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1、Chapter 3 一元线性回归模型,第一节 回归分析与回归方程,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:dependent variable;:independent:random error or disturbance term,A special and simple case(univariate linear regression model):这是本章研究的重点。2.参数估计(Estimation of parameter)3.Testing4.Predicting设有样本为，则,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
2、(CLRM)。,由假设得 Population regression equation(function)The pity is the parameters are unknown.我们要利用样本来估计参数.如得参数估计值,则 称为sample regression equation(function).How to estimate them?The OLS method.,普通最小二乘法(Ordinary least squares procedure):求 使残差平方和最小:Let Then(OLSE),The properties of the OLSE:1.无偏性(unbiased
3、):2.,3.关于样本 的线性性:4.Gauss-Markov theorem: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。,Estimation of the variance of the random disturbance term,:We know and it is unknown.Thus,and so on are also unknown.To estimate them,we have to first evaluate.It is not difficult to show that is an u
4、nbiased estimator for,Whereare the residuals.Example3.1(P39)(how to use Eviews),模型的假设：5.Normality assumption:The properties of the OLSE:5.,Model testing(模型的检验):总离差分解公式:即,TSS=ESS+RSS TSS:Total sum of squares ESS:Error(residual)sum of squares RSS:Regression(explained)sum of squares,1.Goodness-of-fit t
5、esting(R2检验):Coefficient of determination(判定系数):In general,the larger R2,the better.2.Sample coefficient of correlation:,3.Hypothesis testing We have known Let(standard error),ThenAnd we can test the following hypothesis:Moreover,interval estimator for is,Forecasting(预测)1.Point forecastingSince we k
6、now and the sample regression equationthen given,what about and?As(an unbiased estimator for),and(误差均匀)Naturally,we use as a point predictor for both and.2.Interval forecasting(1)Forecast interval for Forecast error:,The variance of the forecast error:Therefore,It is a pity that is unknown.Fortunately,we have Thus,Hence,a Forecast interval for is,(2)Forecast interval for Similarly,we can obtain a forecast interval for:,
