sas多元统计分析例题程序输出结果分析过程.docx
应用数理统计报告所在院系计算机与信息工程学院学科专业农业信息化研究生姓名宋玲指导老师：薛河儒2013年12月21日用线性回归分析方法分析林木生物量的影响因素1.题目在林木生物量生产率研究中，为了了解林地施肥量（x1, kg）、灌水量（x2, 10）与生物量（Y, kg）的关系，在同一林区共进行了 20次试验，观察值见下表， 试建立Y关于x1,x2的线性回归方程。观察值|N123456?391011121314151617181920XI5461527063?9686579花71827592969291S510590X22939264842644530514435503960626150477252Y505152545360506567TO707374788230S78489921.程序DATAct;INPUTx1 x2 y ;XSQ=x1*x2;CARRS54 29 5061 39 5152 26 5270 48 5463 42 5379 64 6068 45 5965 30 6579 51 6776 44 7071 36 7082 50 7375 39 7492 60 7896 62 8292 61 8091 50 8785 47 84106 72 8890 52 92;PROCREGMODEIy=x1 x2/ P CLI;MODEIy=x1 x2 xsq/ P CLI;Run;3.输出结果一元一次及二次回归The REG ProcedureModel： M0DEL1Dependent Variable： yAnalysis of Variance15:47 Monday, December 302002 9SourceUFSum ofSquaresMeanSquareF VaJuePr > F版del2招85.5鸵2g1692.76814240.99<.0001Error119+413727.02434CorrectedTotl1g3504,95000Root USE2.65085R-Square0.8659DependentMean59J500DAdj R-Sq0*8519Caeff Var3.81619VariableDFParameterEst imteStandardPr > HIErrort ValueIntercept1-4.940483,45784-h430.1711xl1L539520,0881617,46<,0001x21-0.943850.10391-9.08<.0001Parameter Est i mat es一元一次及二次回妇15:47 Monday, December 3Q, 2002The REG ProcedureModel： MODEL IDependent Variable： yOutput Stat 1stIqsDependentVariablePredictedValueStd Error Wean Predict95M CLPredictRes I dual50.000050,82131.144444.731156.3126-0.821951.000052.16000.9SS246.131558.1286-1.160052.000050,5744L23824402856V74621.425654.000057,52110.32355L599663.4425-3.521153,000052,40751.010846.422958JS210.5925BO.000056.27521.7QSb49.621162.92923.7246EQ.000057.27360.857751.396363.1508h7264854。叩66,81271.152860.714972J105-1.8127G7,000066,54520.647362.739174.9013-1.545270,000070,53360.8431$4.779578,2875-0.533570.000070.38870.944764.450476.3231-0.386773.000074.10760.62S568.0379.8543-1.107674。叩73,71320.911267.800279.62630.286879,0000SO.OG430.369774.179285.9494-2.064382.000064,33460JS1178,372190J972-2.334680.000079,12040.396673.2t7485.02350.379687.0000S7.36321J36441.879194.0473-0.363284.蒯。81.5576。.睚 2375.637087.47832.442488.000090.29131.376483.930696.5S21-2.291392.0000$4,5360CJ37670.604790,46737.4MoSun* of Reeiduals0Sutn of Squared iduAs119a41372Predicted ResiduetE SS (PRESS) 182,21769ObsI234567891011 U1314151617181820The REC ProcedureMade I： MODEL2Dependent Variable： yRoot MSE Dependent Mean Coeff VarAnalysis cf YarleinceSourceDFSum of SquaresMean SquareF luePr > FModel3碗130604。