# Matrix Notation and Regression Analysis

This article covers the basics of matrix notation and regression analysis, including OLS, t-tests, and FLM. It also discusses dimensionality and sample sizes.

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## About Matrix Notation and Regression Analysis

PowerPoint presentation about 'Matrix Notation and Regression Analysis'. This presentation describes the topic on This article covers the basics of matrix notation and regression analysis, including OLS, t-tests, and FLM. It also discusses dimensionality and sample sizes.. The key topics included in this slideshow are . Download this presentation absolutely free.

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1. 1 y = 0 + 1 x 1 + 2 x 2 + . . . k x k + u 6 . 8

2. 2 - , u , - , . , u x , . : , .

3. 3 . x x 1 x 2 y f( y|x ) x 3 . . E( y | x ) = 0 + 1 x

4. 4 ; OLS , . . , t F LM .

5.

6.

7. 7 , . . n /( n k 1 ) n , 1.

8. 8 F t t - , . Stata, robust reg . F Wald .

9. 9 LM OLS . (q ) 1 , 2 , , q . 1 1 , 2 , , q , . LM n SSR 1 , SSR 1 2 - q .

10. 10 H 0 : Var( u|x 1 , x 2 ,, x k ) = 2 , H 0 : E( u 2 |x 1 , x 2 ,, x k ) = E( u 2 ) = 2 u 2 x j , . , u 2 = 0 + 1 x 1 ++ k x k + v , H 0 : 1 = 2 = = k = 0

11. 11 Breusch-Pagan , OLS . x s, R 2 F LM . F F , F = [ R 2 / k ]/[(1 R 2 )/( n k 1)], F k, n k - 1 LM LM = nR 2 , 2 k

12. 12 White Breusch-Pagan . White - x . F LM x j , x j 2 , x j x h . .

13. 13 White OLS, , x . , 2 , 2 x j , x j 2 , x j x h , 2 R 2 F LM . .

14. 14 OLS , , OLS

15. 15 Var( u| x ) = 2 h ( x ), h ( x ) h i E( u i / h i | x ) = 0, h i x , Var( u i / h i | x ) = 2 , Var( u| x ) = 2 h i , h i .

16. 16 OLS (GLS) GLS ( BLUE , . 3 28) GLS (WLS) Var( u i | x i )

17. 17 OLS , , ( 1/ h i )

18. 18 WLS () WLS Var( u i | x i ) ,

19. 19 , h ( x i ) , , Var( u| x ) = 2 exp( 0 + 1 x 1 + + k x k ) ,

20. 20 ( ) u 2 = 2 exp( 0 + 1 x 1 + + k x k ) v E( v| x ) = 1, E( v ) = 1 ln( u 2 ) = + 1 x 1 + + k x k + e E( e ) = 0 e x , u , OLS

21. 21 ( ) , h = exp( ) , , ; OLS , , , log ln( 2 ) , WLS 1/exp( )

22. 22 WLS () F WLS, WLS WLS - OLS ,

23. 23 Eview Commands Heteroskedasticity -> , Equation : . View/ Residual Test s/ Heteroskedasticity Tests