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
｜
155
4.7.2
样条回归
多项式回归只能捕获非线性关系中一定数量的曲线性质。如果添加更高阶的项，比如三次
多项式，会在回归方程中带来我们不想要的“波动性”。另一种（通常也是更好的）对非
线性关系建模的方法是
样条回归
，它提供了一种在固定点之间平滑地插值的方法。样条最
初是制图员用来绘制平滑曲线的工具，在船舶和飞行器制造中使用得尤其普遍。
样条是通过压铁（俗称“鸭子”）将一支细长的木条弯成曲线形状而制成的（见图
4-1
1
）。
图 4-11：样条最初是使用可弯曲的木条和俗称“鸭子”的压铁而制成的，它是制图员用来拟合曲线
的工具（照片经 Bob Perry 允许，免费使用）
样条的技术定义是一系列连续的分段多项式，它是在第二次世界大战期间由美国阿伯丁武
器试验场的罗马尼亚数学家
I.
J. Schoenberg
首次提出的。分段多项式通过预测变量中的一
系列固定点（称为
节点
）平滑地连接起来。样条回归要比多项式回归复杂得多，通常需要
统计软件来处理样条回归拟合时的细节。
R
包
splines
中有一个
bs
函数，可以在回归模型
中创建一个
b-spline
（基本样条）项
。例如，下面的代码可以向房屋回归模型中添加一个
b-spline
项：
library(splines)
knots <- quantile(house_98105$SqFtTotLiving, p=c(.25, .5, .75))
lm_spline <- lm(AdjSalePrice ~ bs(SqFtTotLiving, knots=knots, ...
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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.