1190.35347150：部<.0001ErrorIE113.888607J181CCorrected Total198604.958002.EE798R*Square0,967563.45000Adj R-Sq0.9S143.64163VariableDFPfirameterE写 t i mat eStandard Errort ValuePr > It!Intercept1-14.6513311,45354-1,27OJ220x111.S68570.171288.74<.000tx21-0.733910.2GOQQ0,0128XSQ1-0.QQ2710.00303-0.830.3914JL一波及二次回归15:47 Mtrtky, December 90, 2002Paranieter Est imates4The REG ProcedureModel: M0CEL2Jeperderit Variable： yOutput StatisticsDependentVariablePredicted Std ErrorValue M&an Predict50.000050,03781.455343.59485E.4即9-0.03785LCOOO52.1S050.9S6046,143358.2176-U18QG62,000049.48C81.759142.705256.25542.519254.00DD57,9381t J43251,8553S4.0109-3.338153400005,5336L03S346.524058.B636Q.406260.000058 ,毅 40t J6534g. 8415B140669.978053.。叩57,61430.946151.6133B3.B1521.335785.000066.61771.181460.432172.8033-1.617767.00QQ68,94150,781863.041874,84127.941570.DOQ070,92610JG6065,031076.8223D.926170.000070.55620J776M.5$"76,6038-0,5962祝0。叩74,48600.7B6868.803280.3728-t.488074.000074.0B020.39S28L0214so.oaea-C.O61278.000073.99060.079674,035485.8458-1.390682.000084,0270L047577.9G089O.fO32-2.027000.000079.007$0.911673.031084.984?0,992187.00DD88,2861L200992.082784.4875-1.ZS51844000081,9783L044075.904388.Q6182.021799.00008BJ824M2J66081,5397S6J0S7-0.824792.000064-79740.96947B.765290.82377.2028质* CL PredictPesiduaISum of Res i duas0Sum of Squared Residuals113.88*$QPredicted Residual S3 (PRESS)190.78001(1)回归模型是否显著，显著水平是多少？复相关系数是多少？答：回归方程显著，显著水平是0.0001。复相关系数是0.9659(2)回归系数的估计值是多少？显著性如何？答：Intercept -4.94048 0.1711X11.53952 <0.0001X2-0.94385 <0.0001X1 与X2的系数对于表达式极显著，intercept 对应的系数对表达式在0.01下不 显著(3)写出回归方程的表达式。y=1.53952x1-0.94385x2 - 4.94048(4)利用残差(实测值与预测值之差)、95明信取间的上下限讨论预测预报效果及预报的稳定性。答：根据上面结果可知残差和95胡信区间的上下限的差异很大，最大的达到7.4640.最小的达到0.2868.幅度比较大。所以稳定性也很差。(5)对本问题再求出Y关于X1、X2的二次多项式回归方程，并与线性回 归方程比较，说明优缺点。Intercept -14.55333 0.2210X11.66857 <0.0001X2-0.73331 0.0126XSQ -0.00271 0.3914由输出结果知：二次模型在0.0001水平下是显著的，预测模型为：y=-14.553333+1.66857x1-0.73311x2-0.00271x1*x2线性模型在0.001水平下也是显著的，预测模型为：y=1.53952X1-0.94385X2-4.94048对比来说：MODEL2相关系数更接近1,预测值与实测值更接近，回归效果更好， 因此y与x的关系应选用二次模型。用线性回归方法分析影响水稻粒重的因素1 .题目本数据来源于2003年所做的试验，数据参考文件reg-4.xls ,观测11个 水稻品种(03DH1、03DH2 03DH3 03DH4、03DH5 03DH6 03DH7 03DH8、03DH9 03DH10 03DH11)勺各种性X犬:穗数xl、枝梗数x2、枇粒x3、200粒重y。每 个水稻品种取5株.以5株为一个单位。研究水稻 200粒重y与穗数xl、枝梗 数x2、秋粒x3之间的关系，分析哪些因素对 200粒重y的影响较大。nonumx1x2x3y03DH151416595.8703DH252713275.5803DH353111945.8303DH452015644.7103DH5524141675.5903DH6519133403.8503DH753013405.5203DH8421121225.303DH952913905.6503DH1053014854.9703DH11541131205.312 .