回归分析答案

试验设计作业1、下表为小麦栽培试验的产量结果kg),随机区组设计，小区计产面积为12m2,试作分析。在表示最后结果时需化为每亩产量(kg)o假定该试验为一完全随机设计，试分析后将其试验误差与随机区组时的误差作一比较，看看划分区组的效果如何？处理 [区 组 ii m wA 6.2B 5.8C 7.2D 5.6E 6.9F 7.56.9 6.16.0 6.36.6 6.8 7.05.4 6.07.2 7.0 7.47.3 7.6完全随机设计的程序如下:datali_1;doi=1to6;doj=1to4;inputx@@;output;end;end;cards;6.66.96.16.766.36.66.875.65.85.467.277.47.87.37.6;procanova;classi;modelx=i;meansi;run;SumofSAS输出结果如下:SumofSourceDFSquaresMeanSquareFValuePr>FModel58.972083331.7944166720.87<.0001Error181.547500000.08597222CorrectedTotal2310.51958333R-Square CoeffVar RootMSE xMean0.8528934.406415 0.293210 6.654167SourceDFAnovaSSMeanSquareFValuePr>Fi58.972083331.7944166720.87<.0001随机区组设计的程序如下:datali_3;doi=1to6;doj=1to4;inputx@@;output;end;end;cards;6.66.96.16.766.36.66.875.65.85.467.277.47.87.37.6;procanova;classij;modelx=ij;run;结果如下：SumofSourceDFSquaresMeanSquareFValuePr>FModel89.243333331.1554166713.58<.0001Error151.276250000.08508333CorrectedTotal2310.51958333R-SquareCoeffVarRootMSE xMeanSourceDFAnovaSSMeanSquareFValuePr>Fi58.972083331.7944166721.09<.0001j30.271250000.090416671.060.39430.8786794.3835760.2916906.654167结果分析：随机区组设计的误差要小一些。2、下表为水稻品种比较试验的产量结果(kg),5x5拉丁方设计，小区计产面积30m2,试分析。B25E23A27C28D20D22A28E20B28C26E18B25C28D24A25A26C26D22E19B24C23D23B26A33E20拉丁方设计的程序如下：datali_4;doi=1to5;doj=1to5;inputfz$x@@;output;end;end;cards;B25E23A27C28D20D22A28E20B28C26E18B25C28D24 A25A26C26D22E19 B24C23D23B26A33E20;procanova;classijfz;modelx=ijfz;run;结果如下：TheANOVAProcedureDependentVariable:xSumofSourceDFSquaresMeanSquareFValuePr>FModel12255.280000021.27333337.400.0008Error1234.48000002.8733333CorrectedTotal24289.7600000R-SquareCoeffVarRootMSE xMean0.881005 6.958501 1.695091 24.36000SourceDFAnovaSSMeanSquareFValuePr>Fi48.56000002.14000000.740.5798j444.560000011.14000003.880.0302fz4202.160000050.540000017.59<.0001结果分析：列间，品种间差异是显著的。3、左下表为玉米播期试验结果，右下表为油菜品比试验结果，皆为随机区组设计，试试分析。播期I区组IIm品 区II组种ImWA20.322.120.7A3.93.93.64.5B19.819.018.6B5.86.35.96.8C18.416.817.4C4.44.45.64.5D16.016.618.1D5.55.25.46.7E15.214.915.3E6.86.97.46.0F14.915.914.0F7.37.27.57.0G14.018.815.3玉米播期试验的产量(kg)结果 油菜品比试验的产量(kg)结果玉米的随机区组设计程序如下：datali_3;doi=1to7;doj=1to3;inputx@@;output;end;end;cards;22.120.71918.616.817.41616.618.114.915.315.9141418.815.3procanova;classij;modelx=ij;run;结果如下：SumofSourceDFSquaresMeanSquareFValuePr>FModel890.694285711.33678577.610.0011Error1217.87714291.4897619CorrectedTotal20108.5714286R-Square CoeffVar RootMSE xMean0.8353427.078630 1.220558 17.24286SourceDFAnovaSSMeanSquareFValuePr>Fi688.1714285714.695238109.860.0005j22.522857141.261428570.850.4529油菜随机区组设计程序如下:datali_3;doi=1to6;doj=1to4;inputx@@;output;end;end;cards;3.93.64.56.35.96.84.45.64.55.25.46.76.97.467.37.27.57;procanova;classij;modelx=ij;run;结果如下:SumofSource DF Squares MeanSquareFValuePr>FModel 8 31.27500000 3.90937500 14.18 <.0001Error 15 4.13458333 0.27563889CorrectedTotal 23 35.40958333R-Square CoeffVar RootMSE xMean0.883235 9.097702 0.525013 5.770833Source DF AnovaSS MeanSquareFValuePr>Fi 5 30.81708333 6.16341667 22.36 <.0001j 3 0.45791667 0.15263889 0.55 0.6535结果分析：两播种期试验均表明，不同播种期对试验结果的影响是显著的。