多元线性回归与逐步回归.doc

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： MATLAB实验目的1.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。实验内容1、建立多元回归模型：编写程序如下：A=6484.004100.60794.008101.40112704.046991.002664.906858.004954.30859.408300.10114333.038474.002937.108087.105146.401015.109415.60115823.055472.003149.4810284.505588.001415.0010993.70117171.051333.003483.3714143.806605.102284.7012462.10118517.048829.004348.9519359.609169.203012.6016264.70119850.055043.005218.1024718.3011884.603819.6020620.00121121.045821.006242.2029082.6013539.804530.5024774.10122389.046989.007407.9932412.1013852.504810.6027298.90123626.053429.008651.1433387.9014241.905231.4029152.50124761.050145.009875.9535087.2014106.205470.6031134.70125786.049981.0011444.0839047.3013873.605888.0034152.60126743.054688.0013395.2342374.6014462.806375.4037595.20127627.052215.0016386.0445975.2014931.507005.0042027.10128453.047119.0018903.6453092.9014870.108181.3045842.00129227.054506.0021715.25;subplot(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(x5(全名人口数) ylabel(y(国家财政收入)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：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间0123456-6922.60.1-0.900.60.10-41630,27785-1,1-1,-1-3,30,10,00,0R2=0 F=620 p 0 s2=141520由此得模型为：y=-6922.6-0.1x1-0.9x2+0.6x4+0.1x52、逐步回归求解：程序：x=6484.004100.60794.008101.40112704.046991.006858.004954.30859.408300.10114333.038474.008087.105146.401015.109415.60115823.055472.0010284.505588.001415.0010993.70117171.051333.0014143.806605.102284.7012462.10118517.048829.0019359.609169.203012.6016264.70119850.055043.0024718.3011884.603819.6020620.00121121.045821.0029082.6013539.804530.5024774.10122389.046989.0032412.1013852.504810.6027298.90123626.053429.0033387.9014241.905231.4029152.50124761.050145.0035087.2014106.205470.6031134.70125786.049981.0039047.3013873.605888.0034152.60126743.054688.0042374.6014462.806375.4037595.20127627.052215.0045975.2014931.507005.0042027.10128453.047119.0053092.9014870.108181.3045842.00129227.054506.00;y=2664.90 2937.10 3149.48 3483.37 4348.95 5218.10 6242.20 7407.99 8651.14 9875.95 11444.08 13395.23 16386.04 18903.64 21715.25;stepwise(x,y,1,2,3,4,5,6,0.05,0.10)得到：剔除变量x3得到：剔除变量x5得到：剔除变量x1得到：剔除变量x6得到：最后得到回归方程：y=519.678-0.81201x2+0.72327x4实验结果分析首先得到的的多元线性回归模型