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This economics handout from economics 210 covers the classical linear regression model and the classical normal linear regression model. It explains the assumptions made, the method of estimation, and the use of t-ratios for testing hypotheses and finding confidence intervals. The document also discusses extensions to non-linear equations, including reciprocal, polynomial, log-log, and semi-log models.
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Economics 210 Econometrics
The Classical Linear Regression Model
We make the following assumptions. ( Gujarati pg 65-75):
The estimated coefficients are random variables. It can be readily shown that
This last result says that is the Best Linear Unbiased Estimator, BLUE, of. This can be stated more generally. Let be any linear function of the coefficients for which a linear unbiased estimator exists. Then is the best linear unbiased estimator of.
The Classical Normal Linear Regression (CNLR) model. If in addition to the above assumptions we assume.
we get the classical normal linear regression model. In this case
Substituting an appropriate estimator for we get the t ratio
We use the t-ratio to test hypotheses about and find confidence intervals for the coefficients.
We estimate by
Extensions: Non-linear equations (Linear in parameters).
(Note that in this formulation is the elasticity of Y with respect to xj.)
4 Semi-log
Note: is equal to the percentage change in Y associated with a unit change in xj. This form of the semi-log equation is widely used in applications involving growth and interest. Semi-log
5 Linear trend