4、下表为水稻栽培试验的小区产量(1<8)结果，5x5拉丁方设计，，试分析。。B14E15C25A12D16E18D12B15C14A11C21A13D13B13E19A10C24E18D14B12D12B15A11E20C26拉丁方设计程序如下：datali_4;doi=1to5;doj=1to5;inputfz$x@@;output;end;end;cards;B14E15C25A12D16E18D12B15C14A11C21A13D13B13E19A10C24E18D14B12D12B15A11E20C26;procanova;classijfz;modelx=ijfz;run;结果如下：SumofSourceDFSquaresMeanSquareFValuePr>FModel12401.920000033.49333334.410.0078Error1291.12000007.5933333CorrectedTotal24493.0400000R-Square CoeffVar RootMSE xMean0.81518717.52926 2.755600 15.72000SourceDFAnovaSSMeanSquareFValuePr>Fi423.04000005.7600000 0.76 0.5717j417.04000004.2600000 0.56 0.6954fz4361.840000090.4600000 11.91 0.0004结果分析：品种间差异对结果的影响是显著的。5、 调查某队元麦及元麦和蚕豆混种、间种田块的产量（混、间种者为麦、豆产量合计）,得结果（kg/0.1亩）于表：（1）设以元麦单种为对照，试以LSD法作多重比较；（2）设预定要作的比较是单种对混、间种，混种对间种，2麦1豆间种对3麦2豆间种，试作单一自由度的独立比较。元麦单种麦豆混种2麦1豆间3麦2豆间2024303024232833222834311821323621243135先作方差分析：datali_1;doi=1to4;doj=1to5;inputx@@;output;end;end;cards;2024221821242328212430283432313033313635;procanova;

classi;modelx=i;meansi;run;结果如下:SumofSourceDFSquaresMeanSquareFValuePr>FModel3483.7500000161.250000028.04<.0001Error1692.00000005.7500000CorrectedTotal19575.7500000R-Square CoeffVar RootMSE xMean0.8402088.799691 2.397916 27.25000SourceDFAnovaSSMeanSquareFValuePr>Fi3483.7500000161.250000028.04<.0001TheANOVAProcedureLevelof xiNMeanStdDev1521.00000002.236067982524.00000002.549509763531.00000002.236067984533.00000002.549509761005(16)=2.12,1001(16)=2.921'2MSLSD005=2.12*,—^e=3.215■2MSLSD001=2.921*| =4.43处理均数差数均数-21均数-24均数-313麦2豆间种3312（极显著）9（极显著）22麦1豆间种3110（极显著）7（极显著）麦豆混种243兀麦单种21有一大豆试验，A因素为品种，有A1、A2、A3、A44个水平，B因素为播期，有B1、B2.B33个水平，随机区组设计，重复3次，小区计产面积25平方米，其田间排列和产量(kg)如下图，试作方差分析。检验：品种、播期，品种X播期的效应是否显著？区组I512A2B213A3B314A4B215A2B113A4B316A3B214A1B313A4B116A1B212A3B114A2B314区组IIA4B2A1B314A2B114A3B315A1B212A2B313A4B116A3B213A2B2A3B115A1B113A4B31716"1FY1誓誓之A1B1A!区组mDATACaP;DOa=1to4;DOb=1to3;DOn=1to3;inputy@@;output;end;end;end;DROPn;CARDS;TOC\o"1-5"\h\z161314151411151412171314161213151613151215131315141713;PROCANOVA;CLASSAB;MODELy=ABA*B;RUN;结果如下：TheANOVAProcedureDependentVariable:ySumofSource DF SquaresMeanSquareFValuePr>F

Model119.333333330.848484850.310.9778ErrorCorrectedTotalR-Square0.122807Source24 66.66666667 2.7777777835 76.00000000CoeffVar RootMSE yMean11.90476 1.666667 14.00000DF AnovaSS MeanSquareFValuePr>Fa32.888888890.962962960.350.7918b20.500000000.250000000.090.9142a*b65.944444440.990740740.360.8989结果分析：品种、播期，品种X播期对试验的影响均不显著。有一小麦裂区试验，主区因素A，分A1（深耕）、A2（浅）两水平，副区因素B，分B1（多肥）、B2（少肥）两水平，重复3次，小区计产面积15平方米，其田间排列和产量（假设数字）如下图，试作方差分析。因素A,因素B及其交互效应是否显著？~~B1~~B19~~B17B26B22~_B23~_B111B15B24~~B21~~B24B16B112区组I区组II区组I区组II区组m解：程序如下：title'裂区试验的统计分析’；datalq;doa=1to2;dob=1to2;dog=1to3;inputyield@;output;end;end;end;cards;911124456231;procanova;classgab;modelyield=gab;meansab/duncan;run;procanova;classgab;modelyield=gaba*bg*ag*a*b;

