第十三章-协方差分析

2023最新整理收集do

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合计

X1Y1X2Y2X3Y3XY（“3.中的分析项目”与方差分析一致）（与回归分析一致）（bc:公共回归系数，）dataanocov1;doc=1to3;doi=1to8;inputxy@@;output;end;end;cards;1585138311651276128016911484179017971690181001895211032210619991894228924912083239525100271023010532110;proc

glm;classc;modely=cx/solutionSS3;/*solution:输出回归系数并检验*/lsmeansc/*输出修正均数*//stderr/*输出修正均数的标准误*/pdiff;/*输出修正均数两两比较的P值*/runTheGLMProcedureDependentVariable:ySumofSourceDFSquaresMeanSquareFValuePr>FModel32328.343765776.11458868.20<.0001Error20227.61456811.380728Corrected232555.958333Total总变异组内估计误差均方SourceDFTypeIIISSMeanSquareFValuePr>Fx11010.7604321010.76043288.81<.0001c2707.218765

353.609382

31.07<.0001F=353.609382/11.380728=31.07修正均数的估计误差平方和检验修正均数总差异的F值

StandardParameterEstimateErrortValuePr>|t|Intercept35.94B6.585.47<.0001x2.400.259.42<.0001c112.79B3.413.750.0013c217.34B2.417.20<.0001c30.000B...公共回归系数

LeastSquaresMeansStandardLSMEANcyLSMEANErrorPr>|t|Number194.95863051.8403872<.00011299.50098071.2033114<.00012382.16538871.9643967<.00013LeastSquaresMeansforeffectcPr>|t|forH0:LSMean(i)=LSMean(j)DependentVariable:yi/j12310.04240.001320.0424<.000130.0013<.0001修正均数修正项C1C2C3C1C2C3（P218:表13-6下边合计）（P218:表13-6右边合计）C1C2C3总lxx饲料lxx白鼠lxx

饲料＋误差：lxx=383620.127+36943.246=420563.373lyy=48297.627+8399.613=56697.240lxy=135607.964+15102.873=150710.837（=总平方和̵区组间平方和）饲料lxx误差lxx饲料lYY误差lYY饲料lXY误差lYY

估计误差：误差：饲料＋误差：（与回归分析一致）误差（饲料+误差）误差lXY

误差lXX

（饲料+误差）lXY

（饲料+误差）lXX

修正均数：(饲料+误差)估计误差(误差)估计误差(修正均数)估计误差误差lXY误差lXXdataa;dob=1to3;doa=1to12;inputxy@@;output;end;end;cards;256.927.0271.641.7210.225.0300.152.0262.214.5304.448.8272.448.0248.29.5242.837.0342.956.5356.976.0198.29.2260.332.0271.147.7214.736.7300.165269.739.0307.537.9278.951.5256.226.7240.841.0340.761.3356.3102.1199.28.1544.7160.3481.296.1418.9114.6556.6134.8394.576.3426.672.8416.199.4549.9133.7580.5147.0608.3165.8559.6169.8371.954.3;proc

glm;classab;modely=xab/solutionSS3；/*solution:输出回归系数及标准误并作检验假设*/lsmeansb/*输出处理b的修正均数*//stderr/*输出修正均数的标准误*/pdiff;/*输出修正均数两两比较的P值*/run;DependentVariable:y

SumofSourceDFSquaresMeanSquareFValuePr>FModel1473529.470805252.1050649.39<.0001Error212233.13892

106.33995Corrected3575762.60972Total估计误差的误差项均方总变异的StandardParameterEstimateErrortValuePr>|t|Intercept-89.11127107B22.52742119-3.960.0007x0.40883873

0.053651367.62<.0001a19.35792946B9.913397400.940.3559a23.26988668B9.572096730.340.7360a324.74717161B8.524578252.900.0085a47.25833106B10.904940980.670.5129a5-2.00952135B8.87619451-0.230.8231a6-7.38646180B9.69901683-0.760.4548a715.43634937B9.134800151.690.1059a8-6.07301243B9.84233062-0.620.5438a910.95811440B9.934221541.100.2825a10-0.55303963B12.57943760-0.040.9653a1123.48323360B12.327776091.900.0706a120.00000000B...b18.37099313B12.540029490.670.5117b216.04318717B12.419235171.290.2105b30.00000000B...bCSourceDFTypeIIISSMeanSquareFValuePr>Fx16175.0305216175.03052158.07<.0001a113761.318706341.9380643.220.0103b2469.156885234.578443

