计量经济学讲义(厦门大学 黄长全)Chap4.pptx

计量经济学讲义(厦门大学 黄长全)Chap4.pptx

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Chapter3多元线性回归模型（Multiplelinearregressionmodel）,Youarerequiredtogetfamiliarwithmatrixalgebraformasteringthischapter!

ClassicalMultiplelinearregressionmodel（CMLRM）:

1.model2.randomsample,Matrixform:

3.Modelassumption:

1.2.3.isnon-random.4.5.Normalityassumption,assumptions1and5implythattheerrorsareIndependent.Asinthecaseoftheunivariatelinearregressionmodels,wecanestimatetheregressioncoefficientsofthemultiplelinearregressionmodelsbyusingtheordinaryleastsquaresprocedure.Inmatrixform,theOLSEis,4.OLSEfortheCMLRM5.PropertiesoftheOLSEfortheCMLRM1.2.3.TheGauss-Markovtheoremisstilltrue:

TheOLSEfortheCMLRMistheBLUE.,6.ResidualandEstimationofthepopulationvariance1.Residual1）Pisidempotent（幂等的）2）3）4）,2.Estimatorfor,7.Goodness-of-fittesting1.1）Totalsumofsquares:

2）Explainedsumofsquares:

2.Coefficientofdetermination:

3.AdjustedR-squared:

8.Hypothesistesting1.Significancetestforthepopulationregressionequation1）Hypothesis:

2）F-statistic:

3）TestingGivenasignificancelevel,pickupthecriticalvalue.if,reject.otherwise,acceptit.2.Significancetestforasingleparameter1）Hypothesis:

2）t-statistic:

9.Forecasting1.Pointforecast:

Given,thenapredictor2.Intervalforecast:

Letthen,LetThenHomework: