应用回归分析习题答案SAS程序

2.16 (1) 绘制y对x的散点图，可以用直线回归描述两者之间的关系吗?程序如下: 结果:表一：由表一，可得可以用直线回归描述两者的关系。(2)建立y对x的线性回归，p r cli clm结果表二:由表二可得，F=112.81，P0.0001，可知，模型的拟合数据较好。表三：又R方=0.6972，故知因变量y总体变异中69.72%被自变量x所解释。表四：由表四P|t|Intercept1-348.28017176.45922-1.970.0959x113.754041.933321.940.1002x217.100712.880282.470.0488x3112.4474710.569331.180.2835回归方程为:(3)均方根误差23.44188R 方0.8055因变量均值231.50000调整 R 方0.7083变异系数10.12608样本决定系数R方为0.8055 则回归方程显著；(4)方差分析源自由度平方和均方F 值PrF模型3136554551.789848.280.0149误差63297.13048549.52175校正合计916953F=8.28 ,P=0.0149 模型有显著性意义；(5)参数估计值变量自由度参数估计值标准误差t值Pr|t|Intercept1-348.28017176.45922-1.970.0959x113.754041.933321.940.1002x217.100712.880282.470.0488x3112.4474710.569331.180.2835工业总产值的P值为0.1002 在显著性水平0.05 上对y货运总量不显著；农业总产值的P值为0.0488 在显著性水平0.05上对y货运总量显著；居民非商品支出P值为0.2835在显著性水平0.05上对y货运总量不显著；(6)剔除重新建立回归方程proc reg data=huoyun;model y=x1 x2/clb;run;方差分析源自由度平方和均方F 值PrF模型2128936446.5995011.120.0067误差74059.30099579.90014校正合计916953F值为11.12 ，P值为0.0067 模型高度显著；参数估计值变量自由度参数估计值标准误差t值Pr|t|Intercept1-459.62365153.05757-3.000.0199x114.675631.816072.570.0368x218.970962.468463.630.0084工业总产值的P值为0.0368 在显著性水平0.05 上对y货运总量显著；农业总产值的P值为0.0084 在显著性水平0.05上对y货运总量显著；(7)参数估计值变量自由度参数估计值标准误差t值Pr|t|95% 置信限Intercept1-459.62365153.05757-3.000.0199-821.54730-97.70001x114.675631.816072.570.03680.381308.96996x218.970962.468463.630.00843.1339814.80794的回归系数置信区间为（0.38130，8.9996）的回归系数置信区间为（3.13398，14.80794）4.9（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。程序：data yd;input x y;cards;679 0.79 292 0.44 1012 0.56 493 0.79 582 2.71156 3.64 997 4.73 2189 9.5 1097 5.34 2078 6.851818 5.84 1700 5.21 747 3.25 2030 4.43 1643 3.16414 0.5 354 0.17 1276 1.88 745 0.77 435 1.39 540 0.56 874 1.56 1543 5.28 1029 0.64 710 4 1434 0.31 837 4.21748 4.88 1381 3.48 1428 7.58 1255 2.63 1777 4.99 370 0.59 2316 8.19 1130 4.79 463 0.51 770 1.74 724 4.1 808 3.94 790 0.96 783 3.29 406 0.44 1242 3.24658 2.14 1746 5.71 468 0.64 1114 1.90 413 0.511787 8.33 3560 14.94 1495 5.11 2221 3.85 1526 3.93;proc plot data=yd;plot y*x=*;run;结果由散点图可知:Y和X有线性关系，故可建立回归方程。程序proc reg data=yd ;model y=x/r;output out=out1 r=residual;run;proc gplot data=out1;plot residual*x;run;结果:由方差分析可得:P0.0655大于0.05,故常数项不显著.需要除去常数项重新拟合方程。程序proc reg data=yd;model y=x/noint;run;结果:由方差分析得:P0.05,所以该回归方程显著,而且F值较有常数项时更大,所以无常数项时拟合方程更好;R方=0.8704,调整R方为0.8679,回归方程的拟合度有较大幅度提高;由参数估计:参数P值均0.05,参数显著有效;所以拟合方程为:y=0.00314x残差散点图如下:（2） 判断该问题是否存在异方差。由残差散点图可以得:误差随X的增加而波动幅度增加,呈大喇叭的形状,因此认为方差项存在异方差.