应用回归分析习题13答案

1、4.13(1)用普通最小二乘法建立y与x回归方程.(2)用残差图及DW检验诊断序列的自相关datadxh;inputobsxy;cards;1127.320.96213021.43132.721.964129.421.52513522.396137.122.767141.123.488142.823.669145.524.110145.324.0111148.324.5412146.424.2813150.22514153.125.6415157.326.4616160.726.9817164.227.5218165.627.7819168.728.242017228.78;run;procp

2、rint;run;procgpiotdata=dxhploty*x;run;procregdata=dxh;|modely=x/clbprspecdw;outputout=outr=residual;run;方差分析源自由度平方和F值Pr>F模型1110.59832110.5983211648.6<.0001wt180.170900.00949校正合计19110.76922P(1<0.05，回归方程显著。均方根误差0.09744R方0.9985因变量均值24.57300调整R方0.9984变异系数0.39653R方=0.9985,调整R方=0.9984,所以回归方程拟合度较高

3、.-i*Qi?QIB4。中白la<aa!*Gba4p-sTl&Fp-d-a-c2pa-4-fl!-«T参数估计值变量自由度参数估计值标准t值Pr>|t|95%置信限Intercept1-1.434830.24196-5.93<.0001-1.94316-0.92650x10.176160.00163107.93<.00010.172730.17959常数项和x的参数估计P值均小于0.05,所以参数显著有效回归方程为y=-1.43483+0.17616残差图成发散状，可能存在异方差。Durbin-WatsonD0.663观测数20第一阶自相关0.644查

4、口帆布表可知n=20,P=2时临界值dL和du分别为1.20和1.41,由于DWt=0.663小于出,故模型存在序列正自相关性.(3)用迭代法处理序列相关，并建立回归方程datadxh1;setout;|ro=1-0.5*0.663;y_t_1=y-ro*lag1(y);x_t_1=xro*lag1(x);run;procprintdata=dxh1;|run;procregdata=dxh1;modely_t_1=x_t_1/clbprspecDWrun;方差分析源自由度平方均方F值Pr>F和模型113.1333013.133302467.41<.0001误差170.090490

5、.00532校正合计1813.22379P值<0.05，回归方程显著。均方根误差0.07296R方0.9932因变量均值8.48413调整R方0.9928变异系数0.85992由R方和调整R方知，方程拟合度较高。参数估计值变量自由度参数标准t值Pr>|t|95%置信限估计值误差-0.300060.17763-1.690.1094-0.674830.07471Interceptx_t_110.172680.0034849.67<.00010.165350.18002n常数性参数检验的p值=0.1094大于0.05,不显著，除去常数项再建立回归方程.Durbin-WatsonD1

6、.360观测数19第一阶自相关0.293DW=1.360在dL和dU又由DW=1.306，查DW知，n=19,k=2时.可知dL=1.18,dU=1.40,之间，所以迭代法建立的回归方程的误差项无自相关.去掉常数项建回归方程。modely_t_1=x_t_1/nointclbprspecDWprocregdata=dxh1;run;结果如下:方差分析源模型自由度平方均方F值Pr>F11380.746041380.74604235188<.0001误差18未校正合计190.105670.005871380.85172P值<0.05，回归方程显著。均方根误差0.07662R方0.

7、9999因变量均值8.48413调整R方0.9999变异系数0.90311由R方和调整R方知，方程拟合度较高。参数估计值变量自由度参数估计值标准误差t值Pr>|t|x_t_110.166840.00034402484.96<.000195%置信限0.166110.16756P值0.05,参数估计显著有效。回归方程：畀=痘1的毛.其中yt=y-py,。=工一加口.用一阶差分法处理数据，并建立回归方程datadxh2;|seta;difx=x-lag1(x);dify=y-lag1(y);run;procregdata=dxh2;modeldify=difx/rpDWrun;结果如下：

8、方差分析源自由度平方均方F值Pr>F和模型12.115932.11593381.34<.0001误差170.094330.00555校正合计182.21025回归方程为:P值<0.05，回归方程显著。均方根误差0.07449R方0.9573因变量均值0.41158调整R方0.9548变异系数18.09839参数估计值变量自由度参数标准t值Pr>|t|估计值Intercept10.032890.025851.270.2203difx10.160960.0082419.53<.0001由R方和调整R方知，方程拟合度较高。M=0-03239+0L16O96Ar其中加二A

