1. GRA 6020 Multivariate Statistics Regression examples Ulf H. Olsson Professor of Statistics

2. Ulf H. Olsson Regression Analysis

3. Ulf H. Olsson Regression analysis OLS Regression parameter St.error T-value P-value Confidence interval R-sq R-sq.adj F-value The error term

4. Ulf H. Olsson Classical Assumptions Y is stochastic, x1, x2,….,xk are not Linearity in the parameters The error term has const.variance The error term is norm. Distributed with expectation equal to zero The error terms are independent The x-variables are linearly independent

5. Ulf H. Olsson GAUSS-MARKOV OLS is BLUE given the Classical Assumptions B = Best L=Linear U=Unbiased E=Estimator

6. Ulf H. Olsson TSLS If the error term is correlated with one or more of the independent variables; The OLS estimate is not consitent, i.e., it is biased even in large samples. If there are instrument variables, that are not correlated with the error term; The TSLS estimator can be used to estimate the Betas consistently. The TSLS is a two-step OLS procedure For every x-variable which is correlated with the error term there must be at least one instrument variable outside the set of x-variables

7. Ulf H. Olsson Regression Analysis The error term has constant variance The error term follows a normal distribution with expectation equal to zero The x-variables are independent of the error term The x-variables are linearly independent

8. Ulf H. Olsson Klein’s equations