多元统计典型相关分析实例(共23页)

1、精选优质文档-倾情为你奉上1、对体力测试（共7项指标）及运动能力测试（共5项指标）两组指标进行典型相关分析Run MATRIX procedure:Correlations for Set-1 X1 X2 X3 X4 X5 X6 X7X1 1.0000 .2701 .1643 -.0286 .2463 .0722 -.1664X2 .2701 1.0000 .2694 .0406 -.0670 .3463 .2709X3 .1643 .2694 1.0000 .3190 -.2427 .1931 -.0176X4 -.0286 .0406 .3190 1.0000 -.0370 .0524 .

2、2035X5 .2463 -.0670 -.2427 -.0370 1.0000 .0517 .3231X6 .0722 .3463 .1931 .0524 .0517 1.0000 .2813X7 -.1664 .2709 -.0176 .2035 .3231 .2813 1.0000Correlations for Set-2 X8 X9 X10 X11 X12X8 1.0000 -.4429 -.2647 -.4629 .0777X9 -.4429 1.0000 .4989 .6067 -.4744X10 -.2647 .4989 1.0000 .3562 -.5285X11 -.462

3、9 .6067 .3562 1.0000 -.4369X12 .0777 -.4744 -.5285 -.4369 1.0000两组变量的相关矩阵说明，体力测试指标与运动能力测试指标是有相关性的。Correlations Between Set-1 and Set-2 X8 X9 X10 X11 X12X1 -.4005 .3609 .4116 .2797 -.4709X2 -.3900 .5584 .3977 .4511 -.0488X3 -.3026 .5590 .5538 .3215 -.4802X4 -.2834 .2711 -.0414 .2470 -.1007X5 -.4295 -

4、.1843 -.0116 .1415 -.0132X6 -.0800 .2596 .3310 .2359 -.2939X7 -.2568 .1501 .0388 .0841 .1923上面给出的是两组变量间各变量的两两相关矩阵，可见体力测试指标与运动能力测试指标间确实存在相关性，这里需要做的就是提取出综合指标代表这种相关性。Canonical Correlations1 .8482 .7073 .6484 .3515 .290上面是提取出的5个典型相关系数的大小，可见第一典型相关系数为0.848，第二典型相关系数为0.707，第三典型相关系数为0.648，第四典型相关系数为0. 351，第五典

5、型相关系数为0. 290。Test that remaining correlations are zero: Wilks Chi-SQ DF Sig.1 .065 83.194 35.000 .0002 .233 44.440 24.000 .0073 .466 23.302 15.000 .0784 .803 6.682 8.000 .5715 .916 2.673 3.000 .445上表为检验各典型相关系数有无统计学意义，可见第一、第二典型相关系数有统计学意义，而其余典型相关系数则没有。Standardized Canonical Coefficients for Set-1 1 2

6、3 4 5X1 .475 .115 .391 -.452 -.462X2 .190 -.565 -.774 .307 .489X3 .634 .048 .288 .321 -.276X4 .040 .080 -.400 -.906 .422X5 .233 .773 -.681 .459 .233X6 .117 .148 .425 .141 .649X7 .038 -.394 .025 -.103 -1.029Raw Canonical Coefficients for Set-1 1 2 3 4 5X1 .141 .034 .116 -.134 -.137X2 .026 -.076 -.104

7、 .041 .066X3 .040 .003 .018 .020 -.018X4 .008 .015 -.075 -.169 .079X5 .016 .054 -.047 .032 .016X6 .020 .025 .071 .024 .109X7 .005 -.048 .003 -.013 -.126上面为各典型变量与变量组1中各变量间标化与未标化的系数列表，由此我们可以写出典型变量的转换公式(标化的)为：L1=0.475X1+0.19X2+0.634X3+0.04X4+0.233X5+0.117X6+0.038X7余下同理。Standardized Canonical Coefficien

