典型相關(guān)分析

1、武夷學(xué)院實(shí)驗(yàn)報(bào)告課程名稱：多元統(tǒng)計(jì)分析項(xiàng)目名稱：典型相關(guān)分析姓名：一專業(yè)：14信計(jì)班級(jí)：1班學(xué)號(hào)：同組成員：匚一、實(shí)驗(yàn)?zāi)康?.對(duì)典型相關(guān)分析問題的思路、理論和方法認(rèn)識(shí)；2.SPSS軟件相應(yīng)計(jì)算結(jié)果確認(rèn)與應(yīng)用；3.SPSS軟件相應(yīng)過程命令。二、實(shí)驗(yàn)內(nèi)容這里通過典型相關(guān)分析來反映我國財(cái)政收入與財(cái)政支出之間的關(guān)系。第一組反映財(cái)政收入的指標(biāo)有國內(nèi)增值稅、營業(yè)稅、企業(yè)所得稅、個(gè)人所得稅、專項(xiàng)U入及行政事業(yè)性收費(fèi)收入等，分別用X1-X6來表示。第二組反映財(cái)政支出的指標(biāo)有一般公共服務(wù)、國防、公共安全、教育、科學(xué)技術(shù)、社會(huì)保障和就業(yè)、醫(yī)療衛(wèi)生與計(jì)劃生育及節(jié)能環(huán)保等，分別用Y1-Y8來表示。原始數(shù)據(jù)如下：北京6

2、74.89103479B02.123338495.564LB9297.129.06255.82B81.18234.67設(shè)天津22S.SB425.17204.3850,31159.9023B121A4.731.6212S.164613s92.81Z河北255.3661210231.6754BO94.001B995524.1410.S82d3.CEB37.63J9.7S5；山西21465375062D2.0748B7320.47967B2B4.1355B155.09542446206十內(nèi)蒙占166.44353.0215S.2B44.97154.8212437338.105.26175.77466.

3、0731.644!遼寧24®.41657.00260.6BG4.15107.12198.(M5Q1.341199244.57669.4811B.99K占琳119.58245.K121.asOS51.40目*97267.31SOBU7.77422,0937.223E里龍江151.7326799陽印35B373.61842227BS055B173.35501.283851%上海96272037.44355.22115.68109.412B0.106.6222651B79.54257.664E江蘇K9.261072.417B3.6B264餡193.11399.60059.4122.5445

4、2.991434.99302.59KuaS51671069.975SS.BB193B4121.Ml347153aBB6.53347.7995O.O&191.873J先搬2245050226190.4643441QS.2615674469.154001637873659109E7K福建234.3155141271.0578.3778.7910734327.067.61189.44574.916D,62&江西146.43423.00138.7120.7762.96106.29337.015.95162.92S64.534632缶山節(jié)儂.55106B.33445.95msa1S3.5

5、8294127499615.2B341.8313S9.67149.14可河南202.6558179235.60476390252247B733.216.51261.221171.5280CO空刷225.68526.43215.235774B8.7326859546.494.12227.04B90.6377.216(陰南175.11461.16136.1750.9262.09176.D1628.45114.70231.09809.4555.J6以廣東1此就1636.2097468340.02213.094501099s.必17.83650.31174i.593M.94九西3375304.20*Q

6、42774407412022413.207.921%日16CB935J36小爆南3165168.9656.4611E811.171711115.404.1B65.10174.5713.B211里慶107.25424.31135.8237.5456.80359.D6276.40075141.22437.203B.6542nnill/W：£7的4M心父4i£繪于勺AOW£i實(shí)驗(yàn)步驟在SPSS中沒有提供典型相關(guān)分析的專門菜單項(xiàng)，必須采用canonicalcorrelation.sps宏來實(shí)現(xiàn)。把canonicalcorrelation.sps安裝在SPSS子目錄下。(1

7、) 按文件-新建-語法打開語法窗口，輸入下圖中的語句：尸S*音法t-即得如出也看悟法編輯器|匕IaI百文件(B»R(E杖儆£|蛆南輪帙分忻®圖塔實(shí)用程序01運(yùn)行®H跳出戰(zhàn)m內(nèi)吉用口四褥斯匕Q昌S口力同前M>.Q陽蜃縹福.|cBn0niCBlCD<TBl8tDniMliVBtM4,V1 rINCLUDECAUsersAdministratortDesklapVStatisticsl7Canonicalcarrslation.sps'.f：；=-X二一2 cancarrsatl=X1X3X4J<EXS3 ilifseQ=71

