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Introduction to OLS Regression Model in Multivariate Statistics

Dive into the world of OLS Regression with Professor Olsson, exploring parameter estimation, error term characteristics, assumption testing, and application in econometric models.

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Introduction to OLS Regression Model in Multivariate Statistics

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  1. GRA 6020Multivariate StatisticsThe regression modelOLS Regression Ulf H. Olsson Professor of Statistics

  2. Regression Analysis Ulf H. Olsson

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

  4. 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 Regression Analysis Ulf H. Olsson

  5. 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 Classical Assumptions Ulf H. Olsson

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

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

  8. 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

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

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