8、ts for Set-2 1 2 3 4 5X8 -.505 -.659 .577 .186 .631X9 .209 -1.115 .207 -.775 -.292X10 .365 -.262 .188 1.153 -.154X11 -.068 -.034 -.579 .340 1.181X12 -.372 -.896 -.649 .569 -.124Raw Canonical Coefficients for Set-2 1 2 3 4 5X8 -1.441 -1.879 1.647 .531 1.798X9 .005 -.026 .005 -.018 -.007X10 .133 -.095

9、 .069 .419 -.056X11 -.018 -.009 -.153 .090 .312X12 -.012 -.029 -.021 .018 -.004Canonical Loadings for Set-1 1 2 3 4 5X1 .689 .235 .099 -.150 -.112X2 .526 -.625 -.408 .225 .237X3 .741 -.212 .263 -.042 .001X4 .242 -.032 -.298 -.809 .182X5 .200 .705 -.558 .257 -.161X6 .364 -.096 .191 .224 .476X7 .115 -

10、.259 -.437 .053 -.471Cross Loadings for Set-1 1 2 3 4 5X1 .584 .166 .064 -.053 -.032X2 .446 -.442 -.265 .079 .069X3 .629 -.150 .170 -.015 .000X4 .205 -.023 -.193 -.284 .053X5 .170 .498 -.362 .090 -.047X6 .309 -.068 .124 .079 .138X7 .098 -.183 -.283 .019 -.136上表为第一变量组中各变量分别与自身、相对的典型变量的相关系数，可见它们主要和第一对

11、典型变量的关系比较密切。Canonical Loadings for Set-2 1 2 3 4 5X8 -.692 -.149 .654 .111 .244X9 .750 -.550 .001 -.346 .127X10 .776 -.183 .275 .538 .020X11 .585 -.108 -.371 -.054 .711X12 -.674 -.265 -.548 .193 -.371Cross Loadings for Set-2 1 2 3 4 5X8 -.587 -.106 .424 .039 .071X9 .636 -.389 .001 -.121 .037X10 .658

12、 -.129 .178 .189 .006X11 .496 -.076 -.240 -.019 .206X12 -.571 -.187 -.355 .068 -.108上表为第二变量组中各变量分别与自身、相对的典型变量的相关系数，结论与前相同。下面即将输出的是冗余度(Redundancy)分析结果，它列出各典型相关系数所能解释原变量变异的比例，可以用来辅助判断需要保留多少个典型相关系数。 Redundancy Analysis:Proportion of Variance of Set-1 Explained by Its Own Can. Var. Prop VarCV1-1 .221CV1

13、-2 .152CV1-3 .125CV1-4 .121CV1-5 .082首先输出的是第一组变量的变化可被自身的典型变量所解释的比例，可见第一典型变量解释了总变化的22.1，第二典型变量能解释15.2，第三典型变量只能解释12.5，第四典型变量只能解释12.1，第五典型变量只能解释8.2。Proportion of Variance of Set-1 Explained by Opposite Can.Var. Prop VarCV2-1 .159CV2-2 .076CV2-3 .052CV2-4 .015CV2-5 .007上表为第一组变量的变化能被它们相对的典型变量所解释的比例，可见第五典

14、型变量的解释度非常小。Proportion of Variance of Set-2 Explained by Its Own Can. Var. Prop VarCV2-1 .488CV2-2 .088CV2-3 .188CV2-4 .092CV2-5 .144Proportion of Variance of Set-2 Explained by Opposite Can. Var. Prop VarCV1-1 .351CV1-2 .044CV1-3 .079CV1-4 .011CV1-5 .012- END MATRIX -2、Run MATRIX procedure:Correlati

15、ons for Set-1 X1 X2 X3 X4X1 1.0000 .3588 .7417 .5694X2 .3588 1.0000 .4301 .3673X3 .7417 .4301 1.0000 .4828X4 .5694 .3673 .4828 1.0000Correlations for Set-2 X5 X6 X7 X8 X9 X10 X11 X12X5 1.0000 .7147 .8489 .8827 .6935 .8956 .9004 .8727X6 .7147 1.0000 .7273 .8328 .7864 .8144 .6825 .7846X7 .8489 .7273 1