8、5;2Y3Y4Y5YBV7Y0.號(hào)PSG3江由沁£處理腓己就隹-In1Col51(2)點(diǎn)擊語句窗口“運(yùn)行”菜單中的“全部”子菜單項(xiàng)。運(yùn)行典型相關(guān)宏命令，得出結(jié)果。四、實(shí)驗(yàn)結(jié)果CorrelationsforSetTXIX2K3X425XI1.0000.9344.9779.9462.5377*5256X2.9344L0000,9151,8460.54To”6592X3,9779,91511.0000*9814.4857,4717K4.9452,8460.98141.0000.4175.3S0OX5.5377.5470.4357.41751.0000.3703.5255,6592.4717

9、.3S00.3TO31*0000表1(第一組變量的自相關(guān)系數(shù)陣)EhSc-t-2¥3¥4Y6Y7nLMX),30盟.8883.6QL1，的用.9J&4MMrz1,LUOU.tibty,rail.日皿YS.8BP31.0000.9223一6汪.7O2D.S57S.FE75T4.3X3oooo,Hoa,7744T5.740'Sl.WX).4M9一C4MYS,7043.r,J44.47491.00O0.8341.74HY?.9斑，密Ll,耶4,0330.8341l.OXX-,8180Y3,8248,9182.8076,8663,6416h747iLOOOO表2（第

10、二組變量的自相關(guān)系數(shù)陣）表1和表2分別為兩組變量的自相關(guān)系數(shù)陣。反映了各組內(nèi)變量間的相關(guān)系數(shù)。CorrelationsBetweenSet-landSet_2Y1Y2T3¥4Y5TOY7YBXL.6103.6646.B458.7572.9768.始99.8131,6667X2.7S00,8249.S106.8694.9343.6O4E.7634.777BXS-5的9,6274,8026.7067.974744514-5820一5254X4,4356,5托士,7305N翼5,9440.4C7E,5253X5.4英4.4441.5303.5856.4867.4804.490T.5S18影

11、.7173.0727.6805.7340.5414.6421.6820,7362表3（兩組變量間的相關(guān)系數(shù)陣）表3為兩組變量間的相關(guān)系數(shù)。從表中可以看出，第一組變量中的X1,X2,X3與第二組變量中的Y3,Y4,Y5之間相關(guān)系數(shù)較高，這進(jìn)一步說明需要提取典型變量來代表這種相關(guān)性。值得注意的是，由于變量間的交互作用，這個(gè)簡(jiǎn)單相關(guān)系數(shù)陣只能作為參考，不能真正反映兩組變量間的實(shí)質(zhì)聯(lián)系。CanonicalCorrelations1.9912.83S3.6854.4825.3966.218表4（典型相關(guān)系數(shù)）表4為典型相關(guān)系數(shù)。從表中可以看出，第一對(duì)典型變量相關(guān)系數(shù)為0.991,第二對(duì)典型變量相關(guān)系數(shù)為

12、0.838,以此類推共有6對(duì)典型變量的典型相關(guān)系數(shù)。由于此處的典型相關(guān)系數(shù)是從樣本數(shù)據(jù)算得的，和簡(jiǎn)單相關(guān)系數(shù)一樣，有必要進(jìn)行總體系數(shù)是否為0的檢驗(yàn)（見表5）。Testthatremainingcoirelatictisaiezero:VTilVsChi-SQDFSig*1.002142.61448.000.802.00752.40435.000.0303.32325,110加.000.4004.S1710.875L5.000.761E.3034.9328.000.7656.9531,0953.000.778表5（典型相關(guān)系數(shù)的顯著性檢驗(yàn)）表5為典型相關(guān)系數(shù)的顯著性檢驗(yàn)。該表從左至右分別為Wil

13、ks統(tǒng)計(jì)量、卡方統(tǒng)計(jì)量、自由度和伴隨概率。從表中伴隨概率可以看出，第一對(duì)和第二對(duì)典型變量的典型相關(guān)系數(shù)顯著不為0;從第三對(duì)典型變量開始,典型相關(guān)系數(shù)的p值都比較大，均相關(guān)性不顯著。因此需要第一對(duì)和第二對(duì)典型變量。5tsd旺dizedC加0micalCoefficintsfoxSat-l1234bXI2S5,4992.3844.659-1.604T.032X2Kl-L670-2.364.647,2771.410X3555.5062.501-a.504-5.512946X4.027.969-2.6643.4B3氏116.747X6OOd-b191.573一,221s65S.870KS-T066-.

