多元线性回归与逐步回归

1、安徽财经大学统计与数学模型分析实验中心数据分析方法实验报告班级：11信计一班学号：20114595姓名：张思琪实验日期：3月17实验地点：2栋406实验名称:多元线性回归与逐步回归使用软件名称:MATLAB1 .熟练掌握线性回归模型的建立方法，掌握regress命令的使用方法。2 .掌握编程求总离差平方和TSS回归平方和RSS残差平方和ESS等相关统计量。3 .掌握逐步回归的思想与方法，掌握stepwise命令的使用方法。1、建立多元回归模型:编写程序如下：A=6484.006858.008087.1010284.5014143.8019359.6024718.3029082.6032412.

2、1033387.9035087.2039047.3042374.6045975.2053092.90;4100.604954.305146.405588.006605.109169.2011884.6013539.8013852.5014241.9014106.2013873.6014462.8014931.5014870.10794.008101.40859.408300.101015.101415.002284.703012.603819.604530.504810.605231.405470.605888.006375.407005.008181.30112704.0114333.094

3、15.6010993.7012462.1016264.7020620.0024774.1027298.9029152.5031134.7034152.6037595.2042027.1045842.0046991.0038474.00115823.0117171.0118517.0119850.0121121.0122389.0123626.0124761.0125786.0126743.0127627.0128453.0129227.02664.902937.1055472.0051333.0048829.0055043.0045821.0046989.0053429.0050145.004

4、9981.0054688.0052215.0047119.0054506.003149.483483.374348.955218.106242.207407.998651.149875.9511444.0813395.2316386.0418903.6421715.25subplot(3,2,1),plot(A(:,1),A(:,7),'*'),xlabel('x1(工业总产值)')ylabel('y(国家财政收入)')subplot(3,2,2),plot(A(:,2),A(:,7),'*'),xlabel('x2(农业

5、总产值)')ylabel('y(国家财政收入)')subplot(3,2,3),plot(A(:,3),A(:,7),'*'),xlabel('x3(建筑业总产值)')ylabel('y(国家财政收入)')subplot(3,2,4),plot(A(:,4),A(:,7),'*'),xlabel('x4(社会商品零售总额)')ylabel('y(国家财政收入)')subplot(3,2,5),plot(A(:,5),A(:,7),'*'),xlabel(

6、9;x5()')ylabel('y(国豕财政收入)')subplot(3,2,6),plot(A(:,6),A(:,7),'*'),xlabel('x6(受灾面积),)ylabel('y(国家财政收入)')得到：>入收政财家y>入收政财家)入收政财家4X10*it*/X1(工业总产值)4X10464X10>入收政财家y>入收政财家4x2(农业总产值)4X1000500010000x3(建筑业总产值)41.11.151.21.251.3X5(全名人口数)x105)入收政财家x4(社会商品零售总额11cx，10

7、4X104-x6(受灾面积)4X10可以看到工业总产值、农业总产值、建筑业总产值、社会商品零售总额、全民人口数、受灾面积都与国家财政收入有线性关系，因此可以建立如下六元线性回归模型。程序：x=ones(15,1),A(:,1),A(:,2),A(:,3),A(:,4),A(:,5),A(:,6);y=A(：,7)b,bint,r,rint,stats=regress(y,x);b,bint,stats,回归模型的系数、系数置信区间与统计量回归系数回归系数估计值回归系数置信区问B0-6922.6-41630,27785B10.1-1,1A-0.9-1,-1330-3,3B40.60,1B50.1

8、0,03600,0R2=0F=620p<0s2=141520由此得模型为:X1X2X3X4X5X6377376375得至上2、逐步回归求解:程序：x=6484.006858.008087.1010284.5014143.8019359.6024718.3029082.6032412.1033387.9035087.2039047.3042374.6045975.2053092.904100.604954.305146.405588.006605.109169.2011884.6013539.8013852.5014241.9014106.2013873.6014462.8014931.5

9、014870.10y=-6922.6-0.1x1-0.9x2+0.6X4+0.1X5794.008101.40859.408300.10112704.0114333.046991.0038474.001015.101415.002284.703012.603819.604530.504810.605231.405470.605888.006375.407005.008181.309415.6010993.7012462.1016264.7020620.0024774.1027298.9029152.5031134.7034152.6037595.2042027.1045842.00115823

10、.0117171.0118517.0119850.0121121.0122389.0123626.0124761.0125786.0126743.0127627.0128453.0129227.055472.0051333.0048829.0055043.0045821.0046989.0053429.0050145.0049981.0054688.0052215.0047119.0054506.00;y=2664.902937.103149.483483.374348.955218.106242.207407.998651.149875.9511444.0813395.2316386.041

11、8903.6421715.25;stepwise(x,y,1,2,3,4,5,6,0.05,0.10)得到：CoefficientswithErrorBarsCoeff.t-statp-val0.5721060.0919924-3-2-100.1255410.44410.66870.936026-8.58500.00000.03968080.03190.97533.0.0.0.Nextstep：MoveX3outIrilercept=-6922.59R-square=0.997656F=520.561RMSE=376.1970.99590p-3.15656e-010ModelHistory37

12、81-0.04669711.53370.1636XiX2X3X4X5X6CoefficientswithErrorBarsCoeff.t-statP-vaNextstep:MoveX5out卜A-0-00.013379936920396805691585891.-9.0.5.23943303106997910.0.0.0.24009700640053074001NextStep.AAlSteps0.09399320.78260.45-0.0471292-1.83240.10Export-3-2-10123ModelHistoryHercepl=-7124J63R-square=0_997fi5

13、6F=637.65RMSE=364704AcUR-sq=0Se6426p=1J01(J29e-011CoefficientswithErrorBarsCoeff.t-statp-vaiIX180.1392351.31880.2166Nexlslap'X2X3X4X5X6-0.898998-10.57730.00000.3948920.36630.72260.588395.47780.00030.09399320.78260.4540-0.0387174-1.69010.1219MqwsKioutNextStepaiExport.4I9=9-=-卜-2-10123ModelHistory

14、Xikirtercepl=2897.45R-square=0.99771F=1009.12RMSE=347,763AdjR-sq=0.996565p=377254e-013得至上X1X2X3X4X5X6卜0.1392351.31880.2166-0.816182-13.79410.00000.6093161.36010.20370.7276936.09650.00000.1035820.84190.4195Nextslep：|.MoveX6OutNextStep.*r-AlSteps-0.027838-1.26090.2334Export.CoefficientswithErrorBarsCo

15、eff.t-statp-val-1-0.500.511.5Hercepl=1S5277R-sctuare=OJ997312F=1360.17RMSE=369258/MR-sq=0S96334p=2J05391e-014ModelHistory380ESMR3603401剔除变量X6得到：234X10.07497950.70420.4960X2-0.812016-13.41930.0000X390.4634630.99450.3414X4b0.7232735.56870.0000X51工0.01929980.16750.8700X6.-0.027838-1.26090.2334a.ITIT-1-0.500.511.5CoefficientswithErrorBarsCoeff.t-statp-valNextstep：Movenoiterm号NextSlepaiStepsExport.irrtercepl=519.678R-square=0.996923F=1543.91RMSE=367,982AdjR