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. 5
6. 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