多元統(tǒng)計(jì)分析課程設(shè)計(jì)題目

./課程設(shè)計(jì)題目1.下表給出了1991年我國30個(gè)省、區(qū)、市城鎮(zhèn)居民的月平均消費(fèi)數(shù)據(jù),所考察的八個(gè)指標(biāo)如下〔單位均為元/人X1：人均糧食支出；X2：人均副食支出；X3：人均煙酒茶支出；X4：人均其他副食支出；X5：人均衣著商品支出；X6：人均日用品支出；X7：人均燃料支出；X8：人均非商品支出；問題：〔1求樣品相關(guān)系數(shù)矩陣R;〔2從R出發(fā)做主成分分析,求各主成分的貢獻(xiàn)率,及前兩個(gè)主成分的累積貢獻(xiàn)率；〔3求出前兩個(gè)主成分并解釋其意義.按第一主成分將30個(gè)省、區(qū)、市排序,結(jié)果如何？表一1991年我國30個(gè)省、區(qū)、市城鎮(zhèn)居民的月平均消費(fèi)數(shù)據(jù)省市X1X2X3X4X5X6X7X818.3523.537.518.6217.4210.001.0411.2129.2523.756.619.1917.7710.481.7210.5138.1930.504.729.7816.287.602.5210.3247.7329.205.429.4319.298.492.5210.0059.4227.938.208.1416.179.421.559.7669.1627.989.019.3215.999.101.8211.35710.0628.6410.5210.0516.188.391.9610.8189.0928.127.409.6217.2611.122.4912.6599.4128.205.7710.8016.3611.561.5312.17108.7028.127.2110.5319.4513.301.6611.96116.9329.854.549.4916.6210.651.8813.61128.6736.057.317.7516.6711.682.3812.88139.9837.697.018.9416.1511.080.8311.67146.7738.696.018.8214.7911.441.7413.23158.1437.759.618.4913.159.761.2811.28167.6735.718.048.3115.137.761.4113.25177.9039.778.4912.9419.2711.052.0413.29187.1840.917.328.9417.6012.751.1414.80198.8233.707.5910.9818.8214.731.7810.10206.2535.024.726.2810.037.151.9310.392110.6052.417.709.9812.5311.702.3114.6922廣西7.2752.653.849.1613.0315.261.9814.572313.4555.855.507.459.559.522.2116.302410.8544.687.3214.5117.1312.081.2611.57257.2145.797.6610.3616.5612.862.2511.69267.6850.3711.3513.3019.2514.592.7514.87277.7848.448.0020.5122.1215.731.1516.61287.9439.6520.9720.8222.5212.411.757.90298.2864.348.0022.2220.0615.120.7222.893012.4776.395.5211.2414.5222.005.4625.502.下表是49位女性在空腹情況下三個(gè)不同時(shí)刻的血糖含量〔用X1,X2,X3表示和攝入等量食糖一小時(shí)后的三個(gè)時(shí)刻的血糖含量〔用小X4,X5,X6表示的觀測值〔單位：mg/100ml.問題：分別從樣本協(xié)方差陣S和樣本相關(guān)系數(shù)矩陣R出發(fā)做主成分分析,求主成分的貢獻(xiàn)率和各個(gè)主成分.在兩種情況下,你認(rèn)為應(yīng)保留幾個(gè)主成分？其意義如何解釋？就此而言,你認(rèn)為基于S和R的分析那個(gè)結(jié)果更為合理？表二49位女性在空腹和攝入食糖后三個(gè)不同時(shí)刻的血糖含量編號(hào)空腹攝入食糖X1X2X3X4X5X616069629769982565384103781073806976669913045580908085114562756811613091674647010910110376471667710213087370641151101099686775768511910698274721331271160676113013412112707478150158100136674781501311421483707499981051568669011985109167863751649813817103777716011712118776874144711531966776877828920707072114931222175657177701092291749311811515023667573170147121247582761531321152574716614310510026767064114113129277490867310611628747780116817729677169638770307875801051328031646671839413332718076818786336375731208959349010374107109101356076619911198364877751131249737669397136112122387470761098810539607471729071406375661301019041668086130117144427767748392107437067100150142146447376811191201194578907712215514946736880102901224772836810469964865607011994894952707692941003.