數(shù)學(xué)建模實驗報告

1、 16/16 數(shù)學(xué)建模實驗報告實驗序號：實驗8實驗項目名稱：統(tǒng)計回歸模型學(xué)號1210012143姓名詹建妹專業(yè)、班12信計實驗地點實4-401指導(dǎo)教師吳春紅實驗時間2014.4.29一、實驗?zāi)康募耙笸ㄟ^對具體實例的分析，學(xué)會運用統(tǒng)計回歸方法建立模型的方法。二、實驗設(shè)備（環(huán)境）及要求多媒體機房，單人單機，獨立完成三、實驗內(nèi)容與步驟1. 表1列出了某城市18位3544歲經(jīng)理的年平均收入x1（千元），風(fēng)險偏好度x2和人壽保險額y（千元）的數(shù)據(jù)，其中風(fēng)險偏好度是是根據(jù)每個發(fā)給經(jīng)理的問卷調(diào)查表綜合評估得到的，它的數(shù)值越大，就越偏愛高風(fēng)險，研究人員想研究此年齡段中的經(jīng)理所投保的人壽保險額與年均收入及風(fēng)險

2、偏好度之間的關(guān)系。研究者預(yù)計，經(jīng)理年均收入和人壽保險之間存在著二次關(guān)系，并有把握的認為風(fēng)險偏好度對人壽保險額有線性效應(yīng)，但對于風(fēng)險偏好度對人壽保險額是否有二次效應(yīng)以及兩個自變量是否對人壽保險額有交互效應(yīng)，心中沒底。序號yX1X2119666.290726340.9645325272.9961048445.0106512657.204461426.852574938.122484935.8406926675.7969104937.40851110554.3762129846.1867137746.1304141430.3663155639.06051624579.38011713352.7668

3、1813355.91662. 某公司想用全行業(yè)的銷售額作為自變量來預(yù)測公司的銷售額，下表給出了1977-1981年公司銷售額和行業(yè)銷售額的分季度數(shù)據(jù)（單位：百萬元）。畫出數(shù)據(jù)的散點圖，觀察用線性回歸模型擬合是否合適。建立公司銷售額對全行業(yè)銷售額的回歸模型，并用DW檢驗診斷隨機誤差項的自相關(guān)性。建立消除了隨機誤差項自相關(guān)性后的回歸模型。年季t公司銷售額y行業(yè)銷售額x19771120.96127.32221.41303321.96132.74421.52129.419781522.391352622.76137.13723.48141.24823.66142.819791924.1145.5210

4、24.01145.331124.54148.341224.3146.4198011325150.221425.64153.131526.36157.341626.98160.7198111727.52164.221827.78165.631929.24168.742028.78171.7四、實驗結(jié)果與數(shù)據(jù)處理1.Matlab代碼： X1=66.290 40.964 72.996 45.010 57.204 26.852 38.122 35.840 75.796 37.408 54.376 46.186 46.130 30.366 39.060 79.380 52.766 55.916; Y=1

5、96 63 252 84 126 14 49 49 266 49 105 98 77 14 56 245 133 133; X=ones(18,1) X1 (X1.2); b,bint,r,rint,stats=regress(Y,X)處理結(jié)果：b = -60.5239 1.7886 0.0302bint = -143.4598 22.4121 -1.4742 5.0513 0.0002 0.0603r = 5.0447 -0.4989 20.7987 2.7433 -14.7658 4.6881 -2.6174 6.5692 17.1895 0.2908 -21.1635 11.3961 -

6、9.3474 -7.6785 0.5151 -27.0424 14.9336 -1.0552rint = -22.6123 32.7016 -29.0151 28.0174 -3.0151 44.6125 -25.5842 31.0708 -41.2961 11.7646 -17.4529 26.8291 -30.9763 25.7415 -21.2462 34.3845 -6.0579 40.4368 -28.0301 28.6116 -46.2827 3.9558 -16.1444 38.9366 -37.1409 18.4462 -33.0744 17.7174 -27.9507 28.