14、233.440一,191l+079-,994表6（第一組典型變量的標(biāo)準(zhǔn)化系數(shù)）=湖彳036%-035溫+0.027<-Bl004<-0.066J口二0.4為留-LC70JP；+03防+0Jfi9/；-0J9Lt；-0J33/；RawCmunicalCoefficientsfur1Set-123456XI-.001.002.009.018-.006004X2-.001004-.007.002.001.003X3-.001.002.010-.033-.021004X4.000.010-.026.034.060.007X5.000-.003.008-.003.010.013猊-.001-

15、.002.004-.002.009-.009表7（第一組典型變量的為標(biāo)準(zhǔn)化系數(shù)）SienidzxdtizedC皿cmczlCoefficieiitisfor2et-212j45GY1.22L-.b24-.371L.S83,L06-3.135'建-.OQd-.E3S-L5西300.341.SOBT3-.：05.日丁,27B.901,6193,912Y4-2G1-1,GCO3.O5C,3G3-1.444L05Q-.皿.992-5*7-.311.QIS-1.785的.032.02.冏-.402k19S.210TTOdO.SL6-2.277-2.171-1.217-.22P7S-.0G3-.2

16、73.697-.E&),E=9-1,OSS表8（第二組典型變量的標(biāo)準(zhǔn)系數(shù)）耳二心2琢-。颯兄-。105彳-0J251；-0741X+03說-0.0537；&=462%-033胱+0胸月-L6K+092+0023+0卻田-0273RawCanonicalCoefficientsfor1Set-223456Y1.001-.003-.002.009.001014Y2-.018-.104-.295.039.066.117Y3-.001.007.002.008.005.024Y4-.001-.004.008.001-.004.005Y5-.008.011-.007-.004.000-.0

17、20Y6.000.000.003-.002.006.001Y7.000.006-.016-.018-.009-.002YB-.001-.004.011-.009.010-.017表9（第二組典型變量的未標(biāo)準(zhǔn)系數(shù)）表6-表9為各典型變量標(biāo)準(zhǔn)化與未標(biāo)準(zhǔn)化的系數(shù)列表。從表6和表8中第一列和第二列數(shù)據(jù)可以得到第對(duì)典型變量的線性函數(shù)，分別為1=湖X036%-Q35溫+0.027<-Q004石-。.066%4=022%-。.（4兄005工-0251；-074乂+0-03/0_04-0g詞（73=0-499<-10兄+的叫+0J<»<-0J91X-023玩%=-0.62%-

18、053/+0胸兄-1硒+（W92A；+0_023J+0卻端0273Catuouj.CalLoaditssfcrSet-l12345SXI-.g&4j.124.081,091-,034.010i.gTS-.17-oeaoio-osl.ossX3r.g?q.2M-.005-,0?l.004.02314-,925.361-,065-.021.083.MT弱一.542-.272*499-.055,234,575S6-.61-555-172-.077.2S5-.457表10（第一組的典型載荷系數(shù)）CrossLoadingsfor3*tT123456XI-.975.104,005,044-,013

19、*004X2-.969-,150-.067.005'.008.003X3-.965.179-,006-4034.001,006X4-.915.302-.045-,010.035.010X515胃-*22B*342-.027.089,125跖-.009-.4S5.117-,037.105-.100表11（A組的交叉載荷系數(shù)）CanonicalLoadingsfoxSet-2123d56Y1-1689-.629,023，055i黑9-.120Y2一.747-,532321.033.200,118Y3-.B94-.319,068.063,027.110Y4-.826501.102-,077-

20、,136.025Y5-,90S,130-.003.035,003-.072Y6-.553-,525.0830：W4.339-.033Y7-.699566，014、2561156-,016Y8-.730-,505,1561138.224-.052表12（第二組的典型載荷系數(shù)）CxqssLoadingsforSet-2123456Y1-.6S2-.527.016.027-,027-.026Y2740-,446220.016.079.025Y3-.886268.046.。如.011.024Y4-.818-,420.070-,037-,054.005Y5-.977.117-,002.017.001-.

21、016Y6-.548-.440.057-,166.134-.007Y7-.693-.474-,010123-.062二003Y8731-,423.107-,066.089-.011表13（第二組的交叉載荷系數(shù)）表10-表13為典型載荷系數(shù)與交叉載荷系數(shù)的輸出結(jié)果。其中，典型載荷系數(shù)是典型變量與本組觀測(cè)變量之間的兩兩簡(jiǎn)單相關(guān)系數(shù)。交叉載荷系數(shù)是指某一典型變量與另外一組中的觀測(cè)量之間的兩兩簡(jiǎn)單相關(guān)。ProportionVarianceofSet-1EwplairiEdbyItsOwnCan.¥az.PropVarcvi-i,733CV1-2,101CV1-3.0E0CV1-4.004CV

22、1-5,022CV1-0.091表14ProportionofVariariceofSet-1ExplainedbyOppositeCan.Var.PropVarCV2-1.720CV2-2.071CV2-3.023CV2-4.001CV2-5.003CV2-6.004表15ProportionofVarianceofSet-2ExplainedbyItsOwnCan.Var,PropVaiCV2-1,603CV2-2,238CV2-3.019CV2-4.028CV2-5.032CV2-6.006表16ProportionofVarianceofSet_2ExplainedbyOppositeCan.Vai*PropVarcvi-i.592CV1-2.167CV1-3.009CV1-