7第八章--相关分析和回归分析教学文稿.ppt

,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,第八章 相关分析和回归分析,8.1,相关分析和回归分析概述,8.2,相关分析,8.3,直线回归,8.4,多元线性回归,8.5,逐步回归,8.6,非线性回归,8.1 相关、回归分析概述,相关分析计算反映各变量之间相关密切程度和性质的统计数。,8.1.1 相关分析概述,简单相关,：研究两变量直线相关的密切程度和性质，也称直线相关。,偏相关,：排除其余的影响因子，求出x 与y的纯相关，这种相关称偏相关。,复相关,：研究一个变量与一组变量之间的相关性关系。,典型相关,：研究两组变量的相关性。,8.1.2 回归分析概述,由自变数预测因变数的问题都叫回归分析。,相关分析反映各变量间相关密切程度，回归分析反映因变量(Y)和自变量(X)之间的数量关系，用回归方程表示。回归模型不一定是因果关系，自变量可多于一个。,回归分析依,自变量个数,的多少分为：,一元回归和多元回归,因变量和自变量间,关系的性质分,：,线性回归和非线性回归,回归分析的SAS过程：主要有,REG（,回归分析）,GLM,（广义线性模型）,如由温度表水银柱高度（X）来估计温度（Y）时，自变量实际上是依赖于因变量。,1 简单相关,2 偏相关,3 复相关,8.2 相关分析,（Analysis of Correlation),补：秩相关,1 简单相关,简单相关:,是对有联系的两类事物（x与y）表面关系密切程度的衡量。,(Simple Correlation),一、简单相关系数,相关系数,r,（无单位）,的取值：,即：,二、简单相关系数r的显著性测验,由d.f=n-2查出相关系数的临界值r,0.05,、r,0.01,（,degree of freedom,),SAS直接输出prob,|r|概率值，记为,a.,统计假设H,0,：总体相关系数=0,若,a,0.05，接受,H,0,，,相关不显著，即总体x与y间不存在相关关系。,若0.01,a,0.05，拒绝,H,0,，,相关显著，即总体x与y间存在相关关系。,若,a,|R|,under Ho:Rho=0/N=26,X Y,X 1.00000,0.71019,0.0,0.0001,Y 0.71019 1.00000,0.0001 0.0,结论：因r=,0.71019,，其出现的概率=0.0001|r|,x1,x2,x3,x1,1.00000,0.79949,0.0010,0.775490.0018,x2,0.799490.0010,1.00000,0.869310.0001,x3,0.775490.0018,0.869310.0001,1.00000,CORR 过程,1 Partial 变量：,x3,2 变量：,x1 x2,简单统计量,变量,N,均值,标准偏差,总和,最小值,最大值,偏方差,偏标准偏差,x3,13,15.73846,0.99544,204.60000,13.70000,17.90000,x1,13,28.60769,20.18875,371.90000,0.40000,52.30000,177.24259,13.31325,x2,13,15.48462,1.13420,201.30000,13.10000,17.60000,0.34284,0.58552,Pearson 偏相关系数,N=13 当 H0:Partial Rho=0 时，Prob|r|,x1,x2,x1,1.00000,0.40169,0.1956,x2,0.401690.1956,1.00000,统计结论:,r12=0.79949 p=0.0010.01 相关极显著,r13=0.77549 p=0.00180.01 相关极显著,r23=0.86931 p=0.00010.05 相关不显著,r13.2=0.27108 p=0.271080.05 相关不显著,实例：p170,例8.2 腰果分期播种试验，采用10天播种一次，每次,播种10粒。1986年4月至1987年3月，共进行33次分期,播种。表11是腰果种子发芽“普遍期”天数、平均气,温、平均最低气温、及平均最高气温的观察资料。试,求简单相关系数及二级偏相关系数。,普遍天数,平均气温,平均最低气温,平均最高气温,12,29.0,24.2,34.6,15,27.8,23.6,32.6,42,19.2,14.9,25.2,表8.3 腰果种子“普遍期”天数与气温表,data cashew;,input x1 x2 x3 x4;,cards;,12 29.0 24.2 34.6,.,42 19.2 14.9 25.2,;,proc corr;var x1 x2 x3 x4;,proc corr;var x3 x4;partial x2;,proc corr;var x1 x4;,partial x2 x3,;,run;,Correlation Analysis,2 PARTIAL Variables:X2 X3,2 VAR Variables:X1 X4,Pearson Partial Correlation Coefficients/Prob|R|,under Ho:Partial Rho=0/N=33,X1 X4,X1 1.00000,0.07517,0.0,0.6878,X4 0.07517 1.00000,0.6878 0.0,统计结论:,r34.2=-0.8031 p=0.00010.05 相关不显著,部分输出结果：,组合代号 X1 X2 X3 Y,1 10.37 29.56 33.31 10.520,2 10.47 34.25 29.05 10.070,3 9.67 35.25 37.65 12.790,4 9.87 29.25 31.52 9.230,5 8.20 37.85 33.62 10.360,6 8.67 37.78 38.09 12.570,7 10.03 40.97 30.42 12.560,8 9.00 46.00 29.10 11.388,9 10.07 39.73 