Economics: Classical Linear Regression & Hypothesis Testing, Study notes of Probability and Statistics

Download Economics: Classical Linear Regression & Hypothesis Testing and more Study notes Probability and Statistics in PDF only on Docsity! Economics 209 Probability and Statistics Handout # 4 Regression The Classical Linear Regression Model We make the following assumptions. 1. or 2. 3. 4. 5. n > k 6. The explanatory variables each have positive finite variance 7. There is no perfect multicolinearity 8. In addition, we frequently make the assumption that the explanatory variables are non stochastic. 9. We estimate the model by ordinary least squares: OLS 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