# 误差

## 简介

• 样本中每个人的身高与无法观测的总体均值之间的差值是统计误差，
• 样本中每个人的身高与可观测的样本均值之间的差值是残差。

## 单变量分布

${\displaystyle X_{1},\dots ,X_{n}\sim N\left(\mu ,\sigma ^{2}\right)\,}$

${\displaystyle {\overline {X}}={X_{1}+\cdots +X_{n} \over n}}$

${\displaystyle {\overline {X}}\sim N\left(\mu ,{\frac {\sigma ^{2}}{n}}\right).}$

${\displaystyle e_{i}=X_{i}-\mu ,\,}$

${\displaystyle r_{i}=X_{i}-{\overline {X}}.}$

${\displaystyle {\frac {1}{\sigma ^{2}}}\sum _{i=1}^{n}e_{i}^{2}\sim \chi _{n}^{2}.}$

${\displaystyle {\frac {1}{\sigma ^{2}}}\sum _{i=1}^{n}r_{i}^{2}\sim \chi _{n-1}^{2}.}$

## 参考文献

1. ^ Kennedy, P. A Guide to Econometrics. Wiley. 2008: 576 [2022-05-13]. ISBN 978-1-4051-8257-7. （原始内容存档于2022-07-12）.
2. ^ Wooldridge, J.M. Introductory Econometrics: A Modern Approach. Cengage Learning. 2019: 57 [2022-05-13]. ISBN 978-1-337-67133-0. （原始内容存档于2022-07-12）.
3. ^ Das, P. Econometrics in Theory and Practice: Analysis of Cross Section, Time Series and Panel Data with Stata 15.1. Springer Singapore. 2019: 7 [2022-05-13]. ISBN 978-981-329-019-8. （原始内容存档于2022-07-12）.
4. ^ Wetherill, G. Barrie. Intermediate statistical methods. London: Chapman and Hall. 1981. ISBN 0-412-16440-X. OCLC 7779780.