2.210.1350估计误差的修正均数项的均方检验修正均数总差异的F值F=

234.578443/106.33995=2.21

补充：多元协方差分析应用

有30名婴幼儿身高X1(cm)、体重X2（kg)及体表面积Y(cm2)的资料，把身高、体重化为相等后，比较男、女体表面积的修正均值。datali13_b;doi=1to10;doc=1to2;inputx1x2y@@;output;end;end;cards;5432446.25432117.350.52.251928.4532.252200.2512.52094.551.52.51906.256.53.52506.75131850.352321215131632.5769.53845.9777.539348094380.877104180.4749.54314.2779.54246.18094078.47493358.87684134.5737.53809.79613.55830.291125358.497146013.691135601.799166410.694156074.992115283.392125299.494156101.69112.55291.5;proc

glm;classc;modely=cx1x2/solutionSS3;lsmeansc/stderrpdiff;run;

TheGLMProcedureDependentVariable:ySumofSourceDFSquaresMeanSquareFValuePr>FModel368523072.1122841024.04557.41<.0001Error261065399.7640976.91CorrectedTotal2969588471.87

SourceDFTypeIIISSMeanSquareFValuePr>Fc1139769.3397139769.3397

3.410.0762x11938153.7036938153.703622.89<.0001x21368954.7895368954.78959.000.0059

StandardParameterEstimateErrortValuePr>|t|Intercept-1255.559200B493.5333290-2.540.0172c1136.828607B74.08675511.850.0762c20.000000B...x154.47721711.38538034.78<.0001x2130.64510843.53877443.000.0059

TheGLMProcedureLeastSquaresMeansH0:LSMean1=StandardH0:LSMEAN=0LSMean2cyLSMEANErrorPr>|t|Pr>|t|14013.4576452.32694<.00010.076223876.6290352.32694<.0001补充：两因素析因设计

协方差分析例：在棉花产量Y的研究中，考虑2个因素：棉花品种A(A1：37号，A2：213号）；种植行距B(B1:30cm,B2:40cm),完全组合4种处理下的重复次数分别为9、16、8、16。棉籽重量X为协变量，试验数据如下，试作两因素析因设计协方差分析。ABXYABXYABXYABXY37308.42.937308.02.537307.42.737308.93.137305.62.137308.02.737307.62.537305.41.537306.92.537404.51.337409.13.137409.03.137408.02.337407.22.237407.62.537409.03.037402.30.637408.73.037408.02.637407.22.537407.62.437406.92.237406.92.537407.62.437404.71.4213304.61.7213306.81.7213303.51.3213302.41.0213303.01.0213302.80.5213303.60.9213306.91.9213407.42.1213404.91.0213405.71.0213403.00.7213404.71.5213405.01.3213407.01.7213402.80.4213405.21.2213405.61.0213405.31.2213404.51.0213405.61.2213402.00.7213404.21.2213401.20.2dataa;inputABxy@@;cards;…………………..;proc

glm;classab;modely=xaba*b/ss3;run;proc

glm;classab;modely=xab/solutionSS3;lsmeansAB/stderrpdiff;run;DependentVariable:ySourceDFTypeIIISSMeanSquareFValuePr>Fx111.6467271211.64672712231.34<.0001A10.955592960.9555929618.98<.0001B10.465391580.465391589.240.0040A*B10.084886200.084886201.690.2009(A、B无交互作用）SourceDFTypeIIISSMeanSquareFValuePr>Fx111.5628144811.56281448226.23<.0001A11.239672861.2396728624.25<.0001B10.449876530.449876538.800.0048(3个因素都对产量y有作用）StandardParameterEstimateErrortValuePr>|t|Intercept-.2726531659B0.10382857-2.630.0118x0.30020407220.0199593215.04<.0001A370.4166533813B0.084602314.92<.0001A2130.0000000000B...B300.2014621753B0.067905932.970.0048B400.0000000000B

（公共回归系数=0.3002040722，P<.0001）TheGLMProcedureLeastSquaresMeans