考察1985年至20XX全國如下各價(jià)格指數(shù)：X1：商品零售價(jià)格指數(shù)；X2：居民消費(fèi)價(jià)格指數(shù)；X3：城市居民消費(fèi)價(jià)格指數(shù)；X4：農(nóng)村居民消費(fèi)價(jià)格指數(shù)；X5：農(nóng)產(chǎn)品收購價(jià)格指數(shù)；X6：農(nóng)村工業(yè)品零售價(jià)格指數(shù)；觀測數(shù)據(jù)見下表.問題：按年份用下列方法進(jìn)行系統(tǒng)聚類分析,畫出譜系聚類圖,并給出聚為3類的結(jié)果.〔a最短距離法；〔b最長距離法；〔c類平均距離法；表三全國各年度各種價(jià)格指數(shù)年份X1X2X3X4X5X61985128.1100.0134.2100.0166.8111.11986135.8106.5143.6106.1177.5114.71987145.7114.3156.2112.7198.8120.21988172.7135.8188.5132.4244.5138.51989203.4160.2219.2157.9281.2164.41990207.7162.2222.0165.1273.9172.01991213.7170.8233.3168.9268.4177.21992225.7181.7253.4176.8277.5182.71993254.9208.4294.2201.0314.7204.31994310.2258.6367.8248.0440.3239.41995356.1302.8429.6291.4527.9274.61996377.8327.9467.4314.4550.1291.61997380.8337.1481.9322.3525.3294.81998370.9334.4479.0319.1483.3288.31999359.8329.7472.8314.3424.3280.52000354.4331.0476.6314.0409.0277.14.考察1985年至20XX全國如下各價(jià)格指數(shù)：X1：商品零售價(jià)格指數(shù)；X2：居民消費(fèi)價(jià)格指數(shù)；X3：城市居民消費(fèi)價(jià)格指數(shù)；X4：農(nóng)村居民消費(fèi)價(jià)格指數(shù)；X5：農(nóng)產(chǎn)品收購價(jià)格指數(shù)；X6：農(nóng)村工業(yè)品零售價(jià)格指數(shù)；觀測數(shù)據(jù)見下表.問題：先將數(shù)據(jù)標(biāo)準(zhǔn)化,再按年份用下列方法進(jìn)行系統(tǒng)聚類分析,畫出譜系聚類圖,并給出聚為3類的結(jié)果.〔a最短距離法；〔b最長距離法；〔c重心距離法.表四全國各年度各種價(jià)格指數(shù)年份X1X2X3X4X5X61985128.1100.0134.2100.0166.8111.11986135.8106.5143.6106.1177.5114.71987145.7114.3156.2112.7198.8120.21988172.7135.8188.5132.4244.5138.51989203.4160.2219.2157.9281.2164.41990207.7162.2222.0165.1273.9172.01991213.7170.8233.3168.9268.4177.21992225.7181.7253.4176.8277.5182.71993254.9208.4294.2201.0314.7204.31994310.2258.6367.8248.0440.3239.41995356.1302.8429.6291.4527.9274.61996377.8327.9467.4314.4550.1291.61997380.8337.1481.9322.3525.3294.81998370.9334.4479.0319.1483.3288.31999359.8329.7472.8314.3424.3280.52000354.4331.0476.6314.0409.0277.15.研究貨運(yùn)總量y〔萬噸與工業(yè)總產(chǎn)值x1〔億元、農(nóng)業(yè)總產(chǎn)值x2〔億元。居民非商品支出x3〔億元的關(guān)系。數(shù)據(jù)見表。編號(hào)貨運(yùn)總量y<萬噸>工業(yè)總產(chǎn)值x1〔億元農(nóng)業(yè)總產(chǎn)值x2〔億元居民非商品支出x3〔億元116070351．0226075402．4321065402．0426574423．0524072381．2622068451．5727578424．0816066362．0927570443．21025065423．0〔1計(jì)算出y,x1,x2,x3的相關(guān)系數(shù)矩陣；〔2求y關(guān)于x1,x2,x3的三元線性回歸方程；〔3對回歸方程作顯著性檢驗(yàn)；〔4對每一個(gè)回歸系數(shù)作顯著性檢驗(yàn)；〔5如果有的回歸系數(shù)沒通過顯著性檢驗(yàn),將其剔除,重新建立回歸方程,再作回歸方程的顯著性檢驗(yàn)和回歸系數(shù)的顯著性檢驗(yàn)；〔6當(dāng)x1、x2、x3的值為：68,43,2.5時(shí),試對貨運(yùn)總量作出預(yù)測。6.某科學(xué)基金會(huì)的管理人員欲了解從事研究工作的數(shù)學(xué)家的年工資額y與他們的研究成果〔論文、著作等的質(zhì)量指標(biāo)x1、從事研究工作的時(shí)間x2,以及能成功獲得資助的指標(biāo)x3之間的關(guān)系。