1、模糊數(shù)學(xué)實(shí)驗(yàn)報(bào)告實(shí)驗(yàn)名稱：多元線性回歸與逐步回歸實(shí)驗(yàn)?zāi)康氖炀氄莆宅F(xiàn)行回歸模型的建模方法，掌握regress命令的使用方法。掌握編程求總離差平方和TSS、回歸平方和RSS、殘差平方和ESS等相關(guān)統(tǒng)計(jì)量。掌握逐步回歸的思想與方法，掌握stepwise命令的使用方法。一、實(shí)驗(yàn)數(shù)據(jù)與實(shí)驗(yàn)內(nèi)容：選取19892003年的全國的統(tǒng)計(jì)數(shù)據(jù)，考慮的自變量包括：工業(yè)總產(chǎn)值(X),農(nóng)業(yè)總產(chǎn)值(x)，建筑業(yè)總產(chǎn)值(x)，社會(huì)商品零售總額(x)，全民人口數(shù)(x),2345受災(zāi)面積(x)，國家財(cái)政收入(y)，單位均為億元。數(shù)據(jù)見表3.17。6年份x1x2x3x4x5x6y實(shí)驗(yàn)19896484.004100.60794.0

2、08101.40112704.046991.002664.9019906858.004954.30859.408300.10114333.038474.002937.10主19918087.105146.401015.109415.60115823.055472.003149.48要內(nèi)容(具體199210284.505588.001415.0010993.70117171.051333.003483.37199314143.806605.102284.7012462.10118517.048829.004348.95199419359.609169.203012.6016264.7011985

3、0.055043.005218.10199524718.3011884.603819.6020620.00121121.045821.006242.20199629082.6013539.804530.5024774.10122389.046989.007407.99題199732412.1013852.504810.6027298.90123626.053429.008651.14目、199833387.9014241.905231.4029152.50124761.050145.009875.95解答過199935087.2014106.205470.6031134.70125786.04

4、9981.0011444.08200039047.3013873.605888.0034152.60126743.054688.0013395.23程200142374.6014462.806375.4037595.20127627.052215.0016386.04及程刊200245975.2014931.507005.0042027.10128453.047119.0018903.64200353092.9014870.108181.3045842.00129227.054506.0021715.25表11989至2003年統(tǒng)計(jì)數(shù)據(jù)(1)建立多元回歸模型;(2)用逐步回歸求國家財(cái)政收入y與

5、6個(gè)因素的回歸關(guān)系.二、實(shí)驗(yàn)程序：程序1clear，clcA=6484.004100.60794.008101.40112704.046991.002664.90;6858.004954.30859.408300.10114333.038474.002937.10;8087.10；5146.401015.109415.60115823.055472.003149.48;10284.505588.001415.0010993.70117171.051333.00:3483.37;14143.806605.102284.7012462.10118517.048829.004348.95;19359

6、.609169.203012.6016264.70119850.055043.00!5218.10;24718.3011884.603819.6020620.00121121.045821.006242.20;29082.6013539.804530.5024774.10122389.046989.007407.99;32412.1013852.504810.6027298.90123626.053429.008651.14;33387.9014241.905231.4029152.50124761.050145.009875.95;35087.2014106.205470.6031134.7

7、0125786.049981.0011444.08;39047.3013873.605888.0034152.60126743.054688.0013395.23;42374.6014462.806375.4037595.20127627.052215.0016386.04;45975.2014931.507005.0042027.10128453.047119.0018903.64;53092.9014870.108181.3045842.00129227.054506.0021715.25;%自變量數(shù)據(jù)m,n二size(A);subplot(3,2,l),plot(A(:,l),A(:,7

