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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122
｜
第
4
章
4.2
多元线性回归
如果有多个预测变量，就可以简单地扩展一下回归方程，使其包含以下变量。
Y
=
b
0
+
b
1
X
1
+
b
2
X
2
+
…
+
b
p
X
p
+
e
这时得到的就不再是一条直线了，而是一个线性模型——每个系数与它的变量（特征）之
间的关系是线性的。
本节关键术语
均方根误差
对回归误差进行平方，并计算平均数，再算出平方根。均方根误差是比较回归模型
时最常用的方式。
同义词
RMSE
残差标准差
与均方根误差一样，只是根据自由度做了调整。
同义词
RSE
R
方
模型解释的方差的比例，值从
0
到
1
。
同义词
判定系数、
R
2
t
统计量
预测变量的系数除以系数的标准误差。它提供了一种比较变量在模型中的重要性的
方式，参见
3.5
节。
加权回归
记录具有不同权重的回归。
简单线性回归中的其他概念，比如使用最小二乘法进行拟合，以及拟合值与残差的定义，
都可以扩展到多元线性回归中。例如，拟合值可以这样计算：
011, 22
,,
ˆˆ ˆˆ
ˆ
ii
ippi
YbbX bX bX=+ +++
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