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1、统计学Reading11相关和回归Reading12多元线性回归1.相关分析:1)协方差和相关系数的计算;2)相关系数的检验(ρ=0):t=r((n-2)/(1–r2))1/2,df=n–2.2.线性回归:1)模型及假设,dependentvariable(Y)andindependentvariable(X).2)参数估计(minSSE):bi=Cov(Xi,Y)/Var(Xi),b0=E(Y)–Σbi*E(Xi).3)回归系数的置信区间和统计检验:t=(bi–βi)/sbi,df=n–k–1.注：k为independentvariable的数目,不要
2、求计算标准误sbi.3.线性模型的显著性检验:1)Totalsumofsquares(SST)=Σ(Y–E(Y))2,Y–观测值;Regressionsumofsquare(RSS)=Σ(y–E(Y))2,y–拟合值;Sumofsquarederror(SSE)=Σ(Y-y)2;SST=RSS+SSE.2)方差分析表(ANOVA):SourceofvariationSumofsquaresDegreeoffreedomMeansumofsquareRegressionRSSk(#independentvariable)MSR=RSS/kErrorSSEn
3、–k–1MSE=SSE/(n–k-1)TotalSSTn–1Var(Y)=SST/(n-1)StandarderrorofestimateSEE=(MSE)1/2.3)DeterminationcoefficientR2=RSS/SST,AdjustedR2=1–(n-1)/(n–k-1)*(1–R2):adjusttheimpactofadditionalvariables.4)F-检验：F=MSR/MSE,df=(k,n–k-1).4.模型前提假设的检验:1)Heteroskedasticity:A)Effect:Unconditional:hete
4、roskedasticityisunrelatedtothelevelofX,nomajorproblem;Conditional:coefficientestimatesarenotaffected,buts.e.andF-testareunreliable.B)Detecting:a)Residualplot:residual=actual–predicted.b)Breusch-pagantest(H0:noheteroskedasticity):n*Rresid2~χ2(k),其中Rresid2是residual对X回归的决定系数.C)Corre
5、cting:usingrobustorcorrecteds.e.2)Serialcorrelation:residualtermsarecorrelatedwitheachother:A)Effect:Positiveserialcorrelation:underestimatings.e.,unreliableF-test;Negativeserialcorrelation:overestimatings.e.,unreliableF-test.B)Detecting:a)Residualplot.b)Durbin-Watsontest(H0:nose
6、rialcorrelation):DW≈2(1-r),其中r是残差的自相关系数,0≤DW≤4.C)Correcting:correcteds.e.forbothserialcorrelationandheteroskedasticity.3)Multicollinearity:independentvariablesarehighlycorrelatedwitheachother:A)Effect:individualvariablesarenotsignificant(larges.e.)buttheircombinationis.B)Detectin
7、g:a)Noneofindividualcoefficientissignificant,butF-testis.b)Correlationsbetweenvariables(>0.7).注：两变量间的相关系数并未考虑变量线性组合的相关性，因此低相关系数并不一定意味着不存在multicollinearity.C)Correcting:omitcorrelatedvariablesortakestepwiseregression.4)Modelmisspecification:不合适地选取解释变量（实际意义不对或不满足线性模型的前提假设）或不恰当的变量转换
8、等.5.Dummyvariable(0–1variable):1)Indepen
