2024年數(shù)學(xué)實驗實驗報告

《數(shù)學(xué)試驗》試驗匯報4（

年

4月

19曰）班級理學(xué)院數(shù)學(xué)系0902學(xué)號姓名胡冬雲(yún)一、試驗問題1.財政收入預(yù)測問題（中國記錄年鑒上尋找數(shù)據(jù)）財政收入與國民收入、工業(yè)總產(chǎn)值、農(nóng)業(yè)總產(chǎn)值、總?cè)丝?、就業(yè)人口、固定資產(chǎn)投資等原因有關(guān)。查找此前的數(shù)據(jù)（至少10個樣本），試構(gòu)造預(yù)測模型，并預(yù)測，，的財政收入。2．（謝金星）下表列出了某都市18位35歲—44歲經(jīng)理的年平均收入x1仟元,風(fēng)險偏好度x2和人壽保險額y仟元的數(shù)據(jù)建立回歸模型。二、問題的分析（波及的理論知識、數(shù)學(xué)建模與求解的措施等）1.先用逐漸回歸確定模型：設(shè)x1表達國民收入；x2表達工業(yè)總產(chǎn)值；x3表達農(nóng)業(yè)總產(chǎn)值；x4表達總?cè)丝?；x5表達就業(yè)人口；x6表達固定資產(chǎn)投資；y表達財政收入；(1)分別輸入數(shù)據(jù)：x1,x2,x3,x4,x5,x6,y;（2）逐漸回歸：stepwise(x,y)運行的到stepwiseregression圖形可以看出x1明顯.

2.先用逐漸回歸確定模型：設(shè)x1:年平均收入；x2：風(fēng)險偏好度；x3：年平均收入的平方；x4:風(fēng)險偏好度的平方；x5:年平均收入*風(fēng)險偏好度。Y：人壽保險。x=[x1x2x3x4x5]

假設(shè)y=a1*x1+a2*x2+a3*x3+a4*x4+a5*x5+a6+e(1)分別輸入數(shù)據(jù)：x1,x2,x3,x4,x5,y；(2)逐漸回歸：stepwise(x,y)運行的到stepwiseregression圖形可以看出x3明顯下一步x2進入在下布x3進入（3）移去變量x4,x5模型變得明顯，新的記錄中記錄量F的值明顯增大，因此新的回歸模型更好。（4）對變量y和x1,x2,x3作線性回歸：X=[ones(18,1)x1x2x3];[b,bint,r,rint,stats]=regress(X，y)；三、計算過程1.逐漸回歸模型：x1=[83024.388479.298000.5108068.2119095.7135174.0159586.7184088.6213131.7251483.2]';x2=[67737.1472707.0485673.795448.98110776.48142271.222.19251619.50316588.96405177]';x3=[14241.914106.213873.614462.814931.614870.118138.419613.421522.324658.1]';x4=[124761125786126743127627128453129227129988130756131448132129]';x5=[69957705867115073025737407443275200758257640076990]';x6=[28406.1729854.7132917.7337213.4943499.9155566.6170477.488773.6109998.2137323.9]';X=[x1x2x3x4x5x6];y=[9875.9511444.0813395.2316386.0418903.6421715.2526396.4731649.2938760.2051321.78]';stepwise(x,y);.逐漸回歸模型：年份國民收入總產(chǎn)值工業(yè)總產(chǎn)值農(nóng)業(yè)總產(chǎn)值總?cè)丝诰蜆I(yè)人口固定資產(chǎn)投資財政收入199883024.367737.1414241.91247616995728406.179875.95199988479.272707.0414106.21257867058629854.7111444.0898000.585673.713873.61267437115032917.7313395.23108068.295448.9814462.81276277302537213.4916386.04119095.7110776.4814931.61284537374043499.9118903.64135174.0142271.214870.11292277443255566.6121715.25159586.722.1918138.41299887520070477.426396.47184088.6251619.5019613.41307567582588773.631649.29213131.7316588.9621522.313144876400109998.238760.20251483.240517724658.113212976990137323.951321.78X=[ones(10,1)x1x2x3x4x5x6];[b,bint,r,rint,stats]=regress(y,X)成果：b=8.53810.0000-0.0000-0.0001-0.0000-0.0000b=1.0e+005*8.53810.0000-0.0000-0.0000-0.0001-0.0000-0.0000bint=1.0e+006*-0.34892.0565-0.00000.0000-0.00000.0000-0.00000.0000-0.00000.0000-0.00000.0000-0.00000.0000r=1.0e+003*-0.84961.2862-0.56950.23160.21930.1889-0.0514-0.4391-0.75720.7407rint=1.0e+003*-1.94500.24570.53282.0397-0.8955-0.2435-2.90733.3706-1.33991.7786-0.95981.3376-2.26622.1634-3.67602.7977-3.99352.4791-0.12711.6085stats=1.0e+006*0.00000.00020.00001.3852第二題x1=[66.29040.96472.99645.01057.20426.85238.12235.84075.79637.40854.37646.18646.13030.36639.06079.38052.76655.916]';X2=[7510645469527435186]';y=[19663252841261449492664910598771456245133133]';x3=[66.290.^240.964.^272.996.^245.010.^257.204.^226.852.^238.122.^235.840.^275.796.^237.408.^254.376.^246.186.^246.130.^230.366.^239.060.^279.380.^252.766.^255.916.^2]';x4=[7.^25.^210.^26.^24.^25.^24.^26.^29.^25.^22.^27.^24.^23.^25.^21.^28.^26.^2]';x5=[66.290*740.964*572.996*1045.010*657.204*426.852*538.122*435.840*675.796*937.408*554.376*246.186*746.130*430.366*339.060*5379.380*152.766*855.916*6]';x=[x1x2x3x4x5];stepwise(x,y);成果：記錄中有x1,x2,x3即人壽保險與年平均收入之間存在二次關(guān)系，人壽保險與風(fēng)險偏好度之間存在線性關(guān)系，人壽保險與風(fēng)險偏好度之間不存在線性關(guān)系及與兩個自變量交互之間不存在交互效應(yīng)。線性回歸模型：x1=[66.29040.96472.99645.01057.20426.85238.12235.84075.79637.40854.37646.18646.13030.36639.06079.38052.76655.916]';x2=[7510645469527435186]';y=[19663252841261449492664910598771456245133133]';x3=[66.290.^240.964.^272.996.^245.010.^257.204.^226.852.^238.122.^235.840.^275.796.^237.408.^254.376.^246.186.^246.130.^230.366.^239.060.^279.380.^252.766.^255.916.^2]';X=[ones(18,1)x1x2x3];[b,bint,r,rint,stats]=regress(y,X)成果:b=-62.34890.83965.68460.0371bint=-73.5027-51.19520.39511.28405.26046.10890.03300.0412stats=1.0e+004*0.00011.107000.0003

四、問題求解成果的分析與結(jié)論1.有逐漸分析可知：記錄量F=993.794應(yīng)越大越好。從圖中可知Ｙ只跟X1有關(guān)。結(jié)論：Y=8.