chapter4 - Multiple Regression Analysis---Inference (1&amp#215;1).pdf

《chapter4 - Multiple Regression Analysis---Inference (1&amp#215;1).pdf》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、MultipleRegressionAnalysisInferencey=+x+x+...01122kxk+u1ChapterOutlineTheNormalandRelatedDistributions正态分布和相关分布SamplingDistributionofOLSEstimatorsOLS估计量的抽样分布SignificanceTesting显著性检验ConfidenceIntervals置信区间TestingLinearCombinations线性约束检验2THENORMALANDRELATEDDISTRIBUTIONS正态分布

2、与其相关分布3TheNormalandRelatedDistributions正态分布与其相关分布Thenormaldistributionandthosederivedfromitarethemostwidelyuseddistributions.正态以及相关分布是应用最为广泛的分布wewillrelyheavilyonthenormalandrelateddistributionstoconductinference.我们主要依赖正态分布及相关分布进行统计推断4TheNormalDistribution正态分布（1）Anormalrandom

3、variableisacontinuousrandomvariablethatcantakeonanyvalue.正态随机变量是连续随机变量，取值为任意实数。Thenormaldistributionissymmetricaboutthemean.正态分布关于均值对称。Certainrandomvariablesappeartoroughlyfollowanormaldistribution:e.g.,Humanheightsandweights,testscores,andcountyunemploymentrates.常见的随机变量往往大致呈

4、现正态分布：比如，身高、体重、考试成绩、失业率等等5TheNormalDistribution(cont.)正态分布（2）ThepdfofNormalrandomvariableXcanbewrittenas:正态分布的概率密度函数：21x-px()exp-222IfarandomvariableZhasaNormal(0,1)distribution,thenwesayithasastandardnormaldistribution.标准正态分布，记为：N(0，1)67TheNormalDistribution(co

5、nt.)正态分布（3）Anylinearcombinationofnormalrandomvariableshasanormaldistribution.正态分布的线性组合仍然为正态分布！IfXandYarejointlynormallydistributed,thentheyareindependent,if,andonlyif,Cov(X,Y)=0.对于正态分布，独立和不相关等价！Normalrandomvariablehaszeroskewness,thatis:正态分布的偏度为0：3EX()0ThekurtosisoftheNo

6、rmalrandomvariableis3,thatis:正态分布的峰度为3：44EX()/38TheChi‐SquareDistribution卡方分布LetZ,i1,2,…,n,beindependentrandomvariables,eachidistributedasstandardnormal,defineanewrandomvariable:令Z,i1,2,…,n为独立同分布的标准正态随机变量，定义：in2XZii1Xhaswhatisknownasachi‐squaredistributionwithndegre

7、esoffreedom.n个独立的标准正态随机变量的平方和服从自由度为n的卡方分布。自由度为n的卡方分布的期望为n，方差为2n。theexpectedvalueofXisn(degreesoffreedom),andthevarianceofXis2n.910ThetDistributiont分布（1）LetZhaveastandardnormaldistributionandletXhaveachi‐squaredistributionwithndegreesoffreedom.Further,assumethatZandXareindepende

8、nt.令Z为标准正态分布，X为自由度为n的卡方分布，Z与X相互独