R语言线性回归RMSE代码 r语言线性回归画图

展示各类回归模型的回归线绘制方法，包括通用绘制方法以及ggplot2提供的一些回归线简单绘制方法：

• 线性回归
• 多项式回归
• loess（局部加权）回归
• 分段线性回归
• 样条回归
• 稳健回归
• 分位数回归

library(ggplot2)
library(MASS)
library(splines)

示例数据

使用R自带的mtcars汽车数据集，研究mpg与wt这两个连续变量的关系

print(head(mtcars))
#                    mpg cyl disp  hp drat    wt  qsec vs am gear carb
# Mazda RX4         21.0   6  160 110 3.90 2.620 16.46  0  1    4    4
# Mazda RX4 Wag     21.0   6  160 110 3.90 2.875 17.02  0  1    4    4
# Datsun 710        22.8   4  108  93 3.85 2.320 18.61  1  1    4    1
# Hornet 4 Drive    21.4   6  258 110 3.08 3.215 19.44  1  0    3    1
# Hornet Sportabout 18.7   8  360 175 3.15 3.440 17.02  0  0    3    2
# Valiant           18.1   6  225 105 2.76 3.460 20.22  1  0    3    1

str(mtcars)
# 'data.frame':	32 obs. of  11 variables:
#  $ mpg : num  21 21 22.8 21.4 18.7 18.1 14.3 24.4 22.8 19.2 ...
#  $ cyl : num  6 6 4 6 8 6 8 4 4 6 ...
#  $ disp: num  160 160 108 258 360 ...
#  $ hp  : num  110 110 93 110 175 105 245 62 95 123 ...
#  $ drat: num  3.9 3.9 3.85 3.08 3.15 2.76 3.21 3.69 3.92 3.92 ...
#  $ wt  : num  2.62 2.88 2.32 3.21 3.44 ...
#  $ qsec: num  16.5 17 18.6 19.4 17 ...
#  $ vs  : num  0 0 1 1 0 1 0 1 1 1 ...
#  $ am  : num  1 1 1 0 0 0 0 0 0 0 ...
#  $ gear: num  4 4 4 3 3 3 3 4 4 4 ...
#  $ carb: num  4 4 1 1 2 1 4 2 2 4 ...

绘制mpg与wt的散点图

p <- ggplot() +
  geom_point(data = mtcars, mapping = aes(x = mpg, y = wt)) +
  theme_bw()
p

绘制各类回归模型的回归线的通用方式

• 拟合回归模型
• 利用模型求出给定x，y的拟合值，以及拟合值的置信区间
• 利用geom_line绘制回归线，利用geom_ribbon绘制置信区间阴影

线性回归

# 拟合简单线性回归模型
lm <- lm(wt ~ mpg, data = mtcars)

# 利用模型求出给定x，y的拟合值，以及拟合值的置信区间
new_mpg <- seq(min(mtcars$mpg), max(mtcars$mpg), 0.01)
pred_wt <- data.frame(predict(lm, newdata = data.frame(mpg = new_mpg),
                                 interval = "confidence"), 
                      new_mpg = new_mpg)
print(head(pred_wt))
#        fit      lwr      upr new_mpg
# 1 4.582291 4.240349 4.924232   10.40
# 2 4.580882 4.239197 4.922566   10.41
# 3 4.579473 4.238045 4.920901   10.42
# 4 4.578065 4.236893 4.919236   10.43
# 5 4.576656 4.235741 4.917571   10.44
# 6 4.575247 4.234589 4.915906   10.45

# 利用geom_line绘制回归线，利用geom_ribbon绘制置信区间阴影
p + 
  geom_line(data = pred_wt, mapping = aes(x = new_mpg, y = fit), 
            color = "red", size = 1, alpha = 0.5) +
  geom_ribbon(data = pred_wt, mapping = aes(x = new_mpg, 
                                            ymin = lwr, ymax = upr), 
              fill = "grey", alpha = 0.5)

绘制线性回归线的另一种方式，根据斜率和截距使用geom_abline绘图

p + 
  geom_abline(slope = lm$coefficients[2], intercept = lm$coefficients[1], 
              color = "red", size = 1, alpha = 0.5) +
  geom_ribbon(data = pred_wt, mapping = aes(x = new_mpg, 
                                            ymin = lwr, ymax = upr), 
              fill = "grey", alpha = 0.5)