為此,按一定的設(shè)計(jì)方案調(diào)查了24位此類型的數(shù)學(xué)家,得數(shù)據(jù)見下表。編號(hào)yx1x2x3133.23.596.1240.35.3206.4338.75.1187.4446.85.8336.7541.44.2317.5637.56.0135.9739.06.8256.0840.75.5304.0930.13.155.81052.97.2478.31138.24.5255.01231.84.9116.41343.38.0237.61444.15.6357.01542.86.6395.01633.63.7214.41734.26.275.51848.07.0407.01938.04.0356.02035.94.5233.52140.45.9334.92236.85.6274.32345.24.8348.02435.13.9155.0〔1計(jì)算出y,x1,x2,x3的相關(guān)系數(shù)矩陣；〔2求y關(guān)于x1,x2,x3的三元線性回歸方程；〔3對回歸方程作顯著性檢驗(yàn)；〔4對每一個(gè)回歸系數(shù)作顯著性檢驗(yàn)；〔5如果有的回歸系數(shù)沒通過顯著性檢驗(yàn),將其剔除,重新建立回歸方程,再作回歸方程的顯著性檢驗(yàn)和回歸系數(shù)的顯著性檢驗(yàn)；〔6假設(shè)某位數(shù)學(xué)家的關(guān)于x1、x2、x3的值為：5.1,20,7.2,試預(yù)測他得年工資額。7.在某地區(qū)抽取了14塊巖石標(biāo)本,其中7塊含礦,7塊不含礦。每塊巖石測定了Cu,Ag,Bi三種化學(xué)成分,數(shù)據(jù)如下：含礦編號(hào)CuAgBi12.580.900.9522.901.231.0033.551.151.0042.351.150.7953.541.850.7962.702.231.3072.701.700.48不含礦12.251.981.0622.161.801.0632.331.741.1041.961.481.0451.941.401.0063.001.301.0072.781.701.48〔1生成SAS數(shù)據(jù)集；〔2用DISCRIM程序進(jìn)行判別分析〔假定先驗(yàn)概率相等,兩類樣本協(xié)差陣相等；〔3在顯著性水平下討論已知類型的兩組企業(yè)特征是否有顯著差異；〔4寫出距離判別的線性判別函數(shù)；〔5現(xiàn)在取一塊巖石標(biāo)本測得Cu、Ag、Bi分別為：2.95、2.15和1.54,試判別這塊巖石標(biāo)本是含礦還是不含礦,并統(tǒng)計(jì)已知類別樣品的錯(cuò)判概率。8.為了研究中小企業(yè)的破產(chǎn)模型,選定4個(gè)經(jīng)濟(jì)指標(biāo)：X1總負(fù)債率〔現(xiàn)金收益/總負(fù)債、X2收益性指標(biāo)〔純收入/總財(cái)產(chǎn)、X3短期支付能力〔流動(dòng)資產(chǎn)/流動(dòng)負(fù)債、X4生產(chǎn)效率性指標(biāo)〔流動(dòng)資產(chǎn)/純銷售額。對17個(gè)破產(chǎn)企業(yè)〔1類和21個(gè)正常運(yùn)行企業(yè)〔2類進(jìn)行了調(diào)查,調(diào)查資料下表,試對這些指標(biāo)作判別分析。〔1生成SAS數(shù)據(jù)集；〔2用DISCRIM程序進(jìn)行判別分析〔假定先驗(yàn)概率相等,兩類樣本協(xié)差陣相等；〔3在顯著性水平討論已知類型的兩組企業(yè)特征是否有顯著差異；〔4寫出距離判別的線性判別函數(shù)；〔5利用后驗(yàn)概率對8個(gè)待判企業(yè)〔*進(jìn)行判別歸類,并統(tǒng)計(jì)已知類別樣品的錯(cuò)判概率?！沧ⅲ簩⑾铝袌D片數(shù)據(jù)轉(zhuǎn)換成表格數(shù)據(jù)9．表1中的1995年到20XX我國國民經(jīng)濟(jì)數(shù)據(jù)<數(shù)據(jù)來自于中國統(tǒng)計(jì)年鑒>,通過典型相關(guān)分析來來找出郵電業(yè)和國民經(jīng)濟(jì)之間相互影響的在規(guī)律,根據(jù)這個(gè)規(guī)律,給決策者提供一個(gè)當(dāng)前如何發(fā)展郵電業(yè)的參考。采用如下指標(biāo)來衡量我國各年份的郵電業(yè)：：函件〔億件：快遞〔萬件：移動(dòng)年末用戶<萬戶>：固定年末用戶<萬戶>,采用下面的指標(biāo)來衡量我國各年份的經(jīng)濟(jì)〔單位都是萬億：第一產(chǎn)業(yè)：工業(yè)：建筑業(yè)：第三產(chǎn)業(yè)〔1生成SAS數(shù)據(jù)集；〔2數(shù)據(jù)預(yù)處理；〔3在顯著性水平討論已知類型的兩組特征數(shù)據(jù)是否有顯著差異；〔4給出典型相關(guān)變量；〔5給出典型相關(guān)系數(shù)；〔6給決策者提供一個(gè)當(dāng)前如何發(fā)展郵電業(yè)的參考。.年份199579.555562.7362.94070.612135.824950.63728.819978.5199678.687096.6685.35494.714015.429447.64387.423326.2199768.556878.91323.37031.014441.932921.44621.626988.1199865.517331.82386.38742.114817.634018.44985.830580.5199960.529091.34329.610871.614770.035861.55172.133873.4200077.7111031.48453.314482.914944.740033.6552