R语言ggplot绘制时间序列回归直线方程异常问题排查

问题背景 #

在R语言中使用ggplot2为时间序列数据绘制带回归方程的回归直线时，发现回归直线相关显示存在异常，相关代码、模型摘要及示例数据如下：

相关代码 #

p1<-ggplot(df2,aes(x=date_his,y=his))+geom_line(lwd=0.8)+
  scale_x_date(date_labels = "%Y",expand = c(0, 0))+
  theme(plot.title = element_text(size = 14, hjust = 0.5))+
  geom_smooth(method = "lm", se = FALSE, linetype = "dashed", color = "blue", size = 1.2)+
  ggpubr::stat_regline_equation(label.x = -Inf, label.y = Inf, vjust = 1.5, hjust = -0.1, size = 5,color = "blue",
                                formula = y ~ poly(x, 1),
                                show.legend = FALSE
  )

回归模型摘要 #

summary(lm(his ~ date_his, data = df2))
    
Call:
lm(formula = his ~ date_his, data = df2)

Residuals:
    Min      1Q  Median      3Q     Max 
-9.5030 -3.7714  0.0661  4.0350  8.2860 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  1.682e+02  2.246e+00  74.889  < 2e-16 ***
date_his    -6.247e-04  2.138e-04  -2.922  0.00614 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 4.867 on 34 degrees of freedom
Multiple R-squared:  0.2007,    Adjusted R-squared:  0.1772 
F-statistic: 8.538 on 1 and 34 DF,  p-value: 0.00614

示例数据 #

df2 <- data.frame(
  date_his = as.Date(c(
    "1979-04-28", "1980-04-28", "1981-04-28", "1982-04-28", "1983-04-28",
    "1984-04-28", "1985-04-28", "1986-04-28", "1987-04-28", "1988-04-28",
    "1989-04-28", "1990-04-28", "1991-04-28", "1992-04-28", "1993-04-28",
    "1994-04-28", "1995-04-28", "1996-04-28", "1997-04-28", "1998-04-28",
    "1999-04-28", "2000-04-28", "2001-04-28", "2002-04-28", "2003-04-28",
    "2004-04-28", "2005-04-28", "2006-04-28", "2007-04-28", "2008-04-28",
    "2009-04-28", "2010-04-28", "2011-04-28", "2012-04-28", "2013-04-28",
    "2014-04-28"
  )),
  his = c(
    166.008140637138, 169.867917428802, 157.525649715296, 172.567833065154,
    170.267019131607, 168.725866057929, 166.718135941998, 158.34217326036,
    157.493444169524, 164.212162698115, 161.140482761292, 161.851683272819,
    158.688162091076, 159.249075294438, 153.373329948267, 170.934314928049,
    164.557361076648, 169.910429608586, 163.399094199897, 161.238272986288,
    166.19105244493, 162.451935740926, 157.307524920014, 164.886371717477,
    153.843986514936, 157.656023562196, 164.433730558708, 165.485611515611,
    157.622007235028, 165.006218026182, 161.901572985301, 152.963472898683,
    154.013037508575, 156.507409368617, 157.244735400283, 161.214916194711
  )
)

异常原因分析 #

1. 模型公式不匹配
   geom_smooth(method="lm")默认使用y ~ x拟合线性模型，和手动运行的lm(his ~ date_his)完全一致；但stat_regline_equation中指定了formula = y ~ poly(x, 1)，poly(x,1)会对日期变量做正交中心化变换，拟合出的回归系数和原始模型差异极大，导致图表显示的回归方程与实际绘制的回归直线不对应，造成“异常”观感。

2. 日期变量的数值特性
   R中日期类型会被转换为大整数（如1979-04-28对应数值7083），直接作为自变量拟合时，斜率极小（模型中为-6.247e-04）、截距极大（1.682e+02），回归方程会以科学计数法显示，和直观认知不符，也会让你觉得显示异常。

3. 标签位置设置不当
   label.x = -Inf, label.y = Inf的设置会将回归方程标签放到绘图区域之外，可能导致看不到方程或位置奇怪，进而误以为是回归直线的问题。

解决办法 #

• 统一模型公式：将stat_regline_equation的formula改为y ~ x，与geom_smooth保持一致，这样显示的方程就和手动运行的lm模型结果匹配：

  ggpubr::stat_regline_equation(label.x = as.Date("1980-01-01"), label.y = 170, vjust = 1, hjust = 0, size = 5,color = "blue",
                                formula = y ~ x,
                                show.legend = FALSE
  )
  

• 调整标签位置：将label.x和label.y设置为绘图范围内的具体日期或数值（如label.x = as.Date("1980-01-01")、label.y = 170），确保方程在可见区域内。
• 优化自变量形式：将日期转换为年份数值，用年份作为自变量拟合，系数会更直观（代表每年的变化量），方程显示也更易读：

  df2$year <- lubridate::year(df2$date_his)
  p1<-ggplot(df2,aes(x=year,y=his))+geom_line(lwd=0.8)+
    scale_x_continuous(expand = c(0, 0))+
    theme(plot.title = element_text(size = 14, hjust = 0.5))+
    geom_smooth(method = "lm", se = FALSE, linetype = "dashed", color = "blue", size = 1.2)+
    ggpubr::stat_regline_equation(label.x = 1980, label.y = 170, size = 5,color = "blue",
                                  formula = y ~ x,
                                  show.legend = FALSE
    )
  

内容的提问来源于stack exchange，提问作者CovetTachi