多项式回归

# 拟合二次多项式回归模型
poly <- lm(wt ~ mpg + I(mpg ^ 2), data = mtcars)

new_mpg <- seq(min(mtcars$mpg), max(mtcars$mpg), 0.01)
pred_wt <- data.frame(predict(poly, newdata = data.frame(mpg = new_mpg),
                                 interval = "confidence"), 
                      new_mpg = new_mpg)
print(head(pred_wt))
#        fit      lwr      upr new_mpg
# 1 5.052883 4.560239 5.545526   10.40
# 2 5.050333 4.558547 5.542119   10.41
# 3 5.047784 4.556854 5.538714   10.42
# 4 5.045236 4.555162 5.535310   10.43
# 5 5.042689 4.553469 5.531909   10.44
# 6 5.040143 4.551776 5.528509   10.45

p + 
  geom_line(data = pred_wt, mapping = aes(x = new_mpg, y = fit), 
            color = "red", size = 1, alpha = 0.5) +
  geom_ribbon(data = pred_wt, mapping = aes(x = new_mpg, 
                                            ymin = lwr, ymax = upr), 
              fill = "grey", alpha = 0.5)

ggplot2提供了一些回归线的简单绘制方式

线性回归，geom_smooth指定method = “lm”

p + 
  geom_smooth(data = mtcars, mapping = aes(x = mpg, y = wt), 
              method = "lm")

loess（局部加权）回归，geom_smooth指定method = “loess”

p + 
  geom_smooth(data = mtcars, mapping = aes(x = mpg, y = wt), 
              method = "loess")

gam（广义可加模型），geom_smooth指定method = “gam”，同时指定formula的具体形式

广义可加模型拓展了广义线性模型，允许自变量采取各类形式的变换，以2个自变量为例：

• 广义线性模型可表示为：$g(E(x)) = \beta_0 + \beta_1 \times x_1 + \beta_2 \times x_2$
• 广义可加模型可表示为：$g(E(x)) = \beta_0 + f_1(x_1) + f_2(x_2)$

$f(x)$可以是各类变换，如多项式变换$f(x) = x + x^2$；甚至是非参数变换，如$f(x) = loess(x)$（loess为局部加权多项式）

使用gam绘制线性回归

p + 
  geom_smooth(data = mtcars, mapping = aes(x = mpg, y = wt), 
              method = "gam", formula = y ~ x)

使用gam绘制多项式回归

# 二次多项式回归
p + 
  geom_smooth(data = mtcars, mapping = aes(x = mpg, y = wt), 
              method = "gam", formula = y ~ x + I(x ^ 2))

使用gam绘制分段线性回归

p + 
  geom_smooth(data = mtcars, mapping = aes(x = mpg, y = wt), 
              method = "gam", formula = y ~ x + I((x - 20) * (x > 20))) +
  geom_vline(xintercept = 20, linetype = 2, color = "red")

使用gam绘制样条回归

# 样条设置1个节点，立方样条
p + 
  geom_smooth(data = mtcars, mapping = aes(x = mpg, y = wt), 
              method = "gam", formula = y ~ bs(x, knots = 1, degree = 3))

其他的一些回归线绘制

稳健回归

• 可用于解决回归中的离群值问题
• 绘图时，内部调用MASS::rlm()拟合稳健回归

p + 
  geom_smooth(data = mtcars, mapping = aes(x = mpg, y = wt), 
              method = "rlm")

分位数回归

• 可用于解决误差项非正态问题
• 分别绘制0.1、0.5、0.9的$y=\beta_0 + \beta_1 \times x_1$的回归线
• 绘图时，内部调用quantreg::rq()拟合分位数回归

p + 
  geom_quantile(data = mtcars, mapping = aes(x = mpg, y = wt, 
                                             color = "0.1 quantile"),
                quantiles = 0.1) + 
  geom_quantile(data = mtcars, mapping = aes(x = mpg, y = wt, 
                                             color = "0.5 quantile"),
                quantiles = 0.5) + 
  geom_quantile(data = mtcars, mapping = aes(x = mpg, y = wt, 
                                             color = "0.9 quantile"),
                quantiles = 0.9) +
  labs(color = "Quantile")