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薛真 · 2020年03月07日

问一道题:NO.PZ2020010801000009

问题如下:

Find the OLS estimators for the following data:

选项:

解释:

Doing the basic needed calculations:

β^=(XiX)(YiY)(XiX)2=20.83/8.25=2.52\widehat\beta = \frac{\sum (X_i-\overline X)(Y_i-\overline Y)}{\sum (X_i-\overline X)^2}=20.83/8.25=2.52

α^=Yβ^X=9.42.524.5=1.96\widehat\alpha = \overline Y-\widehat\beta \overline X=9.4-2.52*4.5=-1.96

Continuing to estimate the variance:

s2=1n2iϵ^i2=110219.87=5.55s^2=\frac{1}{n-2}\sum_{i} \widehat\epsilon_i ^2=\frac{1}{10-2}19.87=5.55

答案中计算的是谁的方差?方差的计算公式是什么?这个咋看着像均方差的公式

1 个答案

袁园_品职助教 · 2020年03月08日

同学你好!

题目中计算的残差项的方差,应该是44.41/(10-2),算出来的数字没错,但是19.87那里应该不太对。

不过这道题目里其实只需要算出 α 和 β 就行啦~

 

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