典型相關(guān)分析實(shí)現(xiàn)的兩種方法：CANCORR過(guò)程利用“分析員應(yīng)用”系統(tǒng)完成典型相關(guān)分析典型相關(guān)分析過(guò)程介紹1啟動(dòng)“分析員應(yīng)用”，打開(kāi)SAS數(shù)據(jù)集；Solution→Analysis→AnalystFile→OpenbySASName…→選數(shù)據(jù)集在“分析員應(yīng)用”菜單欄目中選擇

Statistics→Multivarite

→canonicalcorrelation；利用“分析員應(yīng)用”系統(tǒng)完成典型相關(guān)分析的具體步驟：2在彈出的典型相關(guān)分析主窗口中分別選擇兩組變量；在主窗口下方按Statistics鍵,選擇取幾對(duì)典型相關(guān)變量、典型變量的前綴、回歸分析等；在主窗口下方按Plots鍵,選擇繪制前幾對(duì)典型變量的散點(diǎn)圖；在主窗口下方按SaveData鍵,選擇是否存貯典型變量得分及統(tǒng)計(jì)量；查看計(jì)算結(jié)果.3一、CANCORR過(guò)程的功能

設(shè)和是兩組隨機(jī)變量，典型相關(guān)分析是處理兩組變量間相關(guān)關(guān)系的方法.簡(jiǎn)單相關(guān)和多重相關(guān)都是典型相關(guān)的特殊情況，此時(shí)兩組變量中有一組或兩組只含一個(gè)變量.CANCORR過(guò)程可完成以下幾方面計(jì)算：51、完成兩組變量間的典型相關(guān)分析.用戶(hù)可根據(jù)實(shí)際問(wèn)題的需要規(guī)定哪些變量構(gòu)成第一組，哪些是第二組.典型變量的名字用戶(hù)也可以自己規(guī)定.62、CANCORR過(guò)程可以檢驗(yàn)一些假設(shè)，如在總體中，每個(gè)典型相關(guān)及所有較小的典型相關(guān)為0.進(jìn)行檢驗(yàn)時(shí)CANCORR過(guò)程使用F近似統(tǒng)計(jì)量，在小樣本情況下，F(xiàn)近似比使用2近似有較好的結(jié)果.進(jìn)行檢驗(yàn)時(shí)要求兩組變量中至少有一組近似正態(tài)分布，以便得到的顯著性概率值（p值）有效.73、該過(guò)程可以計(jì)算標(biāo)準(zhǔn)化和沒(méi)有標(biāo)準(zhǔn)化的典型變量的系數(shù)，典型變量和原始變量的所有相關(guān)；同時(shí)也可以進(jìn)行典型冗余分析.85、該過(guò)程可以生成許多計(jì)算結(jié)果.包括簡(jiǎn)單統(tǒng)計(jì)量、相關(guān)陣、典型相關(guān)；檢驗(yàn)典型相關(guān)系數(shù)為0的檢驗(yàn)統(tǒng)計(jì)量，典型結(jié)構(gòu)等；還有用一組變量預(yù)測(cè)另一組變量的回歸結(jié)果.該過(guò)程還可以生成兩個(gè)輸出數(shù)據(jù)集：一個(gè)包含每個(gè)觀測(cè)在典型變量上得分的數(shù)據(jù)集；另一個(gè)包含有關(guān)統(tǒng)計(jì)量的輸出集.10PROCCANCORR<options>;必需的語(yǔ)句

WITHvariables;

VARvariables;

PARTIALvariables;

FREQvariables;可選擇的語(yǔ)句

WEIGHTvariables;

BYvariables;二、基本語(yǔ)句12AllCorr----輸出原始變量之間的相關(guān)系數(shù).Ncan=n----規(guī)定要求輸出的典型變量的個(gè)數(shù).NoprintShortSimpleVdep|wreg----要求用var變量作為因變量，而with變量作為回歸量的多元回歸分析.Wdep|vreg----要求用with變量作為因變量，而var變量作為回歸量的多元回歸分析.14案例1研究三個(gè)生理指標(biāo)和三個(gè)訓(xùn)練指標(biāo)之間的相關(guān)關(guān)系(見(jiàn)教材329頁(yè)例10.3.2，也是SAS中典型相關(guān)的例題).三個(gè)生理指標(biāo)：weight:體重

waist:腰圍

pulse:脈搏三個(gè)訓(xùn)練指標(biāo)：chins:單杠

situps:仰臥起坐次數(shù)

jumps:跳高15VARVariables3WITHVariables3Observations20輸出結(jié)果16MeansandStandardDeviationsVariableMeanStandardDeviationweight178.60000024.690505waist35.4000003.201973pulse56.1000007.210373chins9.4500005.286278situps145.55000062.566575jumps70.30000051.27747017CorrelationsAmongtheVARVariables

weightwaistpulseweight1.00000.8702-0.3658waist0.87021.0000-0.3529pulse-0.3658-0.35291.000018CorrelationsBetweentheVARVariablesandtheWITHVariables

chinssitupsjumpsweight-0.3897-0.4931-0.2263waist-0.5522-0.6456-0.1915pulse0.15060.22500.034920