9、t=不一r.Durbin-WatsonD1.480观测数19第一阶自相关0.253DW=1.480，查DWn=19,k=2.可知4和4分别为1.18和1.40,DW=1.480在1.40和4-1.40之间，误差项间无自相关.Z(4)比较以上各方法所建回归方程的优良性.在回归模型不存在序列相关时，普通最小二乘法比迭代法和一阶差分法操作起来更简便，但是，当一个回归模型存在序列相关性时，普通最小二乘法所建立的回归方程就不适用了，这时需要使用迭代法或一阶差分法。由于一阶差分法的应用条件是自相关系数P=1,当P接近1时，一阶差分法比迭代法好，当原模型存在较高程度的一阶自相关时，一般使用一阶差分法，因为一

10、阶差分法比迭代法简单而且迭代法需要用样本估计自相关系数P,对P的估计误差会影响迭代法的使用效率，同时迭代法的算法时间复杂度比一阶差分的高，在效率上不如一阶差分好。4.14(1)用最小二乘法建立回归方程，用残差图及DW检验诊断序列的自相关性datadxh;inputyx1x2;cards;893.9351091.2729252521229.9752671045.855379997.2453181495.1463931200.565331747.244204866.4352666035253343.525315472.16271171.794166135.794204925.9553351574.

11、0153521405.335274971.2743331165.25302597.854324490.344327709.595-206987.35310954.663061216.8963501491.525275668.34173915.035360565.9243401267.985380930.246285379.384232500.74529483.655220982.946391722.2842791337.4453221150.5142311514.8463681442.085357767.6452601020.0352981067.4953501484.126320957.68

12、42271344.9152611361.7853031424.6962631158.214215827.564294803.1642881447.466257；run;procprintdata=dxh;run;procregdata=dxh;|modely=x1x2/clbprspecDWoutputout=outr=residual;|run;procgplotdata=out;plotresidual*y;run方差分析源自由度平方和F值Pr>F模型22205552110277610.150.0002495326177108697校正合计517531729P值<0.05，回归

13、方程显著。参数估计值变量自参数标准t值Pr>|t|95%置信限由估计值误差度Intercep1-574.0623349.2707-1.60.1067-1275.9482127.8234t95446x11191.0984973.309172.610.012143.77821338.41878x212.045140.910692.250.02930.215043.87524回归分析方程：y=-57406239+19105849%+204514巧Durbin-WatsonD0.745观测数52第一阶自相关0.615DWt=0.745<dl,误差项存在正相关ns残差图满足线性关系，可建立回

14、归方程。(2)用迭代法处理序列相关，并建立回归方程datadxhl;|setout;|ro=1-0.5*0,745;y_t_1=y-ro*lag1(y);x1_t_1=x1-ro*lag1(x1);x2_t_1=x2-ro*lag1(x2);run;procprintdata=dxh1;run;procregdata=dxh1;modelyt1=x1t1x2t1/clbprspecdw;Run;力差分析源自由度平方和F值Pr>F模型22865658143282921.55<.000148319149766490校正合计506057155P值0.05，回归方程显著。参数估计值变量自参

15、数标准t值Pr>|t|95%置信限由估计值度Intercep1-178.775290.3381-1.90.0536-360.41232.86189t2982x1_t_11211.1104347.74734.42<.0001115.10802307.112825x2_t_111.436480.628642.290.02680.172532.70044畀=-1电77522+211110«4+1_4361t所得回归方程:其中Durbin-WatsonD1.716观测数51第一阶自相关0.122I"dr.二-DW=1.716在和4-之间，误差项无自相关.(3)用一阶差分

16、法处理数据Data=dxh2;|seta;dify=y-lag1(y);difx1=x1-lag1(x1);|difx2=x2-lag1(x2);|run;procregdata=dxh2;modeldify=difx1difx2/rdw;|run;方差分析源自由度平方和F值Pr>F模型24033892201694625.04<.000148386579280537校正合计507899684P值0.05，回归方程显著。参数估计值变量自由度参数估计值标准t值Pr>|t|Intercept17.6981039.754210.190.8473difxl1209.8910644.143164.75<.0001difx211.398980.582822.400.0203回归方程加=7一砂810120列89：106Aq4139893其中国二具一-(4)比较以上各方法所建回归方程的优