计量经济学讲义Chap3课件

Chapter3一元线性回归模型第一节回归分析与回归方程Chapter3一元线性回归模型第一节回归分1回归分析:1.根据经济理论或考察样本数据去设定回归方程

Y:dependentvariable;:independent:randomerrorordisturbanceterm回归分析:2Aspecialandsimplecase(univariatelinearregressionmodel):这是本章研究的重点。2.参数估计(Estimationofparameter)3.Testing4.Predicting设有样本为，则Aspecialandsimplecase(uni3模型的假设：1.2.(同方差)3.4.

满足这四条件的LRM称为

经典线性回归模型(CLRM)。模型的假设：4由假设得

Populationregressionequation(function)Thepityistheparametersareunknown.我们要利用样本来估计参数.如得参数估计值,则称为sampleregressionequation(function).Howtoestimatethem?TheOLSmethod.由假设得5普通最小二乘法(Ordinaryleastsquaresprocedure):求使残差平方和最小:LetThen(OLSE)普通最小二乘法(Ordinaryleastsquares6ThepropertiesoftheOLSE:1.无偏性(unbiased):

2.

ThepropertiesoftheOLSE:73.关于样本的线性性:4.Gauss-Markovtheorem:如果

是经典线性回归模型(CLRM),则其参数的OLSE为BLUE。即,在所有线性无偏估计中，OLSE的方差最小。

3.关于样本的线性性:8

Estimationofthevarianceoftherandomdisturbanceterm,:Weknowanditisunknown.Thus,

andsoonarealsounknown.Toestimatethem,wehavetofirstevaluate.Itisnotdifficulttoshowthatisanunbiasedestimatorfor,Estimationofthevariance9Wherearetheresiduals.Example3.1(P39)(howtouseEviews)Where10模型的假设：5.Normalityassumption:ThepropertiesoftheOLSE:5.模型的假设：11Modeltesting(模型的检验):总离差分解公式:即,

TSS=ESS+RSSTSS:TotalsumofsquaresESS:Error(residual)sumofsquaresRSS:Regression(explained)sumofsquaresModeltesting(模型的检验):121.Goodness-of-fittesting(R2检验):Coefficientofdetermination(判定系数):

Ingeneral,thelargerR2,thebetter.2.Samplecoefficientofcorrelation:

1.Goodness-of-fittesting(R2检验133.HypothesistestingWehaveknownLet(standarderror)

3.Hypothesistesting14ThenAndwecantestthefollowinghypothesis:Moreover,intervalestimatorforis

Then15Forecasting(预测)1.PointforecastingSinceweknowandthesampleregressionequationthengiven,whataboutand?As(anunbiasedestimatorfor)Forecasting(预测)1.Pointfo16and(误差均匀)Naturally,weuseasapointpredictorforbothand.2.Intervalforecasting(1)Forecastintervalfor

Forecasterror:

计量经济学讲义Chap3课件17Thevarianceoftheforecasterror:ThereforeThevarianceoftheforecaste18Itisapitythatisunknown.Fortunately,wehaveThus,Hence,aForecastintervalfor

is

Itisapitythati19(2)

Forecastintervalfor

Similarly,

wecanobtainaforecastintervalfor:计量经济学讲义Chap3课件20计量经济学讲义Chap3课件21Chapter3一元线性回归模型第一节回归分析与回归方程Chapter3一元线性回归模型第一节回归分22回归分析:1.根据经济理论或考察样本数据去设定回归方程

Y:dependentvariable;:independent:randomerrorordisturbanceterm回归分析:23Aspecialandsimplecase(univariatelinearregressionmodel):这是本章研究的重点。2.参数估计(Estimationofparameter)3.Testing4.Predicting设有样本为，则Aspecialandsimplecase(uni24模型的假设：1.2.(同方差)3.4.

满足这四条件的LRM称为

经典线性回归模型(CLRM)。模型的假设：25由假设得

Populationregressionequation(function)Thepityistheparametersareunknown.我们要利用样本来估计参数.如得参数估计值,则称为sampleregressionequation(function).Howtoestimatethem?TheOLSmethod.由假设得26普通最小二乘法(Ordinaryleastsquaresprocedure):求使残差平方和最小:LetThen(OLSE)普通最小二乘法(Ordinaryleastsquares27ThepropertiesoftheOLSE:1.无偏性(unbiased):

2.

ThepropertiesoftheOLSE:283.关于样本的线性性:4.Gauss-Markovtheorem:如果

是经典线性回归模型(CLRM),则其参数的OLSE为BLUE。即,在所有线性无偏估计中，OLSE的方差最小。

3.关于样本的线性性:29

Estimationofthevarianceoftherandomdisturbanceterm,:Weknowanditisunknown.Thus,

andsoonarealsounknown.Toestimatethem,wehavetofirstevaluate.Itisnotdifficulttoshowthatisanunbiasedestimatorfor,Estimationofthevariance30Wherearetheresiduals.Example3.1(P39)(howtouseEviews)Where31模型的假设：5.Normalityassumption:ThepropertiesoftheOLSE:5.模型的假设：32Modeltesting(模型的检验):总离差分解公式:即,

TSS=ESS+RSSTSS:TotalsumofsquaresESS:Error(residual)sumofsquaresRSS:Regression(explained)sumofsquaresModeltesting(模型的检验):331.Goodness-of-fittesting(R2检验):Coefficientofdetermination(判定系数):

Ingeneral,thelargerR2,thebetter.2.Samplecoefficientofcorrelation:

1.Goodness-of-fittesting(R2检验343.HypothesistestingWehaveknownLet(standarderror)

3.Hypothesistesting35ThenAndwecantestthefollowinghypothesis:Moreover,intervalestimatorforis

Then36Forecasting(预测)1.PointforecastingSinceweknowandthesampleregressionequationthengiven,whataboutand?As(anunbiasedestimatorfor)Forecasting(预测)1.Pointfo3