簡單相關分析 [教程]

1、 N YX YXCov Yi N i Xi XY 1 ),( 1 1 n YYXX S n i ii XY 11.866110/775 1 )( 1 n YYXX S n i ii XY YX XY Y Y X X XY YX E N i Yi N i Xi Yi N i Xi XY Y N X N YX N 1 2 1 2 1 11 1 ),( ,),( 11nn yxyx YX XY XY SS S r 之樣本標準差為 之樣本標準差為 之樣本共變異數(shù)為X與 Y:S X:S YS Y X XY : 2 2 1 2 * nt n r r t XY XY 306.2 025.0,8 * tt 8

2、 210 1 2 * t r r t XY XY 306.232899.1 319990171.0 425265.0 210 )425265.0(1 425265.0 2 * t 425265.0 XY r r r Z r 1 1 ln 2 1 3 1 , n ZNZ r 0 0 1 1 ln 2 1 z 3 1 * n ZZ Z r 829. 0 68. 01 68. 01 ln 2 1 Zr 973. 0 75. 01 75. 01 ln 2 1 Z 8272. 0 33 1 973. 0829. 0 336 1 ZZ Z r* 96. 18272. 0 025. 0 * ZZ iii x

3、y XY ii xY 2 , i NY bXaY Y ii bxaY i y i y 2 minmin ii yyQ 2 ii bxayQ 0 0 iii ii xbxay b Q bxay a Q 2 iiii ii xbxayx xbnay xbya xnx yxnyx b i ii ; 22 222 ) 1( ) 1( x xy i ii i ii s s nxx nyyxx xx yyxx b 2 X S XY S 07. 1 2410082, 6 982410864,23 222 xnx yxnyx b i ii 32.722407.198xbya XY07. 132.72 SSES

4、SRSSTO )SSE(errortoduesquaresofsum iationvarlainedexpun y y SSRregressiontoduesquaresofsum iationvarexplainedy y )SSTO(totaltoduesquaresofsum iationvartotalyy ii i i 2 2 2 22 ynySSTO i 22 2 xnx yxnyx SSR i ii SSRSSTOSSE SSTO SSE SSTO SSR R1 2 2 22 2 22 2 2 2 22 2 11 1 XY YX XY ii ii i iii SS S n xx

5、n yy n yxnyx yny xxyxnyx SSTO SSR R 2 R 2 R ) 1/( )2/( 1 2 nSST nSSE R 47296 2 ,yi 432981047296 222 ,ynySSTO i 5031367 24100826 24981086423 2 2 22 2 . , , xnx yxnyx SSR i ii 98y 0826 2 ,xi 24x 86423,yx ii 85070 2 . SSTO SSR R 83200 9432 8496964 1 1 2 1 2 . / /. )n/(SSTO )n/(SSE R MSE n SSE Se 2 2 2

6、ii yySSE 22 ba S,Nb;S,Na 2 2 2 2 22 2 xx S S; xxn Sx S i e b i ei a b * S b t 22 n,/ * tt 2,2/ * n tt b n Stb 2 ,2 76726 0250 071 . . . S b t b * 0250 24100826 06218 22 2 2 . , . xx S S i e b 306.2t7672.6t 025.0,8 * 434617054002503062071.,. a * S a t 2,2/ * n tt 2, 2/ * n tt a n Sta 2 ,2 21 n , * F

7、MSE MSR F ) 2, 1 ( , * n FF 0 Y 0 xX ind Y 0 Y 00 bxaY 00 xYE 2 2 0 22 1 0 xx xx n S i e Y 0 220 Y /,n tY 0 Y X.Y 0713272 83120 24100826 2425 10 1 06218 1 2 2 2 2 0 22 0 . , )( . xx xx n S i e Y )17.101,97.96( 2 2 , 2 0 0 Y n tY ind Y 2 2 0 2 2 2 0 22 22 0 0 2 1 1 1 0 xx xx n S xx xx n SS S Y VarYVar Y YVar i e i ee Y e ind ind Yind 2 0 , ind Y ind XNY ind Y ind Y /,n tY 220 8933. 8 2410082, 6 2425 10 1 10621. 8 xx xx n 1 1s 2 2 2 i 2 02 e 2 Y ind )95.105,19.92( 88. 607.99 9822. 2