计量经济学讲义(厦门大学黄长全)chap3.pptVIP

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. Testing 4. 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(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): 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 unbiased estimator for , Where are 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 testing(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) Then And we can test the following hypothesis: Moreover,