testH=gaE=g*a;testH=ba*bE=g*a*b;run;试验结果：裂区试验的统计分析2 08:07Wednesday,July3,2002AnalysisofVarianceProcedureDependentVariable:YIELDFValuePr>FSourceDFSumofSquaresModel4115.5000000014.270.0018Error714.16666667CorrectedTotal 11129.66666667R-SquareC.V.YIELDMean0.89074624.387545.83333333SourceDFAnovaSSFValuePr>FG20.166666670.040.9599A140.3333333319.930.0029B175.0000000037.060.0005裂区试验的统计分析 6 08:07Wednesday,July3,2002AnalysisofVarianceProcedureDependentVariable:YIELDSourceDFSumofSquaresFValuePr>FModel11129.66666667..Error0.CorrectedTotal 11129.66666667R-SquareC.V.YIELDMean1.00000005.83333333SourceDFAnovaSSFValuePr>FG20.16666667..A140.33333333..B175.00000000..A*B13.00000000..G*A21.16666667..G*A*B410.00000000..TestsofHypothesesusingtheAnovaMSforG*AasanerrortermSourceDFAnovaSSFValuePr>FG20.166666670.140.8750A140.3333333369.140.0142TestsofHypothesesusingtheAnovaMSforG*A*BasanerrortermSourceDFAnovaSSFValuePr>FB175.0000000030.000.0054A*B13.000000001.200.3349结果分析：因素A、因素B的显著性水平为0.0029、0.0005,是显著的，而AXB的F值是1.2,顾AXB是不显著的。B1与B2有显著的差别，A1与A2有显著的差别，最好的是A1B1的组合。设若上题小麦耕深与施肥量试验为条区设计，田间排列和产量将相应如下图，试作分析，并与裂区设计结果相比较）。9 2 9 2 62BiB2Ai [AA。A、A。A、 d Bi511B214Be34B,61221解：程序如下：title'条区试验的统计分析’；datatq;dog=1to3;doa=1to2;dob=1to2;inputyield@;output;end;end;end;cards;9672453461;procanova;classgab;modelyield=gab;meansab/duncan;run;procanova;classgab;modelyield=gaba*bg*ab*gg*a*b;testH=gaE=g*a;testH=ba*bE=g*a*b;run;试验结果：条区试验的统计分析 2 08:42Wednesday,July3,2002AnalysisofVarianceProcedureDependentVariable:YIELDFValuePr>FSourceDFSumofSquaresModel4115.5000000014.270.0018Error714.16666667CorrectedTotal 11129.66666667R-SquareC.V.YIELDMean0.89074624.387545.83333333SourceDFAnovaSSFValuePr>FG20.166666670.040.9599A140.3333333319.930.0029B175.0000000037.060.0005条区试验的统计分析 6 08:42Wednesday,July3,2002AnalysisofVarianceProcedureDependentVariable:SourceModelErrorCorrectedTotalYIELDDF11011Square000000DFSumofSquares129.66666667.129.66666667C.V.0AnovaSSFValue.FValuePr>F.YIELDMean5.83333333Pr>FSourceR-1.G20.16666667..A140.33333333..B175.00000000..A*B13.00000000..G*A21.16666667..G*B23.50000000..G*A*B26.50000000..TestsofHypothesesusingtheAnovaMSforG*AasanerrortermSourceDFAnovaSSFValuePr>FG20.166666670.140.8750A140.3333333369.140.0142TestsofHypothesesusingtheAnovaMSforG*A*BasanerrortermSourceDFAnovaSSFValuePr>FB175.0000000023.080.0407A*B13.000000000.920.4380结果分析：因素A、因素B的显著性水平为0.8750，0.0407,A*B的显著性水平为0.4380，

故均属于不显著。在药物处理大豆种子试验中，使用了大中小三种类型种子，分别用五种浓度、两种处理时间进行试验处理，播种后45天对每种各取两个样本，每个样本取10株测定其干物重，求其平均数，结果如下表。试进行方差分析。处理时间A:种子类型c-浓度BB,(0x10-6)B2(10x10-6)B3(20x10-6)B4(30x10-6)B5(40x10-6)A1（12小时）C1（小粒）7.012.822.021.324.46.511.421.820.323.2C2（中粒）13.513.220.419.024.613.814.221.419.623.8C3（大粒）10.712.422.621.324.510.313.221.822.424.2A2（24小时）C1（小粒）3.610.74.712.413.61.58.83.410.513.7C2（中粒）4.79.82.712.414.04.910.54.213.214.2C3（大粒）8.79.63.413.014.83.59.74.212.712.6解：程序如下：title'三因素随机区组试验的统计分析’；datadsy;doa=1to2;dob=1to5;doc=1to3;dorep=1to2;inputy@;output;end;end;end;end;cards;TOC\o"1-5"\h\z7.0 6.513.810.311.414.213.222.021.821.421.820.319.019.622.423.223.824.2TOC\o"1-5"\h\z1.54.93.58.810.59.73.44.24.210.513.213.012.713.714.014.212.6;procanova;classabcrep;modely=repabca*ba*cb*ca*b*c;meansaba*ba*c;meansab/duncan;run;试验结果：三因素随机区组试验的统计分析 2 09:45Wednesday,July3,2002AnalysisofVarianceProcedureDependentVariable:YSourceDFSumofSquaresFValuePr>FModel302668.6383333394.000.0001Error2927.44350000CorrectedTotal592696.08183333R-SquareC.V.YMean0.9898217.26598113.3883333SourceDFAnovaSSFValuePr>FREP12.521500002.660.1134A11232.160166671302.040.0001B4976.61100000258.000.0001C215.108333337.980.0017A*B4381.98233333100.910.0001A*C20.674333330.360.7033B*C840.215000005.310.0004A*B*C819.365666672.560.0304结果分析:类型A、浓度B、处理时间C、类型AX浓度B、浓度BX处理时间C、类型AX浓度BX处理时间C的显著性水平分别是：0.0001、0.0001、0.0017、0.0001、0.0004是极显著；类型AX浓度BX处理时间C的显著性水平是0.0304是显著；类型AX处理时间C类型显著性水平是0.7033是不显著。

为了研究湿度和温度对粘虫卵发育历期的影响，用3种湿度、4种温度处理粘虫卵，采用随机区组设计，重复4次，结果如下表，试进行方差分析。相对湿度(％)温度(°C)-历期12341002693.291.290.792.22887.685.784.282.43079.274.579.370.43267.769.367.668.1702689.488.786.388.52886.485.386.784.23077.276.374.575.73270.172.170.369.5402699.999.293.394.52891.394.692.391.43082.781.384.586.83275.374.172.371.4解：程序如下：title'二因素随机区组试验的统计分析’；datayield;doa=1to3;dob=1to4;dorep=1to4;inputy@;output;end;end;end;cards;93.291.290.792.287.685.784.282.479.274.579.370.467.769.367.668.189.488.786.388.586.485.386.784.277.276.374.575.770.172.170.369.599.999.293.394.591.394.692.391.482.781.384.586.875.374.172.371.4;procanova;classabrep;modely=repaba*b;run;试验结果：二因素随机区组试验的统计分析 2 10:14Wednesday,July3,2002AnalysisofVarianceProcedureDependentVariable:YSourceDFSumofSquaresFValue Pr>FModel143866.5466666771.44 0.0001Error33127.57250000CorrectedTotal473994.11916667R-SquareC.V.YMean0.9680602.38963682.2791667SourceDFAnovaSSFValue Pr>F

30.26750000 2.61439.18041667 56.803335.61083333 287.6130.26750000 2.61439.18041667 56.803335.61083333 287.6161.487916670.06790.00010.00012.65 0.0328ABA*B结果分析：相对湿度和温度因素著性水平为0.0001，对粘虫卵的发育历期影响显是极显著，而两因素的交互作用的影响显著性水平是0.0328是不显著。某农药厂生产某种农药，指标是农药的收率，越大越好。根据经验，影响农药收率的因素有四个，反应温度A,水平为A1:60度、A2:80度，反应时间B，水平为B1：2。5小时，B2：3。5小时，原料配比C，水平C1：1。1：1，C2：1。2：1；真空度D，水平D1：66500Pa，D2：79800Pa,并考虑交互作用A*B。选用正交表安排试验得以下数据。试进行方差分析。ABABCDy111118611122951221291122219421212912122196221118322122解：程序如下：title'方差分析’；dataf;inputabcdy;cards;1 1 1 1 861 1 2 2 951 2 1 2 912 2 1 941 1 2 912 1 2 1 962 2 1 1 832 2 2 2 88;procanova;classabcdy;modely=abcda*b;run;试验结果：方差分析2 13:22Wednesday,July3,2002AnalysisofVarianceProcedureDependentVariable:YSource DF SumofSquares F Value Pr>FModel 5 141.00000000 11.28 0.0834Error 2 5.00000000CorrectedTotal 7 146.00000000R-Square C.V. YMean0.965753 1.747115 90.5000000Source DF AnovaSS F Value Pr>FA 1 8.00000000 3.20 0.2155B 1 18.00000000 7.20 0.115388

