文档介绍：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:
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.
(P39)(how to use Eviews)