8、),+)xlabel(xl(工業(yè)總產(chǎn)值)ylabel(y(國家財(cái)政收入)subplot(3,2,2),plot(A(:,2),A(:,7),*)xlabel(x2(農(nóng)業(yè)總產(chǎn)值)ylabel(y(國家財(cái)政收入)subplot(3,2,3),plot(A(:,3),A(:,7),o)xlabel(x3(建筑業(yè)總產(chǎn)值)ylabel(y(國家財(cái)政收入)subplot(3,2,4),plot(A(:,4),A(:,7),+)xlabel(x4(社會(huì)商品零售總額)ylabel(y(國家財(cái)政收入)subplot(3,2,5),plot(A(:,5),A(:,7),*)xlabel(x5(全民人口數(shù))ylab

9、el(y(國家財(cái)政收入)subplot(3,2,6),plot(A(:,6),A(:,7),o)xlabel(x6(受災(zāi)面積)ylabel(y(國家財(cái)政收入)x=ones(m,l),A(:,l),A(:,2),A(:,3),A(:,4),A(:,5),A(:,6);%勾造設(shè)計(jì)矩陣y=A(:,7);n,p二size(x);%矩陣x0的行數(shù)即樣本容量db,dbint,dr,drint,dstats二regress(y,x)%調(diào)用多元回歸分析命令TSS二y*(eye(n)T/n*ones(n,n)*y%計(jì)算TSSH二x*inv(x*x)*x;%計(jì)算對稱幕等矩陣ESS二y*(eye(n)-H)*y%計(jì)

10、算ESSRSS二y*(HT/n*ones(n,n)*y%計(jì)算RSSMRS=RSS/p%計(jì)算MRSMSE=ESS/(n-p-l)%計(jì)算MSE%F檢驗(yàn)FO=(RSS/p)/(ESS/(n-p-l)%計(jì)算F0程序2：X=A(:,1),A(:,2),A(:,3),A(:,4),A(:,5),A(:,6);stepwise(X,y,l,2,3,4,5,6,0.05,0.10)%in=l,2,3,4,5,6表示x1、x2、x3、x4、x5、x6均保留在模型中三、實(shí)驗(yàn)結(jié)果與分析：1多元回歸模型運(yùn)行程序可得到國家財(cái)政收入與各因素的散點(diǎn)圖（見圖1）。4弟Xi國0國0246yx1(工業(yè)總產(chǎn)值)x104入x104入

11、4|00+社豐+,十I50001000015000 x2(農(nóng)業(yè)總產(chǎn)值)0國0500010000yx3(建筑業(yè)總產(chǎn)值)00246x4（社會(huì)商品零售總額X）104422攵茨射象HTX+4-十-+十亠+4J_r-+42入收政財(cái)家國-+豐+3、x104y1.11.151.21.251.3x5（全民人口數(shù)）x105x104456x6(受災(zāi)面積)x104圖1國家財(cái)政收入與各因素的散點(diǎn)圖得到B的最小二乘估計(jì)（見表2）及方差分析表（見表3）：表2卩的最小二乘估計(jì)變量pPPPPPP0123456值-6922.60.1-0.900.60.10表3方差分析表方差來源平方和自由度均方和Fp回歸5.2695e+0086

12、7.5278e+007465.42050誤差1.1322e+00681.6174e+005總計(jì)5.2808e+00814F檢驗(yàn)：H:p=B=0H:0（i=1,2,3,4,5,6）不全為001234561i由表2可知，統(tǒng)計(jì)量F0二465.4205，在顯著性水平=0.05，查F分布表，得臨界值F=3.1122。由F0F=3.1122，所以拒絕H，接受備擇假設(shè)。則總aa0體回歸系數(shù)不全為0,即表明模型的線性關(guān)系在95%的置信水平下顯著成立。2逐步回歸X1X2X3X4X5X6-3-2-10123ModelHistory375ESR圖2國家財(cái)政收入與各因素的散點(diǎn)圖ESRcoeff.tatPL0.07497950.70420.4960-0.812016-13.41930.00000.4634630.99450.3414k0.7232735.56870.00000.01929980.16750.8700-0.0278381.26090.2334CoefficientswithErrorBarsX1X2X3X4X5X6Nextstep:Movenoterms-1-0.500.511.5ModelHistory34012345圖