數(shù)學(xué)建模實(shí)驗(yàn)報(bào)告

.《數(shù)學(xué)建?！穼?shí)驗(yàn)報(bào)告實(shí)驗(yàn)序號(hào)：實(shí)驗(yàn)8實(shí)驗(yàn)項(xiàng)目名稱(chēng)：統(tǒng)計(jì)回歸模型學(xué)號(hào)1210012143姓名詹建妹專(zhuān)業(yè)、班12信計(jì)實(shí)驗(yàn)地點(diǎn)實(shí)4-401指導(dǎo)教師吳春紅實(shí)驗(yàn)時(shí)間一、實(shí)驗(yàn)?zāi)康募耙蠼?jīng)過(guò)對(duì)詳盡實(shí)例的解析，學(xué)會(huì)運(yùn)用統(tǒng)計(jì)回歸方法建立模型的方法。二、實(shí)驗(yàn)設(shè)備（環(huán)境）及要求多媒體機(jī)房，單人單機(jī)，獨(dú)立完成三、實(shí)驗(yàn)容與步驟1.表1列出了某城市18位35—44歲經(jīng)理的年平均收入x1（千元），風(fēng)險(xiǎn)偏好度x2和人壽保險(xiǎn)額y（千元）的數(shù)據(jù)，其中風(fēng)險(xiǎn)偏好度是是依照每個(gè)發(fā)給經(jīng)理的問(wèn)卷檢查表綜合評(píng)估得到的，它的數(shù)值越大，就越偏愛(ài)高風(fēng)險(xiǎn)，研究人員想研究此年齡段中的經(jīng)理所投保的人壽保險(xiǎn)額與年均收入及風(fēng)險(xiǎn)偏好度之間的關(guān)系。研究者預(yù)計(jì)，經(jīng)理年均收入和人壽保險(xiǎn)之間存在著二次關(guān)系，并有掌握的認(rèn)為風(fēng)險(xiǎn)偏好度對(duì)人壽保險(xiǎn)額有線性效應(yīng)，但對(duì)于風(fēng)險(xiǎn)偏好度對(duì)人壽保險(xiǎn)額可否有二次效應(yīng)以及兩個(gè)自變量可否對(duì)人壽保險(xiǎn)額有交互效應(yīng)，心中沒(méi)底。序號(hào)yX1X2119666.290726340.9645325272.9961048445.6512657.204461426.852574938.122484935.8406926675.7969104937.40851110554.3762129846.7137746.1304141430.3663155639.06051624579.3801Word文檔資料.1713352.76681813355.91662.某公司想用全行業(yè)的銷(xiāo)售額作為自變量來(lái)展望公司的銷(xiāo)售額，下表給出了1977-1981年公司銷(xiāo)售額和行業(yè)銷(xiāo)售額的分季度數(shù)據(jù)（單位：百萬(wàn)元）。（1）畫(huà)出數(shù)據(jù)的散點(diǎn)圖，觀察用線性回歸模型擬合可否合適。（2）建立公司銷(xiāo)售額對(duì)全行業(yè)銷(xiāo)售額的回歸模型，并用DW檢驗(yàn)診斷隨機(jī)誤差項(xiàng)的自相關(guān)性。（3）建立除掉了隨機(jī)誤差項(xiàng)自相關(guān)性后的回歸模型。年季t公司銷(xiāo)售額y行業(yè)銷(xiāo)售額x19771120.96127.32221.413019781522.391352622.76137.119791924.1145.521024.01145.3198011325150.221425.64153.1198111727.52164.221827.78165.6Word文檔資料.四、實(shí)驗(yàn)結(jié)果與數(shù)據(jù)辦理1.Matlab代碼：X1=[66.29040.96472.99645.57.20426.85238.12235.84075.79637.40854.37646.46.13030.36639.06079.38052.76655.916];X=[ones(18,1)X1'(X1.^2)'];[b,bint,r,rint,stats]=regress(Y',X)辦理結(jié)果：b=-60.52391.78860.0302bint=-143.459822.4121Word文檔資料.r=5.0447-0.498920.79872.7433-14.76584.6881-2.61746.569217.18950.2908-21.163511.3961-9.3474-7.67850.5151-27.042414.9336Word文檔資料.-1.0552rint=-22.612332.7016-29.015128.0174-3.015144.6125-25.584231.0708-41.296111.7646-17.452926.8291-30.976325.7415-21.246234.3845-6.057940.4368-28.030128.6116-16.144438.9366-37.140918.4462-33.074417.7174-27.950728.9809-42.7681-11.3167Word文檔資料.