16、.0000 .8980 .6447 .9150 .7766 .9073X8 .8827 .8328 .8980 1.0000 .6838 .9553 .8446 .9080X9 .6935 .7864 .6447 .6838 1.0000 .7071 .7530 .7475X10 .8956 .8144 .9150 .9553 .7071 1.0000 .8739 .9307X11 .9004 .6825 .7766 .8446 .7530 .8739 1.0000 .7981X12 .8727 .7846 .9073 .9080 .7475 .9307 .7981 1.0000以上，两组变量

17、的相关矩阵说明，农村居民收入与农村居民生活费支出是有相关性的。Correlations Between Set-1 and Set-2 X5 X6 X7 X8 X9 X10 X11 X12X1 .8368 .8523 .8645 .9453 .6702 .9195 .7682 .8736X2 .6060 .3903 .4852 .4397 .5548 .4567 .5096 .5262X3 .8135 .5256 .6417 .8239 .5093 .8138 .8242 .7513X4 .6166 .7269 .5385 .6062 .5615 .6602 .6027 .6543上面给出的是

18、两组变量间各变量的两两相关矩阵，可见体力测试指标与运动能力测试指标间确实存在相关性，这里需要做的就是提取出综合指标代表这种相关性。Canonical Correlations1 .9812 .9063 .6314 .571上面是提取出的5个典型相关系数的大小，可见第一典型相关系数为0. 981，第二典型相关系数为0. 906，第三典型相关系数为0. 631，第四典型相关系数为0. 571。Test that remaining correlations are zero: Wilks Chi-SQ DF Sig.1 .003 132.620 32.000 .0002 .072 59.110 2

19、1.000 .0003 .405 20.310 12.000 .0614 .674 8.871 5.000 .114上表为检验各典型相关系数有无统计学意义，可见第一、第二典型相关系数有统计学意义，而其余典型相关系数则没有。Standardized Canonical Coefficients for Set-1 1 2 3 4X1 -.536 -1.056 -.468 .965X2 -.059 -.293 -.809 -.732X3 -.399 1.480 .154 -.142X4 -.158 -.284 1.023 -.635Raw Canonical Coefficients for Se

20、t-1 1 2 3 4X1 -.001 -.002 -.001 .002X2 .000 -.001 -.002 -.002X3 -.009 .033 .003 -.003X4 -.004 -.007 .026 -.016上面为各典型变量与变量组1中各变量间标化与未标化的系数列表，由此我们可以写出典型变量的转换公式(标化的)为：L1=-0.536X1-0.059X2-0.399X3-0.158X4余下同理。Standardized Canonical Coefficients for Set-2 1 2 3 4X5 -.233 -.151 -1.215 -1.177X6 -.020 -1.459

21、 1.647 -.413X7 .414 -1.577 -1.050 .472X8 -.576 1.319 -1.618 2.259X9 .070 -.071 -1.516 -.028X10 -.388 .683 .797 .562X11 -.034 .521 1.527 -.667X12 -.218 .346 1.283 -1.210Raw Canonical Coefficients for Set-2 1 2 3 4X5 -.001 -.001 -.005 -.005X6 .000 -.030 .034 -.009X7 .003 -.012 -.008 .003X8 -.011 .024

22、-.030 .042X9 .003 -.003 -.068 -.001X10 -.012 .022 .026 .018X11 -.001 .009 .025 -.011X12 -.009 .015 .055 -.052Canonical Loadings for Set-1 1 2 3 4X1 -.943 -.225 -.062 .235X2 -.481 -.139 -.535 -.680X3 -.898 .434 -.048 -.048X4 -.678 -.279 .533 -.423Cross Loadings for Set-1 1 2 3 4X1 -.925 -.204 -.039 .

