### Chapter 04 - Multiple Regression

```Applied Econometrics
Applied Econometrics
Second edition
Dimitrios Asteriou and Stephen G. Hall
Applied Econometrics
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
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 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
Applied Econometrics
• R2 = ESS/TSS = 1 − RSS/TSS
RSS /( n  k )
TSS /( n  1)
 1
TSS ( n  k )
• Similar to R2 but adjusts for degrees of
freedom
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…
```