7、9809 -42.7681 -11.3167 -11.6494 41.5167 -28.8865 26.7760stats =0.9747 289.1934 0.0000 182.0773參數(shù)參數(shù)參考值參數(shù)置信區(qū)間B0-60.5239-143.4598 ,22.4121B11.7886 -1.4742 ,5.0513B20.03020.0002 ,0.0603R= 0.9747 F=289.1934 p0.0000 s=182.0773由于置信水平a=0.05,處理結(jié)果p=0.00,p X1=66.290 40.964 72.996 45.010 57.204 26.852 38.122 35

8、.840 75.796 37.408 54.376 46.186 46.130 30.366 39.060 79.380 52.766 55.916; X2=7 5 10 6 4 5 4 6 9 5 2 7 4 3 5 1 8 6; Y=196 63 252 84 126 14 49 49 266 49 105 98 77 14 56 245 133 133; X=ones(18,1) X2 X1 (X1.2); b,bint,r,rint,stats=regress(Y,X)處理結(jié)果：b = -62.3489 5.6846 0.8396 0.0371bint = -73.5027 -51.1

9、952 5.2604 6.1089 0.3951 1.2840 0.0330 0.0412r = -0.0512 0.3076 -1.3718 -0.6730 -3.7605 -1.3560 2.7129 -0.4817 0.5130 -0.3725 0.6842 2.6781 -1.0293 -0.3930 0.5561 1.3578 2.3248 -1.6456rint = -3.7791 3.6766 -3.5324 4.1475 -4.4124 1.6688 -4.4677 3.1217 -6.6500 -0.8710 -4.2144 1.5023 -0.7344 6.1602 -4.

10、2149 3.2516 -2.6183 3.6443 -4.1840 3.4390 -2.6447 4.0132 -0.7217 6.0779 -4.7396 2.6810 -3.8132 3.0272 -3.2676 4.3798 -0.4637 3.1793 -1.0358 5.6855 -5.2685 1.9773stats = 1.0e+04 * 0.0001 1.1070 0.0000 0.0003B038.743459.7383 ,137.2251B113.52183.3538 . 30.3975R=0.2% F=2.9 p=0.0001 s=5721參數(shù)參數(shù)參考值參數(shù)置信區(qū)間-6

11、2.3489-73.5027 ,-51.1952 5.68465.2604 , 6.1089 0.83960.3951 1.28400.03710.0330 0.0412 1.00 1107.0 0.00 0.00031.00指因變量Y可由X1與X2100%確定，F(xiàn)遠遠小于F的檢驗的臨界值，p遠小于a,的系數(shù)均在置信區(qū)間內(nèi)?？芍猋與X1 ,X2有交互效應(yīng)Y=-62.3489+ 5.6846X2+0.8396X1+0.0371X122.（1）散點圖由散點圖可看出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： y =20.9

12、600 21.4000 21.9600 21.5200 22.3900 22.7600 23.4800 23.6600 24.1000 24.0100 24.5400 24.3000 25.0000 25.6400 26.3600 26.9800 27.5200 27.7800 29.2400 28.7800; x=127.3 130 132.7 129.4 135 137.1 141.2 142.8 145.5 145.3 148.3 146.4 150.2 153.1 157.3 160.7 164.2 165.6 168.7 171.7; b,bint,r,rint,stats=regr

13、ess(y,X)處理結(jié)果：b = -2.2816 0.1822bint = -3.4309 -1.1324 0.1745 0.1900r = 0.0447 -0.0073 0.0607 0.2220 0.0716 0.0589 0.0318 -0.0798 -0.1318 -0.1853 -0.2020 -0.0958 -0.0882 0.0233 -0.0220 -0.0216 -0.1193 -0.1145 0.7807 -0.2260rint = -0.3886 0.4780 -0.4486 0.4340 -0.3859 0.5072 -0.2030 0.6470 -0.3791 0.5222 -0.3956 0.5134 -0.4283 0.4918 -0.5396 0.3800 -0.5898 0.3262 -0.6384 0.2677 -0.6536 0.2496 -0.5563 0.3647 -0.5488 0.3723 -0.4376 0.4843 -0.4786 0.4346 -0.4727 0.4296 -0.5591 0.3204 -0.5510 0.3221 0.6132 0.9481 -0.6315 0.1794stats = 1.0e+03 *0.0010 2.4381 0.0000 0.