matlab多元線性回歸與逐步回歸實驗1

模糊數(shù)學》實驗報告實驗名稱：多元線性回歸與逐步回歸實

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的熟練掌握現(xiàn)行回歸模型的建模方法，掌握實

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的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、實驗數(shù)據(jù)與實驗內(nèi)容:選取1989—2003年的全國的統(tǒng)計數(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)，社會商品零售總額(x)，全民人口數(shù)(x\,2345受災面積(x)，國家財政收入(y)，單位均為億元。數(shù)據(jù)見表3.17。6年份x1x2年份x1x2x3x4x5x6y實驗19896484.004100.60794.008101.40112704.046991.002664.9019906858.004954.30859.408300.10114333.038474.002937.10主19918087.105146.401015.109415.60115823.055472.003149.48要內(nèi)容(具體199210284.505588.001415.0010993.70117171.051333.003483.37199314143.806605.102284.7012462.10118517.048829.004348.95199419359.609169.203012.6016264.70119850.055043.005218.10199524718.3011884.603819.6020620.00121121.045821.006242.20199629082.6013539.804530.5024774.10122389.046989.007407.99題199732412.1013852.504810.6027298.90123626.053429.008651.14目、199833387.9014241.905231.4029152.50124761.050145.009875.95解答過199935087.2014106.205470.6031134.70125786.049981.0011444.08200039047.3013873.605888.0034152.60126743.054688.0013395.23程200142374.6014462.806375.4037595.20127627.052215.0016386.04及200245975.2014931.507005.0042027.10128453.047119.0018903.64程刊200353092.9014870.108181.3045842.00129227.054506.0021715.25表11989至2003年統(tǒng)計數(shù)據(jù)(1)建立多元回歸模型;(2)用逐步回歸求國家財政收入y與6個因素的回歸關(guān)系.二、實驗程序：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;19359.609169.203012.6016264.70119850.055043.00!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;35087.2014106.205470.6031134.70125786.049981.0011444.08;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),'+')xlabel('xl(工業(yè)總產(chǎn)值)’)ylabel('y(國家財政收入)’)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(國家財政收入)’)subplot(3,2,4),plot(A(:,4),A(:,7),'+')xlabel('x4(社會商品零售總額)’)ylabel('y(國家財政收入)’)subplot(3,2,5),plot(A(:,5),A(:,7),'*')xlabel('x5(全民人口數(shù))')ylabel('y(國家財政收入)’)subplot(3,2,6),plot(A(:,6),A(:,7),'o')xlabel('x6(受災面積)')ylabel('y(國家財政收入)’)x=[ones(m,l),A(:,l),A(:,2),A(:,3),A(:,4),A(:,5),A(:,6)];%勾造設計矩陣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%計算TSSH二x*inv((x'*x))*x';%計算對稱幕等矩陣ESS二y'*(eye(n)-H)*y%計算ESSRSS二y'*(HT/n*ones(n,n))*y%計算RSSMRS=RSS/p%計算MRSMSE=ESS/(n-p-l)%計算MSE%F檢驗FO=(RSS/p)/(ESS/(n-p-l))%計算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、實驗結(jié)果與分析：1?多元回歸模型運行程序可得到國家財政收入與各因素的散點圖(見圖1)。0404+亠七■42入收政財家用十廿亠十.+申.2x1044X104050001000015000x2（農(nóng)業(yè)總產(chǎn)值0404+亠七■42入收政財家用十廿亠十.+申.2x1044X104050001000015000x2（農(nóng)業(yè)總產(chǎn)值）-°-420八收政財家」.O0..如◎9.2x1040246x4(社會商品零售總額X)[。40500010000x3（建筑業(yè)總產(chǎn)值）0246x1（工業(yè)總產(chǎn)值）x104x10442入收政財家國23x104x10401.11.151.21.251.3x5（全民人口數(shù)）x105456x6（受災面積）x104圖1國家財政收入與各因素的散點圖得到0的最小二乘估計(見表2)及方差分析表(見表3)：表20的最小二乘估計變量0000000012345（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+00867.5278e+007465.42050誤差1.1322e+00681.6174e+005總計5.2808e+00814F檢驗：H:0=0=0=0=0=0二0H:0(i二1,2,3,4,5,6)不全為001234561i由表2可知，統(tǒng)計量F0=465.4205，在顯著性水平a=0.05，查F分布表，

得臨界值F=3.1122。由F0>F=3.1122，所以拒絕H，接受備擇假設。則總

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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esmr375esmr375CoefficientswithErrorBarsCoefft-statp—valNextstep:MoveX3outX10.1255410.44410.6687X2-0.936026-8.58500.0000NextStepX3■003968080031909753—e—AllStepsX40.5721063.79800.0053X50.09199240.64810.5351X6rirrir-0.0466971-1.53370.1636Export...-3-2-10123Intercept=-6922.59R-square=0.997856F=620.561RMSE=376.197AdjR-sq=0.99598p=3.15856e-010ModelHistory圖2國家財政收入與各因素的散點圖CoefficientswithErrorBarsX1X2X3X4X5X6-0.812016-13.41930.00000.4634630.9945X1X2X3X4X5X6-0.812016-13.41930.00000.4634630.99450.34140.7232735.56870.00000.01929980.16750.8700-0.027838-1.26090.23340.07497950.70420.4960Nextstep:Movenoterms-1-0.500.511.