在R中绘制斜率固定为1的最佳拟合线性回归图

问题背景 #

当前使用Windows 11 + R 4.4.3，基于ggplot2绘制工具A与工具B测量值的回归图，核心需求如下：

• 强制回归斜率为1，仅求解截距b（方程形式：y = b + 1*x）
• 支持facet_wrap/facet_grid实现多面板批量绘制
• 保留散点展示、y=x参考线、回归方程标注等核心元素

数据集代码：

df <- data.frame(
  A= c(1.313, 1.3118, 1.3132, 1.3122, 1.3128, 1.3061, 1.3051, 1.3052, 1.3069, 1.3053, 1.3072, 1.3006, 1.3246, 
       1.3229, 1.3254, 1.3239, 1.3222, 1.3155, 1.313, 1.3147, 1.3174, 1.3174, 1.3188, 1.3134),
  B=c(1.3165, 1.316, 1.3176, 1.316, 1.3169, 1.3104, 1.3094, 1.3095, 1.3107, 1.3101, 1.3112, 1.3047, 
      1.3285, 1.3271, 1.3297, 1.3274, 1.3261, 1.3192, 1.318, 1.319, 1.322, 1.3215, 1.3232, 1.3172)
)

核心解决方案 #

方案一：原生ggplot2+ggpubr适配（简洁版） #

利用lm中的offset()函数强制x的系数为1，直接在geom_smooth和stat_regline_equation中指定约束模型，原生支持分面逻辑。

代码示例：

library(ggplot2)
library(ggpubr)

# 单面板绘图
ggplot(df, aes(x = A, y = B)) +
  geom_point(size = 2) +
  geom_abline(slope = 1, intercept = 0, linetype = "dashed", color = "gray50") +
  # 固定斜率为1的回归：offset(x)强制x系数为1，仅拟合截距b
  geom_smooth(
    color = "red", method = "lm", se = FALSE,
    formula = y ~ 1 + offset(x)
  ) +
  # 匹配约束模型公式，让stat_regline_equation正确计算并标注
  stat_regline_equation(
    label.x = 1.31, label.y = 1.325,
    formula = y ~ 1 + offset(x),
    aes(label = paste(..eq.label.., ..rr.label.., sep = "~~~"))
  ) +
  coord_equal()

# 多面板示例（先给数据集添加分组列）
df_grouped <- df %>% 
  mutate(group = rep(c("Group1", "Group2"), each = 12))

ggplot(df_grouped, aes(x = A, y = B)) +
  geom_point(size = 2) +
  geom_abline(slope = 1, intercept = 0, linetype = "dashed", color = "gray50") +
  geom_smooth(
    color = "red", method = "lm", se = FALSE,
    formula = y ~ 1 + offset(x)
  ) +
  stat_regline_equation(
    label.x = 1.31, label.y = 1.325,
    formula = y ~ 1 + offset(x),
    aes(label = paste(..eq.label.., ..rr.label.., sep = "~~~"))
  ) +
  facet_wrap(~group) +
  coord_equal()

方案二：预计算参数+自定义标注（灵活版） #

先按分组批量计算截距b和R²，再用geom_abline绘制回归线、geom_text标注方程，适合需要对回归结果做额外处理的场景。

代码示例：

library(dplyr)
library(ggplot2)

# 按分组计算回归参数
fit_results <- df_grouped %>%
  group_by(group) %>%
  summarise(
    b = coef(lm(B ~ 1 + offset(A)))[[1]],
    r_squared = summary(lm(B ~ 1 + offset(A)))$r.squared,
    .groups = "drop"
  ) %>%
  mutate(
    eq_label = paste0("y = ", round(b, 4), " + 1*x"),
    r_label = paste0("R² = ", round(r_squared, 4)),
    full_label = paste(eq_label, r_label, sep = "\n")
  )

# 多面板绘图
ggplot(df_grouped, aes(x = A, y = B)) +
  geom_point(size = 2) +
  geom_abline(slope = 1, intercept = 0, linetype = "dashed", color = "gray50") +
  # 绘制固定斜率的回归线
  geom_abline(
    data = fit_results,
    aes(intercept = b, slope = 1),
    color = "red", linewidth = 1
  ) +
  # 标注回归方程与R²
  geom_text(
    data = fit_results,
    aes(x = 1.31, y = 1.325, label = full_label),
    hjust = 0, vjust = 1, size = 4
  ) +
  facet_wrap(~group) +
  coord_equal()

关键说明 #

• offset(x)是R中强制变量系数为1的标准写法，y ~ 1 + offset(x)完全等价于需求中的y = b + 1*x
• 两种方案都原生支持facet_wrap/facet_grid，分面时会自动按面板独立计算回归参数
• 方案一更简洁，直接复用ggplot2生态工具；方案二更灵活，便于对回归结果做二次分析或定制化展示

内容的提问来源于stack exchange，提问作者jeffgoblue