故利用等级相关系数法判断:proc reg data=yd;model y=x/r noint;output out=out1 r=residual;run;data out2;set out1;z=abs(residual);run;proc corr data=out2 spearman;var x z;run;结果:残差绝对值与xi的等级相关系数rs=0.21271,对应的P值=0.126,认为残差绝对值与自变量xi显著相关,存在异方差.(2) 若存在异方差，用幂指数型的权函数建立加权最小二乘回归方程。由（2）结论存在异方差，则程序：data a;set yd;array row10 w1-w10;array p10(-2,-1.5,-1,-0.5,0,0.5,1,1.5,2,2.5);do i=1 to 10;rowi=1/x*pi;end;run;proc print;run;proc reg data=a;model y=x/r;weight w1;output out=out1 r=residual;run;proc gplot data=out1;plot residual*x;run;结果；由方差分析:pF模型1110.59832110.5983211648.6|t|95% 置信限Intercept1-1.434830.24196-5.93.0001-1.94316-0.92650x10.176160.00163107.93卡方21.840.3978Durbin-Watson D0.663观测数20第一阶自相关0.644查DW分布表可得临界值和分别为1.20和1.41,由于DW值=0.663小于,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data aa;set out;ro=1-0.5*0.663;y_t_1=y-ro*lag1(y);x_t_1=xro*lag1(x);run;proc print data=aa;run;proc reg data=aa;model y_t_1=x_t_1/clb p r spec DW;run;结果如下:方差分析源自由度平方和均方F 值PrF模型113.1333013.133302467.41|t|95% 置信限Intercept1-0.300060.17763-1.690.1094-0.674830.07471x_t_110.172680.0034849.67卡方20.870.6467Durbin-Watson D1.360观测数19第一阶自相关0.293又由DW=1.306，查DW，n=19,k=2.可知和分别为1.18和1.40，DW=1.360在和之间，所以迭代法建立的回归方程的误差项无自相关.proc reg data=aa;model y_t_1=x_t_1/noint clb p r spec DW;run;结果如下：方差分析源自由度平方和均方F 值PrF模型11380.746041380.74604|t|95% 置信限x_t_110.166840.484.96F模型12.115932.11593381.34|t|Intercept10.032890.025851.270.2203difx10.160960.0082419.53F模型210.150.0002误差49校正合计51均方根误差329.69302R 方0.2928因变量均值959.80269调整 R 方0.2640变异系数34.35008参数估计值变量自由度参数估计值标准误差t值Pr|t|95% 置信限Intercept1-574.06239349.27075-1.640.1067-1275.94824127.82346x11191.0984973.309172.610.012143.77821338.41878x212.045140.910692.250.02930.215043.87524回归分析方程:第一和第二矩指定的检验自由度卡方Pr卡方55.120.4020Durbin-Watson D0.745观测数52第一阶自相关0.615DW值=0.745小于，所以误差项存在正相关.残差图为：（2） 用迭代法处理序列相关，并建立回归方程data aa;set out;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;proc print data=aa;run;proc reg data=aa;model y_t_1=x1_t_1 x2_t_1/clb p r spec dw;run;方差分析源自由度平方和均方F 值PrF模型221.55|t|95% 置信限Intercept1-178.7752290.33819-1.980.0536-360.412322.86189x1_t_11211.1104347.747324.42卡方54.380.4966Durbin-Watson D1.716观测数51第一阶自相关0.122得回归方程：，DW=1.716在和4-之间，误差项无自相关.