數(shù)學建模實驗報告

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

2、偏好度之間的關系。研究者預計，經理年均收入和人壽保險之間存在著二次關系，并有把握的認為風險偏好度對人壽保險額有線性效應，但對于風險偏好度對人壽保險額是否有二次效應以及兩個自變量是否對人壽保險額有交互效應，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性。建立消除了隨機誤差項自相關性后的回歸模型。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?？芍猋與X1 ,X2有交互效應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，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，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.