C160.5000000024.200.0389D14.500000001.800.3118A*B150.0000000020.000.0465结果分析:A、B、D即反应温度，反应时间和真空度的显著性水平分别是：0.2155、0.1153、0.3118,对农药收率的影响不显著，而C和A*B即原料配比与反应温度和反应时间的交互作用的显著性水平是：0.0389、0.0465，对农药收率的影响显著。设单位产品的成本7与产量X间近似满足双曲线关系j=a+-，试利用下列资料求rX对X的回归方程.X5.684.453.843.843.732.18Y17.718.518.918.818.319.1解：程序如下：Title'一元一次回归’；datact;inputxy@@;xq=1/x;cards;5.6817.74.4518.53.8418.93.8418.83.7318.32.1819.1;procreg;modely=xq/Pcli;run;试验结果：一元一次回归1 14:06Wednesday,July3,2002Model:MODEL1DependentVariable:YAnalysisofVarianceSource DF SumofSquares MeanSquareFValue Prob>FModel 1 0.70107 0.70107Error 4 0.57393 0.14348CTotal 5 1.27500RootMSE 0.37879 R-square 0.5499DepMean 18.55000 AdjR-sq 0.4373C.V. 2.04200ParameterEstimates4.886 0.0916VariableDFParameterEstimateStandardErrorTforH0:Parameter=0 Prob>|T|INTERCEP1 17.483711 0.50656577 34.514 0.0001XQ 1 3.881129 1.75580706 :2.210 0.0916ObsDepVarYDepVarStdErValueLower95%PredictUpper95PredictPredictResidual1 17.7000 18.1670 0.232 16.933419.4006 -0.46702 18.5000 18.3559 0.178 17.194019.5177 0.14413 18.9000 18.4944 0.157 17.356319.6325 0.40564 18.8000 18.4944 0.157 17.356319.6325 0.30565 18.3000 18.5242 0.155 17.387819.6606 -0.22426 19.1000 19.2640 0.358 17.8167SumofResiduals 0SumofSquaredResiduals 0.5739PredictedResidSS(Press) 3.433820.7114 -0.1640结果分析：模型在0.05的显著性水平下不显著。回归方程为y=17.48371+3.8813/x

某种钢材的硬度y与含铜量（%）及温度（。f）之间服从线性关系，试从下面六组数据中求出经验回归方程，并进行方程的检验和回归系数检验并进行相关分析。硬度y78.955.280.957.485.360.7含铜量x（%）0.020.020.100.100.180.18 1 温度x(oF)100012001000120010001200解：程序如下：TITLE1'多元线性回归’；DATAAMO1;INPUTYX1X2;CARDS;78.90.02100055.20.02120080.90.10100057.40.10120085.30.18100060.70.181200;PROCREG;MODELY=X1X2/PCLI;RUN;proccorrnosimple;varx1x2；withy;run;试验结果：多元线性回归1 14:20Wednesday,July3,2002Model:MODEL1DependentVariable:YAnalysisofVarianceSourceDF SumofSquaresMeanSquareFValueProb>FModel2 894.60917447.30458983.6880.0001Error3 1.36417 0.45472CTotal5 895.97333RootMSE0.67433 R-square0.9985DepMean69.73333 AdjR-sq0.9975C.V.0.96701ParameterEstimatesVariable DF ParameterEstimateStandardError TforH0:Parameter=0 Prob> |T|INTERCEP 1 197.647917 3.06979550 64.385 0.0001X1137.1875004.214568408.8240.0031X21-0.1196670.00275294-43.4690.0001ObsDepVarYDepVarStdErValueLower95%PredictUpper95PredictPredictResidua178.900078.72500.51576.024681.42540.1750255.200054.79170.51552.091357.49200.4083380.900081.70000.38979.222084.1780-0.8000457.400057.76670.38955.288760.2447-0.3667585.300084.67500.51581.974687.37540.6250660.700060.74170.51558.041363.4420-0.0417SumofResiduals0SumofSquaredResiduals 1.3642PredictedResidSS(Press) 5.1393多元线性回归2 14:20Wednesday,July3,2002CorrelationAnalysis'WITH'Variables:Y'VAR'Variables:X1 X2PearsonCorrelationCoefficients/Prob>|R|underHo:Rho=0/N=6X1 X2Y 0.19878 -0.979270.7058 0.0006

结果分析:回归方程为Y=197.64792-0.11967X2,由该模型的F检验结果和可决系数知，回归方程显著，由系数的T检验结果知，各个系数均显著。某地区的二化螟的第一代成虫发生量V与4个因素有关数据分别为：其中X1:冬季积雪期限（单位：周）X2:每年化雪日期（以2月1日为1）X；：二月份平均气温（。C）X4：三月份平均气温（。C）观察数据如表所示，试建立y与X「X：、X、4乂4的线性回归方程，并对回归方程和回归系数进行检验. 1 2 3 4序号yXXXX19102630.23.62171226-1.44.43341440-0.81.744216320.21.45401951-1.40.962716330.22.1747262.72.78277251.04.091312172.23.710561124-0.83.011151216-0.54.91287162.04.1132011151.14.7解：程序如下：TITLE1'多元线性回归’；DATAAMO;INPUTYX1-X4;CARDS;910260.23.6171226-1.44.4341440-0.81.74216320.21.4401951-1.40.92716330.22.147262.72.7277251.04.01312172.23.7561124-0.83.0151216-0.54.987162.04.12011151.14.7PROCREG;MODELY=X1X2X3X4/PCLI;RUN;试验结果：多元线性回归1 14:41Wednesday,July3,2002Model:MODEL1DependentVariable:YAnalysisofVariance