(3) 用一阶差分法处理数据data aaa;set a;dify=y-lag1(y);difx1=x1-lag1(x1);difx2=x2-lag1(x2);run;proc reg data=aaa;model dify=difx1 difx2/r dw;run;方差分析源自由度平方和均方F 值PrF模型225.04|t|Intercept17.6981039.754210.190.8473difx11209.8910644.143164.75 |r| under H0: Rho=0yearx1x2x3x4x5x6yyear1.000000.91925.00010.88437.00010.87974.00010.99905.00010.90240.00010.558560.00850.89990.0001x10.91925.00011.000000.99434.00010.99179.00010.90893.00010.99691.00010.506220.01920.98677.0001x20.88437.00010.99434.00011.000000.99881.00010.87144.00010.99890.00010.501910.02040.99161.0001x30.87974.00010.99179.00010.99881.00011.000000.86630.00010.99723.00010.494150.02280.98968.0001x40.99905.00010.90893.00010.87144.00010.86630.00011.000000.89040.00010.571480.00680.88673.0001x50.90240.00010.99691.00010.99890.00010.99723.00010.89040.00011.000000.511340.01780.99432.0001x60.558560.00850.506220.01920.501910.02040.494150.02280.571480.00680.511340.01781.000000.512530.0175y0.89990.00010.98677.00010.99161.00010.98968.00010.88673.00010.99432FIntercept1378.856162197.45957143060.390.5404x1-0.642930.1659215.020.0017x2-0.312350.20285861492.370.1459x3-0.450010.54571247080.680.4234x4-0.002430.02413367.608770.010.9213x50.672860.1273327.930.0001x6-0.007610.00808322060.890.3624条件数字的边界: 2631.8, 31948向后消除: 第 1 步变量 x4 已删除: R 方 = 0.9963 和 C(p) = 5.0101变量参数估计值标准误差II型SSF 值PrFIntercept1160.21420311.3585713.890.0020x1-0.652910.1285125.810.0001x2-0.296960.128705.320.0357x3-0.460750.51721269320.790.3871x50.664520.0934050.62FIntercept1157.06175309.3235513.990.0018x1-0.631060.1253325.350.0001x2-0.377030.0915316.970.0008x50.662590.0927751.01FIntercept874.23324106.6757267.16.0001x1-0.611890.1235924.510.0001x2-0.353570.0881716.080.0009x50.637330.0889451.35F模型11659.45FIntercept710.3696590.8905361.08.0001x50.180060.004421659.45F模型21117.33FIntercept1012.61270135.4078755.92.0001x1-0.415740.151817.500.0135x50.311870.0482841.72F模型31378.63FIntercept873.06066105.5890568.37.0001x1-0.609450.1217325.060.0001x2-0.351960.0874916.180.0009x50.635500.0879652.20F1x510.98870.988725.99251659.45.00012x120.00330.992015.34767.500.01353x230.00390.99592.547016.180.0009结果：变量x5进入模型中，检验结果为：F=1659.45，p0.0001,模型有显著意义，参数x5检验结果为：F=1659.45，p0.0001;参数x5有显著性意义；变量x1进入模型之中，检验结果为：F=1117.33,P0.0001,模型有显著意义。参数x1检验结果为：F=7.50，p=0.0135;参数x5的检验结果为：F=41.72，p0.0001；参数x1和x5都有显著性意义。变量x2进入模型中，检验结果为：F=1378.63，p=0.0001，模型有显著性意义。参数x1的检验结果为：F=25.06 ,P0.0001;参数x2的检验结果为：F=16.18，p=0.0009;参数x5的检验结果为：F=52.20，p|t|容差方差膨胀Intercept11436.762242170.219350.660.5187.0x11-0.635460.16221-3.920.00150.00324308.28483x21-0.323800.20123-1.610.12990.2608.85663x31-0.400130.54145-0.740.47210.00210476.60159x41-0.003040.02380-0.130.90030.0375126.65966x510.673630.126765.310.00010.1860.89459x61-0.007570.00803-0.940.36220.575501.73761共线性诊断（截距已调整）个数特征值条件指数偏差比例x1x2x3x4x5x615.132341.00000.001230.0.0081220.6