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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回归与预测
｜
153
本节关键术语
多项式回归
向回归中添加多项式项（二次项、三次项，等等）。
样条回归
使用多个多项式片段拟合出一条平滑曲线。
节点
分隔样条片段的值。
广义可加模型
能自动选择节点的样条模型。
同义词
GAM
非线性回归
统计学家所说的
非线性回归
是指那些不能使用最小二乘法进行拟合的模型。
什么样的模型是非线性的呢？基本上就是所有响应变量不能表示成预测变量
（或预测变量的某种转换形式）的线性组合的模型。非线性回归模型的拟合
更加困难，也需要更为密集的计算成本，因为它们需要在数值上进行优化。
因此，如果可能，通常还是要选择使用线性模型。
4.7.1
多项式回归
多项式回归
在回归方程中加入多项式项。多项式回归的使用几乎可以回溯到
1815
年
Gergonne
在
一篇论文中提出了回归方法。举例来说，预测变量
X
和响应变量
Y
之间的二次
回归可以表示如下：
Y
=
b
0
+
b
1
X
+
b
2
X
2
+
e
在
R
中
，可以使用
poly
函数拟合多项式回归。例如，以下代码可以为金县房屋数据拟合
一个带有
SqFtTotLiving
二次项的多项式回归：
lm(AdjSalePrice ~ poly(SqFtTotLiving, 2) + SqFtLot +
BldgGrade + Bathrooms + Bedrooms,
data=house_98105)
Call:
lm(formula = AdjSalePrice ~ poly(SqFtTotLiving, 2) + SqFtLot +
BldgGrade + Bathrooms ...
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I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.