应用多元分析第四章多元正态总体

计划学时：2学时教学课型：理论课教学目的与要求：掌握一元总体统计推断的基本原理与方法教学重点：一元总体统计推断的基本原理与方法教学难点：一元总体统计推断的基本原理与方法教学方法、手段与媒介：根据教材用多媒体课件课堂讲授教学过程与内容：,第四章多元正态总体的统计推断,4.1一元情形的回顾,1、置信区间,就称随机区间(，)是的置信度为1-的置信区间，称为置信下限，称为置信上限。,使得对任何0FWilksLambda0.831939801.353200.2876PillaisTrace0.168060201.353200.2876Hotelling-LawleyTrace0.202010051.353200.2876RoysGreatestRoot0.202010051.353200.2876,prociml;sigma1=0.57586206900.3758620690-.1034482759-.1655172414,0.37586206900.5850574713-.0919540230-.1586206897,-.1034482759-.09195402300.43678160920.4137931034,-.1655172414-41379310340.4551724138;mu1=3.90000,3.96667,4.33333,4.40000;sigma2=0.4885057471-.01724137930.04022988510.0229885057,-.01724137930.43793103450.07241379310.1172413793,0.04022988510.07241379310.24022988510.2022988506,0.02298850570.11724137930.20229885060.2574712644;mu2=3.83333,4.10000,4.63333,4.53333;c=1-100,10-10,100-1;mu=(mu1+mu2)/2;a=c*mu;sigma=29#(sigma1+sigma2)/58;t2=60#t(a)*inv(c*sigma*t(c)*a;F=20/(3*22)*t2;printt2f;,4.6多个总体均值的比较检验(多元方差分析),欲检验,方法:方差分析,检验统计量威尔克斯(Wilks)统计量,例4.6.1为了研究销售方式对商品额的影响,选择四种商品(甲、乙、丙、丁)按三种不同的销售方式(I,II,III)进行销,这四种商品的销售额分别为x1,x2,x3,x4,其数据见表4.6.1.问这三种销售方式的平均销售额是否显著不同?(设这三种销售方式的销售额x1,x2,x3,x4均服从正态分布.),经计算,由附录4-3中(4-3.4)可得,查F分布表得,从而,在0.01的显著性水平下,拒绝原假设(p=0.004).,差异的进一步分析(用一元方差分析).,表4.6.1销售额数据,Dataex461;Inputgx1-x4;Cards;,1120603382101119802333301635126020316551429150113065403205169453501901466058520011466627325018754585200111077507200110760364200113061391200180454292701605044219018154260280113587507260157484002851755252026017665403250155424111702665445531028245403210265653122802405147728026754481293238504682102424535119021134039031028055520200276605071892943326028026051429190255403902952654848117725948442225212563312270212056416280270454683702626641622426960377280365334802603100344682953656341626531174846825031146339538035530546235364515073203110904422253606244024831106937726038878299360373633903203114554942403103544163103100332733123140613123453803628625031355446834531306932536036057273260;Procprint;Run;,procanovadata=ex461;classg;modelx1-x4=g;manovah=g;run;,prociml;x=12560338210,11980233330,6351260203,65514291506945350190,46605852008754585240,11077507270,107603642008045429270,6050442190,81542602805748400285,7552520260,7665403250,5542411170;Y=6654455310,8245403210,6565312280,4051477280,6754481293,3850468210,4245351190,11340390310,8055520200,7660507189,9433260280,6051429190,5540390295,6548481177,6948442225,12563312270,12056416280,7045468370,6266416224,6960377280;z=6533480260,10034468295,6563416265,11748468250,11463395380,5530546235,6451507320,11090442225,6062440248,11069377260,8878299360,7363390320,11455494240,10354416310,10033273312803628625013069325360,6057273260;i=t(201);x1=T(x)*i/20;y1=T(y)*i/20;z1=T(z)*i/20;s=(x1+y1+z1)/3;t=60*s*T(s);sstr=20*(x1*T(x1)+y1*T(y1)+z1*T(z1)-t;sst=(T(x)*x+T(y)*y+T(z)*z)-t;sse=sst-sstr;l=det(sse)/det(sst);f=(57-4+1)*(1-sqrt(l)/(4*sqrt(l);f1=sstr1,1*57/(sse1,1*2);f2=sstr2,2*57/(sse2,2*2);f3=sstr3,3*57/(sse3,3*2);f4=sstr4,4*57/(sse4,4*2);printx1y1z1ssstrsstsselff1f2f3f4;,prociml;n1=20;n2=20;n3=20;n=n1+n2+n3;k=3;p=4;x1=260754018,200723417,240874518,170653917,2701103924,2051303423,190692715,200464515,2501172120,2001072820,2251303611,2101252617,170643114,270763313,190603416,280812018,3101192515,27057318,250673114,2601353929;x2=3101223021,310603518,190402715,225653416,170653716,210823117,280673718,210383617,280653023,200764017,200763920,280942611,190603317,295553016,2701252421,2801203218,240623220,280692920,370703020,280403717;x3=320643917,260593711,360882826,2951003612,270653221,3801143621,240554210,260553420,2601102920,295733321,2401143818,3101033218,3301122111,3451272420,250622216,260592119,2251003430,3451203618,3601072523,2501173616;xx=x1/x2/x3;,n1阶单位均矩阵,ln=201;x10=(ln*x1)/n1;printx10;mm1=i(n1)-j(n1,n1,1)/n1;mm=i(n)-j(n,n,1)/n;a1=x1*mm1*x1;printa1;a2=x2*mm1*x2;printa2;a3=x3*mm1*x3;printa3;tt=xx*mm*xx;printtt;a=a1+a2+a3;lambda=det(a)/det(tt);f=(n-p-k+1)*(1-sqrt(lambda)/(p*sqrt(lambda);p0=1-probf(f,8,108);printap0;,产生20个1的行向量,产生x1的均值向量,产生n1行n1列全为1的矩阵,产生离差阵,dt=det(tt/(n-k);da1=det(a1/(n1-1);da2=det(a2/(n2-1);da3=det(a3/(n3-1);m5=(n-k)*log(dt)-19*(log(da1)+log(da2)+log(da3);b=(2*p*p+3*p-1)*(k+1)/(6*(p+3)*(n-k)-(p-k+2)/(n-k)*(p+3);df=p*(p+3)*(k-1)/2;kc=(1-b)*m5;printdtda1da2da3;printm5bdf;p0=1-probchi(kc,df);printkcp0;run;,h=130;t11=h*tt*t(h);a11=h*a*t(h);f1=(t11-a11)/(k-1)/(a11/(n-k);p1=1-probf(f1,2,57);Printf1p1;,4.7总体相关系数的推断,一、简单相关系数的推断,(1)欲检验,(2)欲检验,二、偏相关系数的检验,欲检验,欲检验:,三、复相关系数的推断,欲检验,为研究日、美两国在华投资企业对中国经营环境的评价是否存在差异，今从两国在华投资企业中各抽出10家，让其对中国的政治、经济、法律、文化等环境进行打分，评分结果如表3.2所示（表中序号1-10为美国在华投资企业的代号，11-20为日本在华投资企业的代号，数据来源：国务院发展研究中心APEC在华投资企业情况调查）.,协方差矩阵的检验,其中,则,其中,令,或等价于,其中,例1,prociml;n1=20;n2=20;n3=20;n=n1+n2+n3;k=3;p=4;x1=260754018,200723417,240874518,170653917,2701103924,2051303423,190692715,200464515,2501172120,2001072820,2251303611,2101252617,170643114,270763313,190603416,280812018,3101192515,27057318,250673114,2601353929;x2=3101223021,310603518,190402715,225653416,170653716,210823117,280673718,210383617,280653023,200764017,200763920,280942611,190603317,295553016,2701252421,2801203218,240623220,280692920,370703020,280403717;x3=320643917,260593711,360882826,2951003612,270653221,3801143621,240554210,260553420,2601102920,295733321,2401143818,3101033218,3301122111,3451272420,250622216,260592119,2251003430,3451203618,3601072523,2501173616;xx=x1/x2/x3;,ln=201;x10=(ln*x1)/n1;printx10;mm1=i(n1)-j(n1,n1,1)/n1;mm=i(n)-j(n,n,1)/n;s1=x1*mm1*x1/(n1-1);s2=x2*mm1*x2/(n2-1);s3=x3*mm1*x3/(n3-1);tt=xx*mm*xx/(n-1);s=(s1+s2+s3)*(n1-1)/(n-3);ds1=det(s1);ds2=det(s2);ds3=det(s3);ds=det(s);d=(2*p*2+3*p-1)*(k+1)/(6*p+1)*(n-k);f=p*(p+1)*(k-1)/2;m=(n-k)*log(det(s)-(n1-1)*(log(det(s1)+log(det(s2)+log(det(s3);kc=(1-d)*m;p0=1-probchi(kc,df);prints1s2s3sfdmkc;,记,其中,对例1中的数据，判断三个组(即三个总体)的均值向量和协方差矩阵是否全相等(=0.05),prociml;n1=20;n2=20;n3=20;n=n1+n2+n3;k=3;p=4;x1=260754018,200723417,240874518,170653917,2701103924,2051303423,190692715,200464515,2501172120,2001072820,2251303611,2101252617,170643114,270763313,190603416,280812018,3101192515,27057318,250673114,2601353929;x2=3101223021,310603518,190402715,225653416,170653716,210823117,280673718,210383617,280653023,200764017,200763920,280942611,190603317,295553016,2701252421,2801203218,240623220,280692920,370703020,280403717;x3=320643917,260593711,360882826,2951003612,270653221,3801143621,240554210,260553420,2601102920,295733321,2401143818,3101033218,3301122111,3451272420,250622216,260592119,2251003430,3451203618,3601072523,2501173616;xx=x1/x2/x3;,ln=201;x10=(ln*x1)/n1;printx10;mm1=i(n1)-j(n1,n1,1)/n1;mm=i(n)-j(n,n,1)/n;s1=x1*mm1*x1/(n1-1);s2=x2*mm1*x2/(n2-1);s3=x3*mm1*x3/(n3-1);tt=xx*mm*xx;s=(s1+s2+s3)*(n1-1)/(n-3);ds1=det(s1);ds2=det(s2);ds3=det(s3);dt=det(tt/n-k);d=(2*p*2+3*p-1)*(k+1)/(6*p+1)*(n-k);f=p*(p+3)*(k-1)/2;b=(1/(n1-1)+1/(n2-1)+1/(n3