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1、MultipleRegressionAnalysis:Inference多元回归分析：推断(1)y=b0+b1x1+b2x2+...bkxk+uLectureOutline本课提纲CLMassumptionsandSamplingDistributionsoftheOLSEstimators经典假设与OLS估计量的样本分布Backgroundreviewofhypothesistesting假设检验的背景知识One-sidedandtwo-sidedttests单边与双边t检验Calculatingthepvalues计算p值AssumptionMLR.6(Normality
2、)假设MLR.6（正态）Sofar,weknowthatgiventheGauss-Markovassumptions,OLSisBLUE,我们已经知道当Gauss－Markov假设成立时，OLS是最优线性无偏估计。Inordertodoclassicalhypothesistesting,weneedtoaddanotherassumption(beyondtheGauss-Markovassumptions)为了进行经典的假设检验，我们要在Gauss－Markov假设之外增加另一假设。AssumptionMLR.6(Normality):Assumethatuisinde
3、pendentofx1,x2,…,xkanduisnormallydistributedwithzeromeanandvariances2:u~Normal(0,s2)假设MLR.6（正态）：假设u与x1,x2,…,xk独立，且u服从均值为0，方差为s2的正态分布。CLMAssumptions经典线性模型假设AssumptionsMLR.1–MLR.6arecalledtheclassicallinearmodel(CLM)assumptions.假设MLR.1-MLR.6被称为经典线性模型假设Werefertothemodelunderthesesixassumptions
4、astheclassicallinearmodel.我们将满足这六个假设的模型称为经典线性模型UnderCLM,OLSisnotonlyBLUE,butalsotheminimumvarianceunbiasedestimator,thatis,amonglinearandnonlinearestimators,OLSestimatorgivesthesmallestvariance.在经典线性模型假设下，OLS不仅是BLUE，而且是最小方差无偏估计量，即在所有线性和非线性的估计量中，OLS估计量具有最小的方差。CLMAssumptions经典线性模型假设Wecansumma
5、rizethepopulationassumptionsofCLMasfollows我们对总体的经典线性模型假设做个总结y
6、x~Normal(b0+b1x1+…+bkxk,,s2)Whilefornowwejustassumenormality,sometimesthisisnotthecase尽管现在我们假设了正态，但有时候并不是这种情况CLMAssumptions经典线性模型假设Whatshouldwedowhenthenormalityassumptionfails?如果正态假设不成立怎么办？Usingatransformation,especiallytakingth
7、elog,oftenyieldsadistributionthatisclosertonormal.通过变换，特别是通过取自然对数，往往可以得到接近于正态的分布。Theorem4.1NormalSamplingDistributions定理4.1正态样本分布4.2TestingHypothesesaboutaSinglePopulationParameter:thet-test对单个总体参数的假设检验：t检验Considerapopulationmodel(4.2)whichsatisfiestheCLMassumptions.Wenowstudyhowtotesthypot
8、hesesaboutaparticular考虑总体中满足CLM的模型我们现在研究如何对一个特定的进行假设检验BackgroundReview背景知识回顾Thehypothesistobetestediscalledthenullhypothesis.被检验的假设称为零假设Hypothesistestingentailsusingdatatocomparethenullhypothesiswithasecondhypothesis,i.e.,thealternativehypothesis.假设检验利用数