32.06 12.830,实习四,实 习,作业:21个小麦双列杂交组合F,1,的单株产量y（克），每株穗数x1，每穗的粒数x2,千粒重x3（克）数据如下：,组合代号 X1 X2 X3 Y,10 10.57 36.30 30.59 11.800,11 8.73 37.10 27.17 8.730,12 10.20 35.67 32.21 11.790,13 8.93 35.44 33.22 10.420,14 9.83 34.28 28.40 9.830,15 8.60 33.31 35.49 10.920,16 8.83 35.10 27.54 8.440,17 8.80 34.45 34.20 10.500,18 8.80 30.65 29.47 7.940,19 9.40 31.20 30.75 8.830,20 10.03 39.27 29.21 11.330,试求,r,y1,、r,y3,、r,y1.2,、r,y1.23,并确定其显著性。,&8.3 直线回归分析,(一元线性回归),一、直线回归方程,正相关r0,曲线相关,负相关rF,0.05,，显著，即x与y之间的直线回归关系显著。,若FF,0.01,，极显著。,若FF,0.05,，不显著。,即两变量间不存在线性关系,目的：了解样本所来自的集团中两变数间是否确实存,在回归关系。,二、回归的显著性测验,但必须注意，应用时X的取值范围只能在拟合回归方程时所用样本的范围内，不能外推。,，可用于预测、控制等，,1.预测：当X=x,0,时，用回归方程预测值,三、用直线方程预测,P175例8.3：橡胶树大型系比试验，刺检干胶量（x:毫克）与正式割胶产量（y:克）如下:,编号,刺检干胶量 正式割胶产量,X y,1,2,.,.,.,26,77 8.8,64 7.9,.,.,.,73 3.5,试求y关于x的回归方程，并对回归方程作显著性测验。,data latex;,input x y;,cards;,77 8.8 64 7.9 73 3.5,;,proc reg,corr,;,model y=x/,cli,clm,;,/*CLI输出Y值的95%预测区间*/,Plot y*x/,conf95,;,run;,其SAS程序：,四、直线回归实例,conf95在散点图（x，y）上附加回归直线和均值置信区间,/*选项CORR，要求输出简单相关系数*/,clm输出条件总体平均数的95%置信区间,SAS 系统,The REG Procedure,Correlation,Variable,x,y,x,1.0000,0.7057,y,0.7057,1.0000,SAS输出结果：,说明：proc reg,corr,;选项corr输出变量间的简单相关系数,The REG Procedure,Model:MODEL1,Dependent Variable:y,Analysis of Variance,Source,DF,Sum ofSquares,MeanSquare,F Value,PrF,Model,1,137.80902,137.80902,23.81,|t|,Intercept,1,2.00746,1.53037,1.31,0.2020,x,1,0.07709,0.01580,4.88,.0001,截距,截距,a,=2.00746，其标准误为1.53037。,回归系数b=0.07709，其标准误为0.01580，t=4.88，pF,Model,2,2852.83453,1426.41726,15.37,0.0027,Error,7,649.60947,92.80135,Corrected Total,9,3502.44400,Root MSE,9.63335,R-Square,0.8145,Dependent Mean,28.56000,Adj R-Sq,0.7615,Coeff Var,33.73020,Parameter Estimates,Variable,DF,ParameterEstimate,StandardError,tValue,Pr|t|,Intercept,1,-135.09962,61.37574,-2.20,0.0636,x1,1,10.19568,4.31604,2.36,0.0502,x2,1,1.28360,1.37017,0.94,0.3800,求二元回归方程,Output Statistics,Obs,DependentVariable,PredictedValue,Std ErrorMean Predict,95%CL Predict,Residual,1,11.8000,21.6718,4.9777,-3.9687,47.3123,-9.8718,10,0.5000,-1.5362,6.7356,-29.3314,26.2590,2.0362,11,.,31.0973,8.9945,-0.0675,62.2621,.,预测出1977年最终病情指数值,95%的预测区间为-0.0675，62.2621,2：三元线性回归,P180,例8.4 甘蔗糖分与气象资料如表8.5。试求y关于x,1,，,x,2,，x,3,的线性回归方程，并对方程作显著性测验。当,方程达显著时，再对1984年糖分作预测。