SourceDF SumofSquares MeanSquare FValueProb>FModel4 1993.17075498.29269 4.5460.0329Error8 876.82925 109.60366CTotal12 2870.00000RootMSE10.46918R-square 0.6945DepMean24.00000AdjR-sq 0.5417C.V.43.62157ParameterEstimatesVariableDFParameterEstimateStandardErrorTforH0:Parameter=0 Prob>|T|INTERCEP1138.07097250.553762842.7310.0258X11-1.0087921.42454732-0.7080.4990X21-1.6583530.82923516-2.0000.0805X31-11.1885643.88023702-2.8830.0204X41-16.9789826.42156442-2.6440.0295ObsDepVarYDepVarStdErValueLower95%PredictUpper95PredictPredictResidua19.000021.50383.824-4.198447.2060-12.5038217.000023.80486.618-4.756452.3659-6.8048334.000037.70045.31810.622664.7781-3.7004442.000042.85477.18013.580372.1292-0.8547540.000034.71088.4273.720265.70155.2892627.000029.31115.0172.540056.0822-2.311174.000011.83997.444-17.783241.4629-7.8399827.000010.44616.352-17.791538.683716.5539913.000010.33646.939-18.627539.30032.66361056.000045.18778.28714.397275.978210.81231115.000021.82916.377-6.439050.0972-6.8291128.000012.48485.192-14.463139.4328-4.48481320.00009.99035.776-17.582237.562810.0097SumofResiduals0SumofSquaredResiduals876.8293PredictedResidSS(Press)2757.9005结果分析:在a=0.05的水平下回归模型显著，在0.1的水平下常数项，x2,x3,x4均显著，x1不显著。回归方程为：y=138.07097-1.008792x1-1.65835x2-11.88564x3-16.97898x4。

研究水稻丰产规律，建立产量y与氮、磷、钾肥用量的函数关系，已知如下两表条件，求回归方程并对回归方程进行统计分析.试验设计方案与试验结果试验■号尤0尤尤2x3y11111437.52111-1425.0311-11450.0411-1-1452.551-111462.561-11-1455.071-1-11455.081-1-1-1460.0911.63300415.0101-1.63300430.011101.6330457.51210-1.6330435.0131001.633447.514100-1.633450.0151000457.5161000467.5171000447.5181000470.0191000458.5201000422.5解：程序如下:TITLE1'多元线性回归’；DATAAMO;INPUTx0-x3y;CARDS;11 1 1 437.511 1 -1 42511 -1 1 45011 -1 -1 452.51-1 1 1 462.51-1 1 -1 4551-1 -1 1 4551-1 -1 -1 46011.633 0 0 4151-1.633 0 0 43010 1.633 0 457.510 -1.633 0 43510 0 1.633 447.510 0 -1.633 45010 0 0 457.510 0 0 467.510 0 0 447.510 0 0 47010 0 0 458.510 0 0 422.5;PROCREG;MODELY=x1x2x3/PCLI;RUN;试验结果：多元线性回归1 14:58Wednesday,July3,2002Model:MODEL1DependentVariable:YAnalysisofVarianceSourceDFSumofSquaresMeanSquareFValueProb>FModel3640.08597213.361990.8830.4709Error163866.61403 241.66338CTotal194506.70000RootMSE15.54553 R-square0.1420DepMean447.80000 AdjR-sq-0.0188C.V. 3.47153ParameterEstimatesVariableDFParameterEstimateStandardErrorTforH0:Parameter=0Prob>|T|INTERCEP1447.8000003.47608528128.8230.0001X11-6.8996024.25731049-1.6210.124X21-0.0568124.25731049-0.0130.9895X310.6313104.257310490.1480.8840ObsDepVarYDepVarStdErValueLower95%PredictUpper95PredictPredictResidua1437.5441.58.152404.3478.7-3.97492425.0440.28.152403.0477.4-15.21233450.0441.68.152404.4478.88.41154452.5440.38.152403.1477.512.17415462.5455.38.152418.1492.57.22596455.0454.08.152416.8491.20.98857455.0455.48.152418.2492.6-0.38778460.0454.18.152416.9491.35.87499415.0436.57.773399.7473.4-21.533010430.0459.17.773422.2495.9-29.067011457.5447.77.773410.9484.69.792812435.0447.97.773411.0484.7-12.892813447.5448.87.773412.0485.7-1.330914450.0446.87.773409.9483.63.230915457.5447.83.476414.0481.69.700016467.5447.83.476414.0481.619.700017447.5447.83.476414.0481.6-0.300018470.0447.83.476414.0481.622.200019458.5447.83.476414.0481.610.700020 422.5 447.8SumofResidualsSumofSquaredResidualsPredictedResidSS(Press)3.47603866.61405784.6337414.0481.6-25.3000结果分析:该回归模型不显著，且回归方程中只有常数项可以通过显著性水平检验，其余一次项系数均不显著，回归方程为：y=447.8-6.8896x1-0.05681x2+0.63131x3全钢民用剪高频淬火工艺的二次回归旋转设计。