添加回归线方程和 R2 值

Question

我正在尝试在数据集中添加回归线方程和 R 平方值，其中 y 轴值采用对数刻度，就像在这个 excel 示例中一样：

.

数据框包含以下数据，有 3 个变量和 28 个观测值：

          Method        void.ratio    permeability_m.s
1      Constant load      1.360         1.82e-05
2      Constant load      1.360         1.79e-05
3      Constant load      1.190         7.74e-06
4      Constant load      1.190         5.15e-06
5      Variable load      1.040         1.57e-06
6      Variable load      1.040         1.71e-06
7      Variable load      1.040         1.57e-06
8      Variable load      1.040         1.71e-06
9      Triaxial test      0.780         3.00e-07
10     Triaxial test      0.780         2.70e-07
11 Oedometric test 1      0.690         1.33e-07
12 Oedometric test 1      0.685         5.84e-08
13 Oedometric test 2      0.697         3.35e-07
14 Oedometric test 2      0.629         2.85e-07
15 Oedometric test 2      0.554         7.75e-08
16 Oedometric test 2      0.526         3.27e-09
17 Oedometric test 2      0.528         4.71e-09
18 Oedometric test 2      0.530         4.72e-09
19 Oedometric test 2      0.534         6.70e-09
20 Oedometric test 3      0.705         1.34e-07
21 Oedometric test 3      0.648         1.23e-07
22 Oedometric test 3      0.574         8.29e-08
23 Oedometric test 3      0.530         8.77e-08

运行以下代码后，我只能得到回归线，但无法得到回归方程和 R 平方值。

R 代码：

plot_lab_permeability2<- ggplot(Lab_permeability2,aes(void.ratio, permeability_m.s))+
geom_point(size=3,aes(shape = Method, colour = Method))+
geom_smooth(method="lm",formula= (y ~ x), se=FALSE, linetype = 8,color="grey") +
scale_shape_manual("",breaks = c("Constant load","Variable load","Triaxial test","Oedometric test 1","Oedometric test 2","Oedometric test 3"),
                    values=c("Constant load"=15,"Variable load"=17,"Triaxial test"=18,"Oedometric test 1"=16,"Oedometric test 2"=16,"Oedometric test 3"=16))+
scale_colour_manual("",breaks = c("Constant load","Variable load","Triaxial test","Oedometric test 1","Oedometric test 2","Oedometric test 3"),
                    values = c("Constant load"="darkblue","Variable load"="blue","Triaxial test"="darkgreen","Oedometric test 1"="darkred","Oedometric test 2"="red","Oedometric test 3"="orange"))+
scale_y_continuous(limits = c((1e-9),(1e-4)), trans="log10") +
labs(x=expression ("Void ratio (-)"),y = expression ("Saturated hydraulic conductivity (m/s)"),title="") +
theme_bw()

这是生成的图：

我一直在阅读类似的问题并尝试不同的方法，但经过数小时的尝试，我无法找到解决方案。

我们将不胜感激。

Answer 1

您可以窃取/稍微修改 SO 提问者here 使用的功能：

library(ggplot2)

lm_eqn <- function(df, model_fit){
# From a past Stack Overflow question
    eq <- substitute(italic(y) == a + b %.% italic(x)*","~~italic(r)^2~"="~r2, 
                     list(a = format(coef(model_fit)[1], digits = 2), 
                          b = format(coef(model_fit)[2], digits = 2),
                          r2 = format(summary(model_fit)$r.squared, digits = 3)))
    as.character(as.expression(eq));                 
}

# I think you intend to log transform here?
model_fit <- lm(log10(permeability_m.s) ~ void.ratio, Lab_permeability2)

plot_lab_permeability2 <- ggplot(Lab_permeability2, aes(void.ratio, permeability_m.s)) +
    geom_point(size=3,aes(shape = Method, colour = Method))+
    geom_smooth(method="lm",formula= (y ~ x), se=FALSE, linetype = 8,color="grey") +
    scale_shape_manual("",breaks = c("Constant load","Variable load","Triaxial test","Oedometric test 1","Oedometric test 2","Oedometric test 3"),
                       values=c("Constant load"=15,"Variable load"=17,"Triaxial test"=18,"Oedometric test 1"=16,"Oedometric test 2"=16,"Oedometric test 3"=16))+
    scale_colour_manual("",breaks = c("Constant load","Variable load","Triaxial test","Oedometric test 1","Oedometric test 2","Oedometric test 3"),
                        values = c("Constant load"="darkblue","Variable load"="blue","Triaxial test"="darkgreen","Oedometric test 1"="darkred","Oedometric test 2"="red","Oedometric test 3"="orange"))+
    scale_y_continuous(limits = c((1e-9),(1e-4)), trans="log10") +
    labs(x=expression ("Void ratio (-)"),y = expression ("Saturated hydraulic conductivity (m/s)"),title="") +
    geom_text(aes(x = 0.55, y = 0.5e-4, label = lm_eqn(Lab_permeability2, model_fit)),
              size=5, hjust=0, parse = TRUE, check_overlap = TRUE) +
    theme_bw()

plot_lab_permeability2

结果：

Answer 2

Raul，@duckmayr 为您的原始问题提供了一个很好的解决方案。他共享的代码按照您的要求进行了所有标记。但现在你问了一个不同的问题。您最初要求 y 轴采用“对数刻度”。他为您提供了一个使用 log10 的解决方案，如果您愿意，可以轻松地将答案更改为 ln(y)。例如：

Lab_permeability2$lnperm <- log(Lab_permeability2$permeability_m.s)

那么就可以拟合回归方程了：

model_fit <- lm(lnperm ~ void.ratio, Lab_permeability2)

你的系数当然不会一样...

调用： lm(公式 = lnperm ~ void.ratio, data = Lab_permeability2)

系数： （截取）void.ratio
-21.993 8.406

你应该改变轴以显示 ln

ggplot(Lab_permeability2, aes(void.ratio, lnperm)) +
  geom_point(size=3,aes(shape = Method, colour = Method))+
  geom_smooth(method="lm",formula= (y ~ x), se=FALSE, linetype = 8,color="grey") +
  scale_shape_manual("",breaks = c("Constant load","Variable load","Triaxial test","Oedometric test 1","Oedometric test 2","Oedometric test 3"),
                 values=c("Constant load"=15,"Variable load"=17,"Triaxial test"=18,"Oedometric test 1"=16,"Oedometric test 2"=16,"Oedometric test 3"=16)) +
  scale_colour_manual("",breaks = c("Constant load","Variable load","Triaxial test","Oedometric test 1","Oedometric test 2","Oedometric test 3"),
                values = c("Constant load"="darkblue","Variable load"="blue","Triaxial test"="darkgreen","Oedometric test 1"="darkred","Oedometric test 2"="red","Oedometric test 3"="orange")) +
#  scale_y_continuous(limits = c((1e-9),(1e-4)), trans="log") +
  labs(x=expression ("Void ratio (-)"),y = expression ("Natural Log Saturated hydraulic conductivity (m/s)"),title="") +
  geom_text(aes(x = 0.55, y = -12, label = lm_eqn(Lab_permeability2, model_fit)),
        size=5, hjust=0, parse = TRUE, check_overlap = TRUE) +
  theme_bw()

这会产生

因此，对于 1.0 的 void.ratio 值，我们预计 8.406 - 21.993 = -13.587 这似乎是图表显示的...转换回原始比例

exp(8.406 - 21.993)
[1] 1.256727e-06

我不清楚你为什么认为它应该是 1.34e-6，尽管对于初学者来说，你只给了我们前 23 个观察结果，你所说的是 28