How to add trend line in a log-log plot (ggplot2)?

Question

I need plot a data vector, which follow power law distribution. so if I plot them on log-log axis, and they will be a straight line. However, if I do not explicitly provide "y" parameter, I do not know how to plot. this is code

library("poweRlaw")
library("ggplot2")

xmin = 1; alpha = 1.5
con_rns = rplcon(1000, xmin, alpha)
#convert to data.frame format for ggplot2
df <- data.frame(con_rns =con_rns[con_rns<1000])

#make plot with both axes log scale
ggplot(data = df, aes(x = con_rns))+
  geom_point(stat = 'bin', binwidth = 0.1)+
  geom_smooth(stat = 'bin',mapping = aes(x=con_rns),method = "lm",se=FALSE)+
  scale_x_log10() + 
  scale_y_log10()

The result is this:

But I want this

I know, I can manually bin data, provide "y" explicitly and then plot the line, like this

ggplot(data = data.frame(a = rnorm(50,0,1),b=5+rnorm(50,2,1)),mapping = aes(x = a,y=b))+
  geom_point()+
  geom_smooth(method = "lm",se=FALSE)

result:

But I want to know, how can I plot trend line with this code ( geom_point(stat = 'bin', binwidth = 0.1) ). It implicitly calculates data bin.

PS: Well, thanks for Chris's answer. I still have a problem. If I want to plot different group, how can I draw it? The data are df <- data.frame(con_rns =con_rns[con_rns<1000],col=sample(1:3,size = length(con_rns[con_rns<1000]),replace = T)) . How can I plot different color point group and color line group in log-log axis? like this:

Answer 1

One way would be to recover the binned data from the plot using ggplot_build()

first I made the plot without the line of best fit:

p <- ggplot(data = df, aes(x = con_rns))+
  geom_point(stat = 'bin', binwidth = 0.1)+
  scale_x_log10() + 
  scale_y_log10() 

Then I added the binned data from the plot which can be found with ggplot_build(p)$data (and reversed the log10 transformation)

p + geom_smooth(data = ggplot_build(p)$data[[1]], 
              mapping = aes(x=10^x, y= 10^y),method = "lm",se=FALSE)

UPDATE: The additional problem was how to split the plot by different colour groups. I approached this in the same way but it was necessary for me to create a 'group' aesthetic so this data could be kept in the ggplot_build data.

library(poweRlaw)
library(ggplot2)

xmin = 1; alpha = 1.5
con_rns = rplcon(1000, xmin, alpha)
#convert to data.frame format for ggplot2
df <- data.frame(con_rns =con_rns[con_rns<1000],col=sample(1:3,size = length(con_rns[con_rns<1000]),replace = T))

p <- ggplot(data = df, aes(x = con_rns))+
  geom_point(stat = 'bin', binwidth = 0.1, aes(colour=factor(col), group=factor(col)))+
  scale_x_log10() + 
  scale_y_log10() 


p + geom_smooth(data = ggplot_build(p)$data[[1]], 
                mapping = aes(x=10^x, y= 10^y, colour=factor(group)),method = "lm",se=FALSE)

Note that now we have grouped the data, some of the groups have a count of zero in their bin. This returns a warning when the log10 transformation is applied to zero, giving an infinite value. These points are removed from the plot and ignored in the trend lines.