国内民用剪生产一直是沿袭千百年的传统工艺，近代虽有改进，但绝大多数民用剪的生产工艺仍然存在工序多、工艺流程长、质量不稳定、劳动条件差、生产率低、经济效益少等缺点。在全国民用剪生产新工艺的研究中，某厂成功地应用二次回归旋转设计确定了最佳工艺参数试验因素水平及编码表如下：七：表示淬火裂纹，*:表示剪头里淬硬层宽度，y3:淬火马氏体组织，y4剪刀硬度。因素水平编码表工jZ］剪刀运行速度z2感应器与剪刀的距离Z3屏极电流1.41437010.821.681350101.62030081.46-125061.30-1.4142305.181.24x=f(z)=Z]—300.z2-8_z3-1.46j ji 50i 23 0.16试验方案及结果分析表试验■号XXXXXXXXXXx2x2x2yyyy0123121323123123411-1-1-11111112202211-1-1-1-11111220231-11-1-11-111122024111-11-1-1111201251-1-111-1-1111-4202611-11-11-1111221271-111-1-11111221281111111111201291-1.4140000020022021011.4140000020020221110-1.4140000020220212101.4140000020222213100-1.414000002202-2141001.4140000022202151-1.4140000020022021611.4140000020020221710-1.4140000020220218101.4140000020222219100-1.414000002202-2201001.41400000222022110000000002222221000000000222223100000000022222410000000002222求y、y、y、y与尤、尤、工的二次回归方程并对回归方程进行统计分析。1 2 3 4 1 2 3

解：程序如下:TITLE1'三元二次多项式回归’；DATAyield;INPUTz1z2z3y1y2y3y4@@;CARDS;-1-1-122021-1-12202-11-1220211-12012-1-11-42021-112212-11122121112012-1.4140022021.4140020220-1.4140220201.4140222200-1.414202-2001.4142202-1.4140022021.4140020220-1.4140220201.4140222200-1.414202-2001.41422020002222000222200022220002222;PROCRSREG;MODELY1=z1z2z3;PROCRSREG;MODELY2=z1z2z3;PROCRSREG;MODELY3=z1z2z3;PROCRSREG;MODELY4=z1z2z3;RUN;试验结果：三元二次多项式回归1 16:44Wednesday,July3,2002Z3CodingCoefficientsfortheIndependentVariablesFactor SubtractedoffDividedbyZ1 0 1.414000Z2 0 1.4140000 1.414000Regression三元二次多项式回归 2 16:44Wednesday,July3,2002ResponseSurfaceforVariableY1ResponseMean 1.739130RootMSE 0.987190R-Square 0.6321Coef.ofVariation 56.7635DegreesofFreedomTypeISumofSquaresR-SquareF-RatioProb>FLinear36.751019 0.1961 2.3090.1243Quadratic31.514679 0.0440 0.5180.6771Crossproduct313.500000 0.3920 4.6180.0207TotalRegress921.765698 0.6321 2.4820.0666ResidualDegreesofFreedomSumofSquares MeanSquareTotalError1312.669085 0.974545Degreesof ParameterStandard TforH0:ParameterestimateParameterFreedomEstimateError Parameter=0Prob>|T|fromDataINTERCEPT1 2.3158650.506341 4.574 0.00052.315865

Z11 0.375057 0.246816 1.5200.15260.530330Z21 0.375057 0.246816 1.5200.15260.530330Z31 -0.375057 0.246816 -1.5200.1526-0.530330Z1*Z11 -0.276394 0.299637 -0.9220.3731-0.552620Z2*Z11 -0.750000 0.349025 -2.1490.05111.499547Z2*Z21 -0.276394 0.299637 -0.9220.3731-0.552620Z3*Z11 0.750000 0.349025 2.1490.05111.499547Z3*Z21 0.750000 0.349025 2.1490.05111.499547Z3*Z31 -0.276394 0.299637 -0.922三元二次多项式回归 3 16:44Wednesday,July3,0.37312002-0.552620FactorDegreesofFreedom SumofSquares MeanSquareF-RatioProb>FZ14 12.079556 3.019889 3.099 0.0537Z24 12.079556 3.019889 3.099 0.0537Z3 4 12.079556 3.019889 3.099 0.0537三元二次多项式回归 4 16:44Wednesday,July3,2002CanonicalAnalysisofResponseSurface(basedoncodeddata)CriticalValueFactor Coded UncodedZ1 0.129212 0.182706Z2 0.129212 0.182706Z3 -0.129212 -0.182706Predictedvalueatstationarypoint 2.418652EigenvectorsEigenvalues Z1 Z2 Z30.197153 -0.408248 0.816497 0.4082480.197153 0.707107 0 0.707107-2.052167 0.577350 0.577350 -0.577350Stationarypointisasaddlepoint.