向均值回归

R 中的回归入门

Richie Cotton

Data Evangelist

核心概念

响应值 = 拟合值 + 残差
"已解释的部分" + "未能解释的部分"
残差源于模型问题和固有随机性
极端情况多由随机性导致
向均值回归意味着极端不会长期持续

皮尔逊父子数据集

1078 对父子
高个父亲是否有高个儿子？

father_height_cm	son_height_cm
165.2	151.8
160.7	160.6
165.0	160.9
167.0	159.5
155.3	163.3
...	...

¹ 改编自 https://www.rdocumentation.org/packages/UsingR/topics/father.son

散点图

plt_son_vs_father <- ggplot(
  father_son, 
  aes(father_height_cm, son_height_cm)
) +
  geom_point() +
  geom_abline(color = "green", size = 1) +
  coord_fixed()

儿子身高与父亲身高的散点图，并有父子同高的对角线。父亲越高，儿子通常越高。

添加回归线

plt_son_vs_father +
  geom_smooth(method = "lm", se = FALSE)

带线性趋势线的儿子身高与父亲身高散点图。趋势线比父子同高的对角线更平缓。

运行回归

mdl_son_vs_father <- lm(
  son_height_cm ~ father_height_cm, 
  data = father_son
)

Call:
lm(formula = son_height_cm ~ father_height_cm, data = father_son)

Coefficients:
     (Intercept)  father_height_cm  
          86.072             0.514

做出预测

really_tall_father <- tibble(
  father_height_cm = 190
)
predict(mdl_son_vs_father, really_tall_father)

183.7

really_short_father <- tibble(
  father_height_cm = 150
)
predict(mdl_son_vs_father, really_short_father)

163.2

让我们练习吧！

R 中的回归入门