Introductory Econometrics

Classical Linear Regression Models and Relaxing their Assumptions

Seid Nuru [e-mail]
August 2012

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The Classical Linear Regression Models

Introduction The Simple Regression Model The Multiple Linear Regression Models Violations of the Assumptions of CLRMs

Definition
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Econometrics is the application of statistical, and mathematical techniques to the analysis of economic data with a purpose of verifying or refuting economic theories.
Theory Mathematical Model Econometric Model

As income increases, consumption also increases, but not as much as income.

yi = f ( xi ) = β0 + β1xi

y i = f ( x i ) = β0 + β1x i + εi

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The Classical Linear Regression Models

Introduction The Simple Regression Model The Multiple Linear Regression Models Violations of the Assumptions of CLRMs

Definition
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Why do we need to include the stochastic (random) component, for example in the consumption function? function?
— Omission of variables leads to misspecification problem. For example, income is not the only determinants of consumption. — There may be measurement error in collecting data. — We may use poor proxy variables. — The functional form may not be correct.

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The Classical Linear Regression Models

Introduction The Simple Regression Model The Multiple Linear Regression Models Violations of the Assumptions of CLRMs

Some Concepts: Regression, Causation, and Correlation
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Regression is estimation or prediction of the average value of a dependent variable on the basis of the fixed values of other variables. Causation comes from theory rather than statistics. Thus, regression does not necessarily imply causation. Correlation measures the strength of linear association between variables. In regression, we have stochastic dependent variable and nonnon-stochastic independent variable (fixed) while in correlation, variables involved are stochastic.

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The Classical Linear Regression Models