Econometircs

TOPIC 02 MULTIPLE REGRESSION ANALYSIS

Wang Jia

FIN401 Financial Modeling Macau University of Science and Technology September 2009

OUTLINE

1. Motivation for Multiple Regression 2. The Linear Regression Model (with Many Regressors) 3. Recap 4. Statistical Properties of OLS

Wang Jia

Topic 2: Multiple Regression Analysis

September 2009

2

1. Motivation for Multiple Regression

MOTIVATION FOR MULTIPLE REGRESSION

Will our innovations increase is we:

grow more? employ more people? spend more money on R&D?

You consider models:

log ( y ) = β 0 + β1lsales + ε log ( y ) = α 0 + α1employ + υ log ( y ) = γ 0 + γ 1lR & D + θ

Problem: error correlated with explanatory variables in all these models

Wang Jia Topic 2: Multiple Regression Analysis September 2009 3

OUTLINE

1. Motivation for Multiple Regression 2. The Linear Regression Model (with Many Regressors)

1. Obtaining the OLS estimates 2. Interpretation of multiple regression 3. Goodness of fit

3. Recap 4. Statistical Properties of OLS

Wang Jia

Topic 2: Multiple Regression Analysis

September 2009

4

2. The Linear Regression Model (with many regressors)

THE LINEAR REGRESSION MODEL

There is an (unknown) relation in the population:

y = f ( x1 , x2 , … , xk ) + u

Steps:

Collect sample Assumptions on sampling process and on y = f x1 , x2 , … , xk + u Obtain an estimate of y = f x1 , x2 , … , xk which has desirable properties under these assumptions Hopefully, the new assumptions are more likely to hold!!!

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Wang Jia

Topic 2: Multiple Regression Analysis

September 2009

5

2. The Linear Regression Model (with many regressors)

THE LINEAR REGRESSION MODEL

As. 1: We assume that the population relation is linear:

y = β 0 + β1 x1 + β 2 x2 +… + β k xk + u

x j = independent variable j y = dependent variable u = error term β0 = intercept

Dy βj = slope of variable j Dx j

Wang Jia

Topic 2: Multiple Regression Analysis...