GRA 6020 Multivariate Statistics The regression model OLS

GRA 6020 Multivariate Statistics The regression model OLS Regression Ulf H. Olsson Professor of Statistics

Regression Analysis Ulf H. Olsson

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

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

Classical Assumptions • Y is stochastic, x 1, x 2, …. , 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 Ulf H. Olsson

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

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

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