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I am trying to add the regression line equation and the R square value in a dataset with y axe values in logarithmic scale, like in this excel example:

this is what i want to obtain in R, done with excel.

Data frame contains the following data, with 3 variables and 28 obs.:

 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

After running the following code I only obtain the regression line, but I am not able to obtain the regression equation and the R square value.

R code:

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()

This is the generated plot: plot generated with R

I have been reading similar questions and trying differents approaches, but after hours trying, I am not able to find the solution.

Any help will be highly appreciated.

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2 Answers 2

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You can steal/slightly modify a function used by a SO question asker here:

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

Result:

enter image description here

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Thanks man. The R square value fits well, like in excel, but I was searching for another type of equation.When I use your given equation y=-9.6+3.7x, for example with void ratio 1, I am getting a value of -5.9, instead of 1.34e-6 as it should be. How can I get an equation that fits with the expected result? Thanks in advance
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Raul, @duckmayr has given you a nice solution to your original ask. The code he shared does all the labelling as you requested. But now you're asking a different question. You originally asked for the y axis to be in "logarithmic scale". He gave you a solution that used log10, trivial to change the answer to ln(y) if you prefer. For example:

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

Then you can fit the regression equation:

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

Your coefficients will of course not be the same...

Call: lm(formula = lnperm ~ void.ratio, data = Lab_permeability2)

Coefficients: (Intercept) void.ratio
-21.993 8.406

and you should change the axis to show 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()

This produces

R Plot Sample

So for a void.ratio value of 1.0 we would expect 8.406 - 21.993 = -13.587 which appears to be what the graph shows... to convert back to the original scale

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

I'm not clear on why you think it should be 1.34e-6 although for starters you only gave us the first 23 observations of what you said were 28

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