econometrics

MULTIPLE REGRESSION

1. The Multiple Regression Model 2. The OLS Method of Estimation3. The R2 and the Adjusted R2

4. Hypothesis Testing5. How to Estimate a Simple Regression in EViews

Applied Econometrics

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.

Applied Econometrics

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.

Applied Econometrics

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)

Applied Econometrics

R2 and adjusted R2

• R2 measures 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)

Applied Econometrics

R2 and adjusted R2

• R2 = ESS/TSS = 1 − RSS/TSS

• Adj R2=

• Similar to R2 but adjusts for degrees of freedom

)(

)1(1

)1/(

)/(1

knTSS

nRSS

nTSS

knRSS

Applied Econometrics

Criteria for Model Selection• Akaike Information Criterion (AIC)

• Finite Prediction Error (FPE)

• Schwarz Bayesian Criterion (SBC)

• Hannan and Quin Criterion (HQC)

Applied Econometrics

Multiple Regression in EViews• Step 1 Open EViews.• Step 2 Click File/New/Workfile in 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’)

Applied Econometrics

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…