23、134X2 -.472 -.126 -.338 -.388X3 -.881 .393 -.030 -.027X4 -.665 -.253 .337 -.241上表为第一变量组中各变量分别与自身、相对的典型变量的相关系数，可见它们主要和第一对典型变量的关系比较密切。Canonical Loadings for Set-2 1 2 3 4X5 -.924 -.036 -.200 -.251X6 -.821 -.489 .173 .001X7 -.850 -.285 -.234 .080X8 -.976 -.088 -.082 .155X9 -.698 -.304 -.174 -.330X10 -.

24、968 -.097 .000 .032X11 -.883 .097 -.046 -.231X12 -.921 -.166 -.079 -.113Cross Loadings for Set-2 1 2 3 4X5 -.907 -.032 -.126 -.143X6 -.805 -.443 .109 .000X7 -.833 -.258 -.148 .046X8 -.957 -.080 -.052 .088X9 -.684 -.276 -.110 -.188X10 -.949 -.088 .000 .018X11 -.866 .088 -.029 -.132X12 -.903 -.151 -.0

25、50 -.064上表为第二变量组中各变量分别与自身、相对的典型变量的相关系数，结论与前相同。下面即将输出的是冗余度(Redundancy)分析结果，它列出各典型相关系数所能解释原变量变异的比例，可以用来辅助判断需要保留多少个典型相关系数。 Redundancy Analysis:Proportion of Variance of Set-1 Explained by Its Own Can. Var. Prop VarCV1-1 .597CV1-2 .084CV1-3 .144CV1-4 .175首先输出的是第一组变量的变化可被自身的典型变量所解释的比例，可见第一典型变量解释了总变化的59.7

26、，第二典型变量能解释8.4，第三典型变量只能解释14.4，第四典型变量只能解释17.5。Proportion of Variance of Set-1 Explained by Opposite Can.Var. Prop VarCV2-1 .574CV2-2 .069CV2-3 .057CV2-4 .057上表为第一组变量的变化能被它们相对的典型变量所解释的比例，可见第一典型变量的解释度较大，其余相差不大。Proportion of Variance of Set-2 Explained by Its Own Can. Var. Prop VarCV2-1 .782CV2-2 .059CV2

27、-3 .021CV2-4 .034Proportion of Variance of Set-2 Explained by Opposite Can. Var. Prop VarCV1-1 .752CV1-2 .048CV1-3 .008CV1-4 .011- END MATRIX -习题10.3、Run MATRIX procedure:Correlations for Set-1 x1 x2x1 1.0000 .7346x2 .7346 1.0000Correlations for Set-2 y1 y2y1 1.0000 .8393y2 .8393 1.0000从这里开始进行分析，首先给

28、出的是两组变量内部各自的相关矩阵，可见头宽和头长是有相关性的。Correlations Between Set-1 and Set-2 y1 y2x1 .7108 .7040x2 .6932 .7086上面给出的是两组变量间各变量的两两相关矩阵，可见兄弟的头型指标间确实存在相关性，这里需要做的就是提取出综合指标代表这种相关性。Canonical Correlations1 .7892 .054上面是提取出的两个典型相关系数的大小，可见第一典型相关系数为0.789，第二典型相关系数为0.054。Test that remaining correlations are zero: Wilks Ch

29、i-SQ DF Sig.1 .377 20.964 4.000 .0002 .997 .062 1.000 .803上表为检验各典型相关系数有无统计学意义，可见第一典型相关系数有统计学意义，而第二典型相关系数则没有。Standardized Canonical Coefficients for Set-1 1 2x1 -.552 -1.366x2 -.522 1.378Raw Canonical Coefficients for Set-1 1 2x1 -.057 -.140x2 -.071 .187上面为各典型变量与变量组1中各变量间标化与未标化的系数列表，由此我们可以写出典型变量的转换公式(标化的)为：L1=0.552*xl+0.522*x2L2=1.366*xl-1.378*x2Standardized Canonical Coefficients for Set-2 1 2y1 -.504 -1.769y2 -.538 1.7