实验报告五 回归分析

学号：班级：姓名：实验五回归分析SAS过程（2）实验目的：1.会对实际问题建立有效的多元回归模型，能对回归模型进行残差分析；2.掌握SAS输出结果用于判别回归方程优良性的不同统计量，能对回归模型进行运用，对实际问题进行预测或控制.实验要求:编写程序，结果分析．实验内容：2.6注意：可以选课外综合题目。2.6程序：datatest2_6;inputx1x2y;cards;8.37010.38.66510.38.86310.210.57216.410.78118.810.88319.711.06615.611.07518.211.18022.611.27519.911.37924.211.47621.011.47621.411.76921.312.07519.112.97422.212.98533.813.38627.413.77125.713.86424.914.07834.514.28031.714.57436.316.07238.316.37742.617.38155.417.58255.717.98058.318.08051.518.08051.020.68777.0;run;procregdata=test2_6;modely=x1-x2;outputout=ap=predictr=residh=hstudent=r;run;datab;seta;dropx1-x2;run;procprintdata=b;run;TheSASSystem13:52Friday,October15,20121TheREGProcedureModel:MODEL1DependentVariable:yAnalysisofVarianceSumofMeanSourceDFSquaresSquareFValuePr>FModel27684.162513842.08126254.97<.0001Error28421.9213615.06862CorrectedTotal308106.08387RootMSE3.88183R-Square0.9480DependentMean30.17097AdjR-Sq0.9442CoeffVar12.86612ParameterEstimatesParameterStandardVariableDFEstimateErrortValuePr>|t|Intercept1-57.987668.63823-6.71<.0001x114.708160.2642617.82<.0001x210.339250.130152.610.0145TheSASSystem13:58Friday,October15,20121Obsypredictresidrh110.34.83775.462341.496490.11583210.34.55395.746151.602950.14721310.24.81705.383021.528460.17686416.415.87410.525880.139670.05919518.819.8690-1.06901-0.293680.12066619.721.0183-1.31833-0.369620.15575715.616.1927-0.59269-0.162280.11480818.219.2459-1.04595-0.276660.05148922.621.41301.186980.320900.092011019.920.1876-0.28758-0.075930.047971124.222.01542.184600.584770.073831221.021.4685-0.46846-0.123690.048091321.421.4685-0.06846-0.018080.048091421.320.50620.793850.212370.072761519.123.9541-4.85411-1.274690.037651622.227.8522-5.65220-1.482750.035671733.831.58402.216030.612500.131311827.433.8065-6.40648-1.783240.143461925.730.6010-4.90098-1.306850.066662024.928.6970-3.79704-1.101370.211242134.534.38820.111820.029330.035812231.736.0083-4.30832-1.135960.045422336.335.38530.914740.241760.049952438.341.7690-3.46900-0.948030.111432542.644.8777-2.27770-0.608210.069312655.450.94294.457131.202600.088422755.752.22383.476250.941880.096032858.353.42854.871491.327570.106422951.553.8993-2.39933-0.655110.109833051.053.8993-2.89933-0.791630.109833177.068.51538.484702.486140.22706由表student对应列可知,中有落在(-1,1)内;有落在(-1.5,1.5)内;有落在(-2,2)内.由此可见学生化残差落在上述各区间内的频率与分布的相应概率有差别，因此对所给数据拒绝模型误差项服从正态分布的假定．程序：proccapabilitydata=agraphicsnoprint;qqplotr/normal(mu=0sigma=1);run;procsortdata=a;byr;prociml;usea;readallvar{r}intorr;doi=1to31;qi=probit((i-0.375)/31.25);q=q//qi;end;rq=rr||q;createcorrelvar{rq};appendfromrq;quit;procprintdata=correl;run;proccorrdata=correl;run;由学生化残差的正态QQ图可知，其点不在一条直线上;datatest2_6;inputx1x2y;cards;8.37010.38.66510.38.86310.210.57216.410.78118.810.88319.711.06615.611.07518.211.18022.611.27519.911.37924.211.47621.011.47621.411.76921.312.07519.112.97422.212.98533.813.38627.413.77125.713.86424.914.07834.514.28031.714.57436.316.07238.316.37742.617.38155.417.58255.717.98058.318.08051.518.08051.020.68777.0;run;procregdata=test2_6;modely=x1-x2;outputout=ap=fittedyr=residual;run;procprintdata=a;run;procgplotdata=a;plotresidual*fittedyresidual*x1residual*x2;symbolv=doti=none;run;Y拟合值的残差图也表明与不满足线性关系对因变量作Box-Cox变换datatest2_6;inputx1x2y;cards;8.37010.38.66510.38.86310.210.57216.410.78118.810.88319.711.06615.611.07518.211.18022.611.27519.911.37924.211.47621.011.47621.411.76921.312.07519.112.97422.212.98533.813.38627.413.77125.713.86424.914.07834.514.28031.714.57436.316.07238.316.37742.617.38155.417.58255.717.98058.318.08051.518.08051.020.68777.0;run;prociml;n=31;t=1;usetest2_6;readallvar{x1x2y}intom;doi=1ton;t=t#m[i,3];end;prod=t##(1/n);j=j(n,1,1);xx=j||m[,1:2];h=xx*inv(xx`*xx)*xx`;dolamb=-0.5to0.5by0.01;iflamb=0thenzlamb=prod#log(m[,3]);elsezlamb=(m[,3]##lamb-j)/(lamb#(prod##(lamb-1)));sse=zlamb`*(i(n)-h)*zlamb;lsse=lsse//(lamb||sse);end;tt=prod#log(m[,3]);sse0=tt`*(i(n)-h)*tt;lsse[51,1]=0;lsse[51,2]=sse0;index=lsse[>:<,];minlsse=index[1,2];lambda0=lsse[minlsse,1];printlambda0;createplotdatavar{lambdasse};appendfromlsse;transy=(m[,3]##lambda0-j(n,1,1))/lambda0;outm=m[,1:2]||transy;createtransvar{xx1xx2yy};appendfromoutm;quit;procprintdata=trans;run;goptionsreset=all;procgplotdata=plotdata;plotsse*lambda;symbolv=pointi=spline;run;TheSASSystem14:25Friday,October15,20121LAMBDA00.31TheSASSystem14:56Sunday,October6,20023ObsXX1XX2YY18.3703.4210728.6653.4210738.8633.40100410.5724.45205510.7814.78410610.8834.90105711.0664.33393811.0754.70396911.1805.254511011.2754.926541111.3795.436251211.4765.063651311.4765.112281411.7695.100191512.0754.823501612.9745.207691712.9856.381521813.3865.776231913.7715.599252013.8645.513162114.0786.442762214.2806.192372314.5746.596412416.0726.761082516.3777.095992617.3817.971832717.5827.990592817.9808.150352918.0807.721283018.0807.688223120.6879.17501由图可知，在时达到最小，因此，在Box-Cox变换式中取．procregdata=trans;modelyy=xx1-xx2;outputout=cp=predict1r=resid1student=student1;run;goptionsreset=all;proccapabilitygraphicsnoprintdata=c;qqplotresid1/normal;run;goptionsreset=all;procgplotdata=c;plotresid1*predict1;symbolv=doti=none;run;TheSASSystem14:56Sunday,October6,20023TheREGProcedureModel:MODEL1