三元二次多项式回归 5 16:44Wednesday,July3,2002CodingCoefficientsfortheIndependentVariablesFactor SubtractedoffDividedbyZ1 0 1.414000Z2 0 1.414000Z3 0 1.414000三元二次多项式回归 6 16:44Wednesday,July3,2002ResponseSurfaceforVariableY2ResponseMean 1.478261RootMSE 0.540925R-Square 0.7856Coef.ofVariation 36.5920RegressionDegreesofFreedomTypeISumofSquaresR-SquareF-RatioProb>FLinear3 8.828125 0.497710.0570.0011Quadratic3 3.107210 0.17523.5400.0453Crossproduct3 2.000000 0.11272.2780.1277TotalRegress9 13.935335 0.78565.2920.0037ResidualTotalErrorDegreesofFreedom SumofSquares MeanSquare13 3.803795 0.292600Degreesof Parameter Standard TforH0:ParameterestimateParameterFreedomEstimate Error Parameter=0Prob>|TfromDataINTERCEPT1 1.789296 0.277446 6.4490.00001.789296Z11 -0.603591 0.135241 -4.4630.0006-0.853478Z21 -0.250038 0.135241 -1.8490.0873-0.353553Z31 0.353553 0.135241 2.6140.02140.499924Z1*Z11 -0.315777 0.164184 -1.9230.0766-0.631364Z2*Z11 -0.500000 0.191246 -2.6140.0214-0.999698Z2*Z21 0.184374 0.164184 1.1230.28180.368636Z3*Z11 2.589628E-17 0.191246 135E-181.00005.177691E-17Z3*Z21 2.443114E-17 0.191246 128E-181.00004.884753E-17Z3*Z31 -0.315777 0.164184 -1.923三元二次多项式回归 7 16:44Wednesday,July3,0.07662002-0.631364FactorDegreesofFreedom SumofSquares MeanSquareF-RatioProb>FZ148.9106422.2276607.6130.0022Z243.3691370.8422842.8790.0656Z343.0820630.7705162.6330.0826三元二次多项式回归816:44Wednesday,July3,2002CanonicalAnalysisofResponseSurface(basedoncodeddata)CriticalValueFactorCodedUncodedZ1-0.509069-0.719824Z2-0.210726-0.297966Z30.3959080.559814Predictedvalueatstationarypoint2.142749EigenvectorsEigenvaluesZ1Z2Z30.575636-0.3826140.9239080-0.631364001.000000-0.8383640.9239080.3826140Stationarypointisasaddlepoint.三元二次多项式回归 9 16:44Wednesday,July3,2002CodingCoefficientsfortheIndependentVariablesFactorSubtractedoffDividedbyZ101.414000Z201.414000Z301.414000三元二次多项式回归10 16:44Wednesday,July3,2002ResponseSurfaceforVariableY3ResponseMean0.956522RootMSE0.670051R-Square0.6921Coef.ofVariation70.0507RegressionDegreesofFreedomTypeISumofSquaresR-SquareF-RatioProb>FLinear38.1634210.43066.0610.0082Quadratic34.9565210.26153.6800.0407Crossproduct300.000001.0000TotalRegress913.1199420.69213.2470.0269ResidualDegreesofFreedomSumofSquaresMeanSquareTotalError135.8365800.448968DegreesParameterofParameterStandardTforH0:estimateParameterFreedomEstimateError Parameter=0Prob>|T| fromDataINTERCEPT11.9998090.3436765.8190.00011.999809Z110.4785720.1675252.8570.01350.676701Z210.4785720.1675252.8570.01350.676701Z31-0.2285350.167525-1.3640.1957-0.323148Z1*Z11-0.4999840.203377-2.4580.0288-0.999666Z2*Z113.12364E-170.2368