1. GRA 6020 Multivariate Statistics The regression model OLS Regression 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 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 The dependent variable is normally distributed

5. 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

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

7. Ulf H. Olsson Econometric Model Klein’s Model (1950 )

8. Ulf H. Olsson Making Numbers (OLS and TSLS) CT = 16.237+0.193*PT+0.0899*PT_1+0.796*WT, R² = 0.981 (1.303) (0.0912) (0.0906) (0.0399) 12.464 2.115 0.992 19.933 CT = 15.324+0.0763*PT+0.186*PT_1+0.828*WT, R² = 0.979 (1.453) (0.138) (0.146) (0.0439) 10.546 0.553 1.275 18.844

9. Ulf H. Olsson Estimate Klein’s equations by OLS Regression