2024年数学实验实验报告

《数學试验》试验汇报4（

年

4月

19曰）班级理學院数學系0902學号姓名胡冬雲一、试验問題1.财政收入预测問題（中国记录年鉴上寻找数据）财政收入与国民收入、工业總产值、农业總产值、總人口、就业人口、固定资产投资等原因有关。查找此前的数据（至少10個样本），试构造预测模型，并预测，，的财政收入。2．（謝金星）下表列出了某都市18位35岁—44岁經理的年平均收入x1仟元,風险偏好度x2和人寿保险额y仟元的数据建立回归模型。二、問題的分析（波及的理论知识、数學建模与求解的措施等）1.先用逐渐回归确定模型：设x1表达国民收入；x2表达工业總产值；x3表达农业總产值；x4表达總人口；x5表达就业人口；x6表达固定资产投资；y表达财政收入；(1)分别输入数据：x1,x2,x3,x4,x5,x6,y;（2）逐渐回归：stepwise(x,y)运行的到stepwiseregression图形可以看出x1明显.

2.先用逐渐回归确定模型：设x1:年平均收入；x2：風险偏好度；x3：年平均收入的平方；x4:風险偏好度的平方；x5:年平均收入*風险偏好度。Y：人寿保险。x=[x1x2x3x4x5]

假设y=a1*x1+a2*x2+a3*x3+a4*x4+a5*x5+a6+e(1)分别输入数据：x1,x2,x3,x4,x5,y；(2)逐渐回归：stepwise(x,y)运行的到stepwiseregression图形可以看出x3明显下一步x2進入在下布x3進入（3）移去变量x4,x5模型变得明显，新的记录中记录量F的值明显增大，因此新的回归模型更好。（4）對变量y和x1,x2,x3作线性回归：X=[ones(18,1)x1x2x3];[b,bint,r,rint,stats]=regress(X，y)；三、计算過程1.逐渐回归模型：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);.逐渐回归模型：年份国民收入總产值工业總产值农业總产值總人口就业人口固定资产投资财政收入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：记录中有x1,x2,x3即人寿保险与年平均收入之间存在二次关系，人寿保险与風险偏好度之间存在线性关系，人寿保险与風险偏好度之间不存在线性关系及与两個自变量交互之间不存在交互效应。线性回归模型：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与結论1.有逐渐分析可知：记录量F=993.794应越大越好。從图中可知Ｙ只跟X1有关。結论：Y=8.