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

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

Ulf H. Olsson Regression Analysis

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

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

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

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 = *PT *PT_ *WT, R² = (1.303) (0.0912) (0.0906) (0.0399) CT = *PT+0.186*PT_ *WT, R² = (1.453) (0.138) (0.146) (0.0439)

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