程序TITLE '多元线性回归分析；DATAAMO;INPUTY X1-X3;CARDS 5.87 14 16 59 5.58 27 13 27 5.83 31 11 94 4.71 20 15 64 5.59 24 14 167 3.85 19 13 340 5.52 30 13 40 5.65 29 13 90 4.97 30 14 85 5.31 41 13 120 ;PROCREGMODEL=x1 x2 x3;MODEY=X1 X2 X3/ SELECTIONSTEPWISE3LI; RUN3 .输出结果The REQ ProcedureModel: MODELSDependent Variable： YAnalysts of VariarnceInxlx2x37.453953.104632,400,0531-0.00S760.Q3145-0.180,B607-UJ07020J753S-0.610.5B41-0.005260.00200-2.540.0440SourceDFSun uf SquaresMeanSquareF ValuePr > FModel3ErrorSCorrected Total91,923391.573973,497360,641130.262332.440.162。Root MSEDependent MeanCoeff Var0.512185.298009,68570R-SquareAdj R SqG.55OG0.3249Pa rmeter Est tiftatesVariableDFPa raeieterStandardEstimateErrort ValuePr >10:32 Wectiesday, December 22, 19!I lie REG ProcedureM(jdel： MODELSDererident Yariatle： YStepwise Selection： Step 1Variable X3 Entered： R-Square = 0.5142 and C(p) = 0.4767Anilj/sis of VarlartceSum ofMeanSourceDFSquaresSquare F 1心duePr > FModel11.73834L79834S.47 (Ml 耻Errore1.B99020.21236Corrected Totalg3.43736ParameterStandardVariableEst i sateErrorType II S3 F ValuePr > FIntercept6.Bisai0.234S9180.76715 Bit即<0001X3-0.0049S0.001S9L790348.470.013BBountfcon ccrtd i t i onriMKr： 1T iA11 variables left i n the 的*1 are sienif icEint al the 0.I5QQ level.No other variable n*etthe Q,I5O(J sijnif icance tevel for entry into the nodul.StepVariableEnteredVariableRemtwedSumniary ofNumber Vars InStepwisePartialR-Square和1ect ionModel R-SqUirftC(p)F VilutPr > FThe REG ProcedureModel： MODEL?Dependent Variable： YOutput Stat 1st Ics0b<DependentVariableP redictedValueStd ErrorMean Predict951 CLPredictResidua115.87005.53250.16824.40126.86380.3375215.58005.69Q20.20094.53106.8495-OJ10235.83005.360。0J47S4.24396.47S00.4700414.710056”$D.1B424.3797B.6360-0.797855.C0010.17613.86256.13780.58996；3.85004 J 4740.4182?.71245.5824-0.297475.52006.G2610.1S644.47988.7725-O.IOfil85* 85005.379?0.14914.28270703S4.97005 MO 430.15114.28596.5227-0.4343105 J1005,23180.14704 J1636.34730.0782Sum of Res i duaIsQSum of Squared Residuals1.69902Predicted Resi duaI SS (PRESS) 4.945414 .分析结果REGS程中，MODE悟句可以交互使用，本例我们建立了两个模型，第一个 MODEL有做变量筛选，第二个MODE指定逐步回归方法筛选变量。 并且用CLI 输出预测值与预测区问。REGS程拟合带截距项的直线回归方程，用最小二乘法估计模型的参数，并 给出模型及参数的方差分析及 T检验。本例的两个模型1检验P值大于0.05, 无统计学意义。模型2为逐步回归法，只纳入了 X3,由参数估计表可知，对常数检验t值 为t=615.68 , Pr>|t|的值小于0.0001 ,远小于0.05,说明截距项（即常数项 Intercept ）通过检验，估计值为5.82331.对自变量x1分析同样可以得知，x1 系数通过检验，估计值为-0.00493.所以回归方程为：y=0.00493*x1+5.82331.综上所述：在研究影响水稻粒重的因素中，只有秋粒对它的影响较大。