-11.649441.5167-28.886526.7760stats=參數(shù)參數(shù)參照值參數(shù)置信區(qū)間B0-60.5239[-143.4598,22.4121]B11.7886[-1.4742,5.0513]B20.0302[0.0002,0.0603]R2=0.9747F=289.1934p<0.0000s2=182.0773由于置信水平a=0.05,辦理結(jié)果p=0.00,p<0.05R2=0.9747，指因變量Y的97.47%可由模型確定，Y與X1存在二次關(guān)系。,所以獲取回歸模型：Y=0.5239+1.7886*X1+0.0302*X1^2;結(jié)果表示年均收入和人壽保險(xiǎn)額之間存在二次關(guān)系。Word文檔資料.接下來(lái)辦理兩個(gè)自變量X1,X2對(duì)Y可否有交互效應(yīng)。由于Y與X1之間存在二次關(guān)系，所以我們?cè)O(shè)Y01X22X3X211Matlab代碼：X1=[66.29040.96472.99645.57.20426.85238.12235.84075.79637.40854.37646.46.13030.36639.06079.38052.76655.916];X=[ones(18,1)X2'X1'(X1.^2)'];[b,bint,r,rint,stats]=regress(Y',X)辦理結(jié)果：b=-62.34895.68460.83960.0371bint=-73.5027-51.1952Word文檔資料.r=-0.05120.3076-1.3718-0.6730-3.7605-1.35602.7129-0.48170.5130-0.37250.68422.6781-1.0293-0.39300.5561Word文檔資料.1.35782.3248-1.6456rint=Word文檔資料.stats=1.0e+04*B038.7434[59.7383,137.2251]B113.5218[3.3538.30.3975]R2=0.2%F=2.9p=0.0001s2=5721參數(shù)參數(shù)參照值參數(shù)置信區(qū)間0-62.3489[-73.5027,-51.1952]15.6846[5.2604,6.1089]20.8396[0.39511.2840]Word文檔資料3R21.00

.0.0371[0.03300.0412]F1107.0p0.00s20.0003R21.00指因變量Y可由X1與X2100%確定，F(xiàn)遠(yuǎn)遠(yuǎn)小于F的檢驗(yàn)的臨界值，p遠(yuǎn)小于a,03的系數(shù)均在置信區(qū)間?？芍猋與X1,X2有交互效應(yīng)Y=-62.3489+5.6846X2+0.8396X1+0.0371X1^22.（1）散點(diǎn)圖3029282726252423222120130135140145150155160165170175125由散點(diǎn)圖可看出x與y存在線性相關(guān)，可用線性回歸模型擬合。（2）由散點(diǎn)圖可看出，x與y存在正相關(guān)，所以使用一次回歸模型Matlab代碼：Word文檔資料.27.780029.240028.7800];x=[127.3130132.7129.4135137.1141.2142.8145.5145.3148.3146.4150.2153.1157.3160.7164.2165.6168.7171.7];[b,bint,r,rint,stats]=regress(y',X)辦理結(jié)果：b=-2.28160.1822bint=-3.4309-1.13240.17450.1900r=0.0447Word文檔資料.-0.00730.06070.22200.07160.05890.0318-0.0798-0.1318-0.1853-0.2020-0.0958-0.08820.0233-0.0220-0.0216-0.1193-0.11450.7807-0.2260Word文檔資料.rint=-0.38860.4780-0.44860.4340-0.38590.5072-0.20300.6470-0.37910.5222-0.39560.5134-0.42830.4918-0.53960.3800-0.58980.3262-0.63840.2677-0.65360.2496-0.55630.3647-0.54880.3723-0.43760.4843-0.47860.4346-0.47270.4296-0.55910.3204-0.55100.32210.61320.9481Word文檔資料.-0.63150.1794stats=1.0e+03*0.00102.43810.00000.0000參數(shù)參數(shù)參照值參數(shù)置信區(qū)間0-2.2816[-3.4309,-1.1324]10.1822[0.