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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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
