June 2020
Beginner to intermediate
522 pages
9h 6m
Chinese
Content preview from R 语言经典实例（原书第 2 版）
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334
｜
第
11
章
11.11.4 另请参阅
有关交互项的更多信息，请参阅 11.7 节。有关回归数据的其他变换，请参见 11.12 节。
11.12 对变换后的数据进行回归
11.12.1 问题
要为
x
和
y
建立一个回归模型，但它们没有线性关系。
11.12.2 解决方案
可以在回归公式中嵌入所需的变换。例如，如果必须将
y
转换为 log(
y
)，则回归公式变为：
lm(log(y) ~ x)
11.12.3 讨论
回归函数 lm 的一个关键假设是变量具有线性关系。在一定程度上，如果这种假设不成
立，由此产生的回归变得毫无意义。
幸运的是，在应用 lm 之前，许多数据集可以转换为线性关系。
图 11-1 显示了一个指数衰减的示例。左侧部分显示原始数据
z
。虚线表示原始数据的线
性回归；显然，这是一个糟糕的拟合。
TransformedObserved
1
0
-
1
-
2
log(
z
)
2.0
1.5
1.0
0.5
0.0
z
Time Time
0.0 0.00.5 0.51.0 1.01.5 1.5
图 11-1：数据变换的示例
如果数据真的是指数关系，那么一个可能的模型是：
线性回归和方差分析
｜
335
z
= exp[
β
0
+
β
1
t
+
ε
]
其中
t
是时间，exp[] 是指数函数（e
x
）。当然，这不是线性的，但我们可以通过取对数来
使它线性化： ...
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