Canonical

CorrelationAdjusted

Canonical

CorrelationApproximate

Standard

ErrorSquared

Canonical

Correlation10.7956080.7540560.0841970.63299220.200556-.0763990.2201880.04022330.072570.0.2282080.00526621

Test

of

H0:

The

canonical

correlations

in

the

current

row

and

all

that

follow

are

zero

Likelihood

RatioApproximate

FValueNum

DFDen

DFPr

>

F10.350390532.05934.2230.063520.954722660.184300.949130.994733550.081160.774823MultivariateStatisticsandFApproximationsS=3M=-0.5N=6StatisticValueFValueNum

DFDen

DFPr

>

FWilks'Lambda0.350390532.05934.2230.0635Pillai'sTrace0.678481511.569480.1551Hotelling-LawleyTrace1.771941462.64919.0530.0357Roy'sGreatestRoot1.724738749.203160.0009NOTE:FStatisticforRoy'sGreatestRootisanupperbound.24RawCanonicalCoefficientsfortheWITHVariables

EXER1EXER2EXER3chins-0.066113986-0.071041211-0.245275347situps-0.0168462310.00197374540.0197676373jumps0.01397156890.0207141063-0.00816747226StandardizedCanonicalCoefficients

fortheVARVariables

PHYS1PHYS2PHYS3weight-0.7754-1.8844-0.1910waist1.57931.18060.5060pulse-0.0591-0.23111.050827StandardizedCanonicalCoefficients

fortheWITHVariables

EXER1EXER2EXER3chins-0.3495-0.3755-1.2966situps-1.05400.12351.2368jumps0.71641.0622-0.418828CorrelationsBetweentheWITHVariables

andTheirCanonicalVariables

EXER1EXER2EXER3chins-0.72760.2370-0.6438situps-0.81770.57300.0544jumps-0.16220.9586-0.233930CorrelationsBetweentheVARVariables

andtheCanonicalVariablesofthe

WITHVariables

EXER1EXER2EXER3weight0.4938-0.1549-0.0098waist0.7363-0.0757-0.0022pulse-0.26480.00830.068431CorrelationsBetweentheWITHVariables

andtheCanonicalVariablesofthe

VARVariables

PHYS1PHYS2PHYS3chins-0.57890.0475-0.0467situps-0.65060.11490.0040jumps-0.12900.1923-0.0170第一對(duì)典型變量為身材與運(yùn)動(dòng)能力.32CanonicalRedundancyAnalysisStandardizedVarianceoftheVARVariablesExplainedbyCanonicalVariable

NumberTheirOwn

CanonicalVariablesCanonical

R-SquareTheOpposite

CanonicalVariablesProportionCumulative

ProportionProportionCumulative

Proportion10.45080.45080.63300.28540.285420.24700.69780.04020.00990.295330.30221.00000.00530.00160.296933StandardizedVarianceoftheWITHVariablesExplainedbyCanonicalVariable

NumberTheirOwn

CanonicalVariablesCanonical

R-SquareTheOpposite

CanonicalVariablesProportionCumulative

ProportionProportionCumulative

Proportion10.40810.40810.63300.25840.258420.43450.84260.04020.01750.275830.15741.00000.00530.00080.2767CanonicalRedundancyAnalysis34RawVarianceoftheWITHVariablesExplainedbyCanonicalVariable

NumberTheirOwn

CanonicalVariablesCanonical

R-SquareTheOpposite

CanonicalVariablesProportionCumulative

ProportionProportionCumulative

Proportion10.41110.41110.63300.26020.260220.56350.97460.04020.02270.282930.02541.00000.00530.00010.283035RawVarianceoftheVARVariablesExplainedbyCanonicalVariable

NumberTheirOwn

CanonicalVariablesCanonical

R-SquareTheOpposite

CanonicalVariablesProportionCumulative

ProportionProportionCumulative

Proportion10.37120.37120.63300.23490.234920.54360.91480.04020.02190.256830.08521.00000.00530.00040.257336SquaredMultipleCorrelationsBetween

theVARVariablesandtheFirstMCanonical

VariablesoftheWITHVariablesM123weight0.24380.26780.2679waist0.54210.54780.5478pulse0.07010.07020.074937SquaredMultipleCorrelationsBetween

theWITHVariablesandtheFirstM

CanonicalVariablesoftheVARVariablesM123chins0.33510.33740.3396situps0.42330.43650.4365jumps0.01670.05360.053938案例2研究工作滿(mǎn)意度和工作特征的相關(guān)關(guān)系(SAS系統(tǒng)中典型相關(guān)關(guān)系的開(kāi)始案例).Jobcharacteristics:(1)taskvariety:degreeofvarietyinvolvedintasks,expressedasap