应用回归分析习题49答案

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(1)用普通最小二乘法建立y与x的回归方程,并画出残差散点图.

datad1;inputxy@@;cards;

6790.792920.4410120.564930.795822.711563.649974.7321899.510975.3420786.8518185.8417005.217473.2520304.4316433.164140.53540.1712761.887450.774351.395400.568741.5615435.2810290.64710414340.318374.217484.8813813.4814287.5812552.6317774.993700.5923168.1911304.794630.517701.747244.18083.947900.967833.294060.4412423.246582.1417465.714680.6411141.904130.5117878.33356014.9414955.1122213.8515263.93;

procprint;run;

procplotdata=d1;ploty*x='.';run;

由散点图知，y和x满足线性关系，建立回归方程，作残差散点图。

procregdata=d1;modely=x/r;

outputout=outr=residual;run;

procgplotdata=out;plotresidual*x;run;

方差分析源模型误差自由度151平方和均方F值Pr>F302.63314302.63314121.66|t|-1.880.0655-0.831300.441610.003680.0003339011.030.05，不显著。去掉常数项重新拟合。

procregdata=d1;modely=x/noint;run;

方差分析源模型误差自由度152平方和均方F值Pr>F911.26758911.26758349.25|t|0.003140.0001677618.69|r|underH0:Rho=0xx1.00000z0.212710.12621.00000z0.212710.1262

残差绝对值ei与xi的等级相关系数rs=0.21271,P值=0.126,认为ei与自变量xi显著相关,存在异方差。

(3)假使存在异方差，用幂指数型的权函数建立加权最小二乘回归方程。

datad2;setd1;

arrayrow{10}w1-w10;

arrayp{10}(-2,-1.5,-1,-0.5,0,0.5,1,1.5,2,2.5);doi=1to10;row{i}=1/x**p{i};end;run;

procprint;run;

procregdata=d2;modely=x/r;weightw1;

outputout=outr=residual;run;

procgplotdata=out;plotresidual*x;run;

方差分析源模型误差自由度151平方和均方F值Pr>F12913086441291308644228.46|t|-3.860.0003-2.400380.621830.00