,年份,糖份（y）,912月份降雨量（x,1,）,10月份相对湿度（x,2,）,12月份最低温度（x,3,）,64/65,13.93,408.6,83,4.3,65/66,13.85,460.9,83,3.0,66/67,14.21,151.8,82,4.7,83/84,390.0,80,4.6,data sgca;,input y x1-x3;,cards;,13.93 408.6 834.3,13.85 460.9 833.0,.,11.59 480.4 831.5,.390.0 804.6,;,proc reg;,model y=x1-x3/stb cli;,run;,SAS结果及解释P147,Analysis of Variance,Source,DF,Sum ofSquares,MeanSquare,F Value,PrF,Model,3,7.79038,2.59679,9.08,0.0011,Error,15,4.29100,0.28607,Corrected Total,18,12.08138,Parameter Estimates,Variable,DF,ParameterEstimate,StandardError,tValue,Pr|t|,StandardizedEstimate,Intercept,1,19.71462,3.18926,6.18,F,Model,1,4.28805,4.28805,9.35,0.0071,Error,17,7.79333,0.45843,Corrected Total,18,12.08138,Variable,ParameterEstimate,StandardError,TypeIISS,F Value,PrF,Intercept,24.90350,3.51331,23.03367,50.24,F,Model,2,6.21553,3.10777,8.48,0.0031,Error,16,5.86585,0.36662,Corrected Total,18,12.08138,Variable,ParameterEstimate,StandardError,TypeIISS,F Value,PrF,Intercept,22.95199,3.25508,18.22753,49.72,F,Model,3,7.79038,2.59679,9.08,0.0011,Error,15,4.29100,0.28607,Corrected Total,18,12.08138,Variable,ParameterEstimate,StandardError,TypeIISS,F Value,PrF,Intercept,19.71462,3.18926,10.93112,38.21,F,Model,2,7.07663,3.53831,11.31,0.0009,Error,16,5.00475,0.31280,Corrected Total,18,12.08138,Variable,ParameterEstimate,StandardError,TypeIISS,F Value,PrF,Intercept,14.72728,0.47031,306.71958,980.57,0,B20,B30,的图象,的图象,最简单的多项式是,二次多项式,，其方程为：,b20,B2F,Model 1 29.00024 29.00024,0.998,0.3563,Error 6 174.33476 29.05579,C Total 7 203.33500,Root MSE 5.39034 R-square,0.1426,Dep Mean 9.72500 Adj R-sq -0.0003,C.V.55.42769,Parameter Estimates,Parameter Standard T for H0:,Variable DF Estimate Error Parameter=0 Prob|T|,INTERCEP 1,5.154762,4.95571021 1.040 0.3384,X 1,0.830952,0.83174792 0.999 0.3563,Model:MODEL2,Source,DF,Sum ofSquares,MeanSquare,F Value,PrF,Model,2,198.60405,99.30202,104.95,|t|,Intercept,1,30.27381,2.07842,14.57,.0001,x,1,-10.22143,0.83905,-12.18,.0001,x2,1,1.00476,0.07505,13.39,F,Model,3,201.48950,67.16317,145.57,0.0002,Error,4,1.84550,0.46137,Corrected Total,7,203.33500,Root MSE,0.67925,R-Square,0.9909,Dependent Mean,9.72500,Adj R-Sq,0.9841,Coeff Var,6.98453,Parameter Estimates,Variable,DF,ParameterEstimate,StandardError,tValue,Pr|t|,Intercept,1,22.22381,3.53102,6.29,0.0033,x,1,-4.54113,2.34574,-1.94,0.1250,x2,1,-0.14524,0.46283,-0.31,0.7694,x3,1,0.06970,0.02787,2.50,0.0667,回归方程为：,data new;,input x y;,cards;,2 13.0 3 9.2 4 6.6 5 4.7 6 4.0 7 7.1 8 13.2 9 20.0,;,Proc GLM,;,MODEL Y=X X*X;,RUN;,Parameter,Estimate,Standard Error,tValue,Pr|t|,Intercept,30.27380952,2.07841528,14.57,.0001,x,-10.22142857,0.83905350,-12.18,.0001,x*x,1.00476190,0.07504723,13.39,|t|,Intercept 130.6235863 3.14436916 41.54|t|,Intercept 128.7147914 2.54503370 50.57,.0001,rate -21.4326668 2.17191314 -9.87,|r|,x1 x2,x1 1.00000 0.87879,0.0008,x2 0.87879 1.00000,0.0008,Kendall,Tau b 相关系数,N=10,当 H0:Rho=0 时，Prob|r|,x1 x2,x1 1.00000 0.73333,0.0032,x2 0.73333 1.00000,0.0032,