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I am putting together a regression model with data of carseat sales from the ISLR dataset. It is sales as a function of the independent variables.

One of the variables has a bimodal distribution

histo

I split it up using a modeling technique from the mixtools package. The information on the technique is here.

library('ISLR')
data(Carseats)

library('mixtools')

mixmdl = normalmixEM(x)
plot(mixmdl,which=2)
lines(density(x), lty=2, lwd=2)

That got me this great visualization of the two distributions

distro

How do I find the cutoff point? How do I find the value to use to split education into education-low and education-high?

For kicks, I also used another technique

library('devtools')
devtools::install_github("choisy/cutoff")
library(cutoff)
library('bbmle')

mixmodel <- em(Carseats$Education,"normal","normal")

confint(mixmodel,level=.95)

hist(Carseats$Education,100,F)
lines(mixmodel,lwd=1.5,col="red")

cut_off <- cutoff(mixmodel)

polygon(c(cut_off[-1],rev(cut_off[-1])),c(0,0,.55,.55),
                 col=rgb(0,0,1,.2),border=NA)
abline(v=cut_off[-1],lty=2,col="blue")
abline(v=cut_off[1],col="blue")
cut_off

That puts the cutoff point at 

Estimate    2.5 %   97.5 % 
14.70389 14.58239 14.82539

Sidenote, it also makes this terrible visual

enter image description here

Sebastian
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    Why do you want to split it into binary? – Tim Jan 17 '19 at 05:51
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    What @Tim says. Discretization loses an enormous amount of information and is rarely necessary, so we would like to understand why you believe you need it. See [Classification probability threshold](https://stats.stackexchange.com/q/312119/1352). – Stephan Kolassa Jan 17 '19 at 07:40
  • There are regions with high education and regions with low education and I want to see the affect on Y based on whether the region is strongly educated. – Sebastian Jan 17 '19 at 07:43

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