数学模型——财政预测问题.doc

数学建模第六次作业财政收入预测问题：财政收入与国民收入、工业总产值、农业总产值、总人口、就业人口、固定资产投资等因素有关。下表列出了1952-1981年的原始数据，试构造预测模型。年份国民收入（亿元）工业总产值(亿元)农业总产值（亿元）总人口（万人）就业人口（万人）固定资产投资（亿元）财政收入(亿元)195259834946157482207294418419535864554755879621364892161954707520491602662183297248195573755852961465223289825419568257155566282823018150268195783779857564653237111392861958102812355986599426600256357195911141681509672072617333844419601079187044466207258803805061961757115643465859255901382711962677964461672952511066230196377910465146917226640852661964943125058470499277361293231965115215816327253828670175393196613221911687745422980521246619671249164769776368308141563521968118715656807853431915127303196913722101688806713322520744719701638274776782992344323125641971178031567908522935620355638197218333365789871773585435465819731978368485589211366523746911974199336968919085937369393655197521214254932924213816846269219762052430995593717388344436571977218949259719497439377454723197824755590105896259398565509221979270260651150975424058156489019802791659211949870541896568826198129276862127310007273280496810解：一、 问题假设：财政收入只与题目中提到的6个因素相关。二、 符号说明：财政收入：y；国民收入：x1；工业总产值：x2；农业总产值：x3；总人口：x4；就业人口：x5；固定资产投资：x6；回归系数：0、1、2、3、4、5、6；随即误差：。三、 问题分析、模型建立：1、由表格中的数据关系得出y与6因素具有以下关系：y=0+1x1+2x2+3x3+4x4+5x5+6x6+.2、将表格中数据存入Excel中：book1.xls。在Matlab中运行为： A=xlsread(book1.xls); x=ones(30,1) A(:,2:7); y=A(:,8); b,bint,r,rint,starts=regress(y,x)b = 159.1440 0.4585 -0.0112 -0.5125 0.0008 -0.0028 0.3165bint = -118.6528 436.9407 0.1781 0.7389 -0.0601 0.0376 -0.9115 -0.1136 -0.0035 0.0051 -0.0058 0.0003 -0.0746 0.7076r = -11.8891 20.4348 3.4696 15.7104 -10.6809 16.4186 -13.5604 -34.7243 -1.1746 -25.5999 2.0632 16.1006 24.1192 12.9971 29.7667 -29.5457 -49.2651 -3.3849 7.6343 20.7855 17.7107 15.8781 -13.7668 -29.0663 -13.2104 2.0944 91.9213 4.8706 -70.0305 3.9236rint = -70.8405 47.0624 -41.4970 82.3666 -60.1321 67.0714 -47.6628 79.0836 -73.1130 51.7512 -45.7616 78.5988 -70.8672 43.7465 -90.6558 21.2073 -48.7773 46.4282 -82.9934 31.7935 -54.6269 58.7533 -44.8551 77.0563 -40.3464 88.5848 -52.9624 78.9566 -33.5360 93.0694 -91.9184 32.8270 -107.0027 8.4726 -67.1719 60.4022 -57.3345 72.6032 -42.7095 84.2805 -43.6300 79.0515 -45.5098 77.2659 -77.3331 49.7994 -91.4273 33.2946 -66.7875 40.3667 -58.5244 62.7132 45.3886 138.4541 -52.3522 62.0933 -110.7399 -29.3211 -1.1206 8.9677starts = 1.0e+003 *0.0010 0.2283 0 1.0488 rcoplot(r,rint)分析得：由于第27和第29项是异常点，所以将其剔除。3、于是，将剩下的数据进行逐步回归分析，即： A=xlsread(book1.xls); x=A(:,2:7); y=A(:,8); stepwise(x,y)从图中分析得出，去掉x2、x4、x6，剩下x1、x3、x5（即国民收入、农业总产值、就业人口），也就是在X中的x1、x2、x3。 4、再进行多元线性回归分析，即： X=ones(28,1) A(:,2) A(:,4) A(:,6); b,bint,r,rint,stats=regress(y,X);则点估计及估计区间为：b = 267.0695 0.5963 -0.7021 -0.0043bint = 219.0182 315.1208 0.5366 0.6560 -0.8861 -0.5180 -0.0062 -0.0024r = -25.9119 25.8326 -1.0529 15.8930 -0.6267 26.5690 12.3779 -16.2460 19.7153 -31.5560 -7.9812 11.0557 24.1712 7.3031 22.4789 -36.5851 -55.7652 -10.7718 8.3220 18.9577 7.6684 4.0103 -12.5430 -19.6119 5.5755 3.4750 -4.5221 9.7683rint = -67.7965 15.9728 -15.6259 67.2911 -44.7752 42.6694 -26.6813 58.4673 -43.9413 42.6879 -14.6918 67.8298 -31.6822 56.4380 -56.3136 23.8215 -13.6389 53.0695 -71.1679 8.0558 -51.1085 35.1461 -32.2808 54.3922 -18.5538 66.8963 -37.1853 51.7914 -21.0767 66.0345 -77.7238 4.5535 -92.4110 -19.1194 -55.0858 33.5423 -36.0004 52.6444 -24.0547 61.9701 -35.2187 50.5555 -39.1029 47.1235 -55.7945 30.7084 -61.7273 22.5035 -37.1713 48.3222 -39.1747 46.1247 -40.3657 31.3215 -3.2179 22.7544stats =0.9901 800.1905 0 466.5820 由于0，即常数项的区间范围较大，于是将其剔除，于是，将参数估计值代入模型得到，y=