計(jì)量經(jīng)濟(jì)學(xué)講義Chap3課件

Chapter3一元線性回歸模型第一節(jié)回歸分析與回歸方程Chapter3一元線性回歸模型第一節(jié)回歸分1回歸分析:1.根據(jù)經(jīng)濟(jì)理論或考察樣本數(shù)據(jù)去設(shè)定回歸方程

Y:dependentvariable;:independent:randomerrorordisturbanceterm回歸分析:2Aspecialandsimplecase(univariatelinearregressionmodel):這是本章研究的重點(diǎn)。2.參數(shù)估計(jì)(Estimationofparameter)3.Testing4.Predicting設(shè)有樣本為，則Aspecialandsimplecase(uni3模型的假設(shè)：1.2.(同方差)3.4.

滿足這四條件的LRM稱為

經(jīng)典線性回歸模型(CLRM)。模型的假設(shè)：4由假設(shè)得

Populationregressionequation(function)Thepityistheparametersareunknown.我們要利用樣本來估計(jì)參數(shù).如得參數(shù)估計(jì)值,則稱為sampleregressionequation(function).Howtoestimatethem?TheOLSmethod.由假設(shè)得5普通最小二乘法(Ordinaryleastsquaresprocedure):求使殘差平方和最小:LetThen(OLSE)普通最小二乘法(Ordinaryleastsquares6ThepropertiesoftheOLSE:1.無偏性(unbiased):

2.

ThepropertiesoftheOLSE:73.關(guān)于樣本的線性性:4.Gauss-Markovtheorem:如果

是經(jīng)典線性回歸模型(CLRM),則其參數(shù)的OLSE為BLUE。即,在所有線性無偏估計(jì)中，OLSE的方差最小。

3.關(guān)于樣本的線性性:8

Estimationofthevarianceoftherandomdisturbanceterm,:Weknowanditisunknown.Thus,

andsoonarealsounknown.Toestimatethem,wehavetofirstevaluate.Itisnotdifficulttoshowthatisanunbiasedestimatorfor,Estimationofthevariance9Wherearetheresiduals.Example3.1(P39)(howtouseEviews)Where10模型的假設(shè)：5.Normalityassumption:ThepropertiesoftheOLSE:5.模型的假設(shè)：11Modeltesting(模型的檢驗(yàn)):總離差分解公式:即,

TSS=ESS+RSSTSS:TotalsumofsquaresESS:Error(residual)sumofsquaresRSS:Regression(explained)sumofsquaresModeltesting(模型的檢驗(yàn)):121.Goodness-of-fittesting(R2檢驗(yàn)):Coefficientofdetermination(判定系數(shù)):

Ingeneral,thelargerR2,thebetter.2.Samplecoefficientofcorrelation:

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

3.Hypothesistesting14ThenAndwecantestthefollowinghypothesis:Moreover,intervalestimatorforis

Then15Forecasting(預(yù)測)1.PointforecastingSinceweknowandthesampleregressionequationthengiven,whataboutand?As(anunbiasedestimatorfor)Forecasting(預(yù)測)1.Pointfo16and(誤差均勻)Naturally,weuseasapointpredictorforbothand.2.Intervalforecasting(1)Forecastintervalfor

Forecasterror:

計(jì)量經(jīng)濟(jì)學(xué)講義Chap3課件17Thevarianceoftheforecasterror:ThereforeThevarianceoftheforecaste18Itisapitythatisunknown.Fortunately,wehaveThus,Hence,aForecastintervalfor

is

Itisapitythati19(2)

Forecastintervalfor

Similarly,

wecanobtainaforecastintervalfor:計(jì)量經(jīng)濟(jì)學(xué)講義Chap3課件20計(jì)量經(jīng)濟(jì)學(xué)講義Chap3課件21Chapter3一元線性回歸模型第一節(jié)回歸分析與回歸方程Chapter3一元線性回歸模型第一節(jié)回歸分22回歸分析:1.根據(jù)經(jīng)濟(jì)理論或考察樣本數(shù)據(jù)去設(shè)定回歸方程

Y:dependentvariable;:independent:randomerrorordisturbanceterm回歸分析:23Aspecialandsimplecase(univariatelinearregressionmodel):這是本章研究的重點(diǎn)。2.參數(shù)估計(jì)(Estimationofparameter)3.Testing4.Predicting設(shè)有樣本為，則Aspecialandsimplecase(uni24模型的假設(shè)：1.2.(同方差)3.4.

滿足這四條件的LRM稱為

經(jīng)典線性回歸模型(CLRM)。模型的假設(shè)：25由假設(shè)得

Populationregressionequation(function)Thepityistheparametersareunknown.我們要利用樣本來估計(jì)參數(shù).如得參數(shù)估計(jì)值,則稱為sampleregressionequation(function).Howtoestimatethem?TheOLSmethod.由假設(shè)得26普通最小二乘法(Ordinaryleastsquaresprocedure):求使殘差平方和最小:LetThen(OLSE)普通最小二乘法(Ordinaryleastsquares27ThepropertiesoftheOLSE:1.無偏性(unbiased):

2.

ThepropertiesoftheOLSE:283.關(guān)于樣本的線性性:4.Gauss-Markovtheorem:如果

是經(jīng)典線性回歸模型(CLRM),則其參數(shù)的OLSE為BLUE。即,在所有線性無偏估計(jì)中，OLSE的方差最小。

3.關(guān)于樣本的線性性:29

Estimationofthevarianceoftherandomdisturbanceterm,:Weknowanditisunknown.Thus,

andsoonarealsounknown.Toestimatethem,wehavetofirstevaluate.Itisnotdifficulttoshowthatisanunbiasedestimatorfor,Estimationofthevariance30Wherearetheresiduals.Example3.1(P39)(howtouseEviews)Where31模型的假設(shè)：5.Normalityassumption:ThepropertiesoftheOLSE:5.模型的假設(shè)：32Modeltesting(模型的檢驗(yàn)):總離差分解公式:即,

TSS=ESS+RSSTSS:TotalsumofsquaresESS:Error(residual)sumofsquaresRSS:Regression(explained)sumofsquaresModeltesting(模型的檢驗(yàn)):331.Goodness-of-fittesting(R2檢驗(yàn)):Coefficientofdetermination(判定系數(shù)):

Ingeneral,thelargerR2,thebetter.2.Samplecoefficientofcorrelation:

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

3.Hypothesistesting35ThenAndwecantestthefollowinghypothesis:Moreover,intervalestimatorforis

Then36Forecasting(預(yù)測)1.PointforecastingSinceweknowandthesampleregressionequationthengiven,whataboutand?As(anunbiasedestimatorfor)Forecasting(預(yù)測)1.Pointfo3