October 2021
Intermediate to advanced
289 pages
8h 31m
Chinese
Content preview from 数据科学中的实用统计学(第2版)
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146
｜
第
4
章
用。离群点也可能是由其他问题造成的，比如由于“胖手指”按错键而造成的输入错误，
或者单位不匹配（例如，销售额单位使用了千美元，而不是美元）。
图 4-4：最大负残差记录的法定担保契约
对于大数据问题，在拟合用于预测新数据的回归模型时，离群点通常不会造成什么影响。
不过，离群点在异常检测中极其重要。异常检测就是要找出离群点，离群点可以对应于一
次欺诈或者一次意外的行为。在任何情况下，检测离群点都是一种重要的业务需求。
4.6.2
强影响值
如果有一个值，缺少了它会显著改变回归方程，那这个值就称为
强影响观测
。在回归中，这
种值不一定有很大的残差。下面看一个例子，如图
4-5
所示
，实线是使用所有数据进行的回
归，而虚线是除去了右上角数据点之后的回归。显然，这个数据点对回归有巨大的影响，但
对于全数据回归来说，它并不是一个明显的离群点。这种数据值就是回归的
高杠杆值
。
图 4-5：回归中强影响数据点的一个例子
除了标准化残差（参见
4.6.1
节），统计学家还提出了几种度量方式来确定单条记录对回归
的影响。杠杆值的一种常用测量方式是
帽子值
（
hat-value
）
。如果帽子值大于
2(
P
+ 1)/
n
，
回归与预测
｜
147
就说明这是一个高杠杆数据值。
6
另外一种度量方式是
库克距离
（
Cook
’
s distance ...
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