在R语言中比较对数回归模型的两个斜率

一、回归图绘制代码 #

我使用以下R代码绘制了带有对数拟合公式的回归散点图：

df %>%
  mutate(absVO2 = absVO2*1000) %>%
  ggplot(aes(x = VE, y = absVO2, color = group)) +
  geom_point(size = 0.5) +
  geom_smooth(aes(colour=group), method = "lm", formula = y ~ log(x)) +
  stat_regline_equation(label.x = 25, label.y = c(2400,2800), 
                        formula = y ~ log(x),
                        aes(color = group, label =  paste(..eq.label.., ..adj.rr.label.., sep = "~~~~")),) +
  xlab("VE (L/min)") + 
  ylab(expression(paste("V", O[2]," (mL/min)"))) +
  scale_x_continuous(limits = c(0, 100), breaks = seq(0, 100, by = 25)) +
  theme_classic() +
  theme(
    panel.background = element_rect(fill="white", colour = "white"),
    axis.line = element_line(colour = "black"),
    legend.title = element_text(face = "bold"),
    legend.position = "none",
    strip.text = element_blank()
  )

二、回归图可视化结果 #

上述代码生成的可视化结果如下：

三、分析需求 #

现需要对对数回归模型VO2 = a * log(VE) + b中两组（CAD组和Healthy组）的斜率（分别为910和970）进行统计比较，判断两者是否存在显著差异。

四、数据集 #

用于分析的数据集如下（R数据结构）：

structure(list(VE = c(22.75, 23.75, 26.75, 32.5, 39.5, 48.25, 
55.75, 24, 26.5, 29, 36.5, 44.75, 55.25, 63.75, 78, 19, 20.75, 
25, 29, 39.25, 51, 25, 25.5, 28.5, 34.25, 35.5, 40.25, 47, 52.5, 
59.5, 64.5, 83, 92.25, 18.25, 19.75, 20.75, 23.5, 26.25, 28, 
32.75, 37.25, 24.25, 26.75, 29.5, 31, 32, 39, 43.25, 46.25, 51.75, 
52.75, 64.5, 72.75, 15.75, 16.25, 20.25, 28, 34.75, 45.75, 64.75, 
18.25, 21.25, 22.25, 24.75, 29.5, 21.25, 20.75, 26, 30.75, 34, 
38.5, 46.75, 53.75, 70.5, 82.75, 98.25, 17.25, 22, 25.75, 29.75, 
33.75, 38.75, 44.5, 50.75, 56.25, 65, 71.75, 81, 99, 30, 29, 
29.75, 38.25, 40.75, 47.25, 52.75, 65.5, 22.75, 24.75, 28.75, 
34, 48, 53.75, 61.5, 73.75, 22, 21.75, 24.25, 28, 34.5, 40, 48.5
), absVO2 = c(0.739, 0.81975, 0.95125, 1.07525, 1.199, 1.34575, 
1.49775, 0.66125, 0.7485, 0.855, 0.9845, 1.1495, 1.3465, 1.451, 
1.5985, 0.61675, 0.717, 0.86275, 0.98575, 1.13, 1.262, 0.8835, 
0.94575, 1.08125, 1.244, 1.30475, 1.4735, 1.679, 1.79075, 1.96, 
2.0405, 2.34425, 2.4435, 0.5925, 0.661, 0.7435, 0.87875, 0.9435, 
0.99675, 1.11425, 1.20275, 0.9255, 1.02925, 1.11675, 1.19725, 
1.24775, 1.42625, 1.54225, 1.59425, 1.69675, 1.776, 1.94525, 
2.0395, 0.535, 0.5845, 0.76875, 0.982, 1.09975, 1.259, 1.3265, 
0.7205, 0.86825, 0.9235, 1.01075, 1.17275, 0.7435, 0.76575, 0.96075, 
1.0975, 1.21975, 1.34525, 1.50625, 1.6755, 1.86325, 2.0465, 2.1395, 
0.613, 0.85525, 0.98, 1.076, 1.287, 1.4615, 1.59325, 1.6965, 
1.884, 1.998, 2.1425, 2.31275, 2.474, 0.81075, 0.8035, 0.8645, 
1.076, 1.119, 1.255, 1.33825, 1.499, 0.8105, 0.8865, 1.03725, 
1.134, 1.26675, 1.36275, 1.4455, 1.52875, 0.64675, 0.6645, 0.742, 
0.81675, 0.983, 1.06875, 1.155), group = c("CAD", "CAD", "CAD", 
"CAD", "CAD", "CAD", "CAD", "CAD", "CAD", "CAD", "CAD", "CAD", 
"CAD", "CAD", "CAD", "Healthy", "Healthy", "Healthy", "Healthy", 
"Healthy", "Healthy", "Healthy", "Healthy", "Healthy", "Healthy", 
"Healthy", "Healthy", "Healthy", "Healthy", "Healthy", "Healthy", 
"Healthy", "Healthy", "Healthy", "Healthy", "Healthy", "Healthy", 
"Healthy", "Healthy", "Healthy", "Healthy", "CAD", "CAD", "CAD", 
"CAD", "CAD", "CAD", "CAD", "CAD", "CAD", "CAD", "CAD", "CAD", 
"Healthy", "Healthy", "Healthy", "Healthy", "Healthy", "Healthy", 
"Healthy", "Healthy", "Healthy", "Healthy", "Healthy", "Healthy", 
"CAD", "CAD", "CAD", "CAD", "CAD", "CAD", "CAD", "CAD", "CAD", 
"CAD", "CAD", "Healthy", "Healthy", "Healthy", "Healthy", "Healthy", 
"Healthy", "Healthy", "Healthy", "Healthy", "Healthy", "Healthy", 
"Healthy", "Healthy", "CAD", "CAD", "CAD", "CAD", "CAD", "CAD", 
"CAD", "CAD", "Healthy", "Healthy", "Healthy", "Healthy", "Healthy", 
"Healthy", "Healthy", "Healthy", "CAD", "CAD", "CAD", "CAD", 
"CAD", "CAD", "CAD")), class = c("tbl_df", "tbl", "data.frame"
), row.names = c(NA, -112L))

内容的提问来源于stack exchange，提问作者MaxB