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: