Linear model of geom_histogram data - r

Question

I'm working with dataset in which I have continuous variable x and categorical variables y and z. Something like this:
set.seed(222)
df = data.frame(x = c(0, c(1:99) + rnorm(99, mean = 0, sd = 0.5), 100),
y = rep(50, times = 101)-(seq(0, 50, by = 0.5))+rnorm(101, mean = 30, sd = 20),
z = rnorm(101, mean = 50, sd= 10))
df$positive.y = sapply(df$y,
function(x){
if (x >= 50){"Yes"} else {"No"}
})
df$positive.z = sapply(df$z,
function(x){
if (x >= 50){"Yes"} else {"No"}
})
Then using this dataset I can create histograms to see either there is correlation between variables x and positive.y(z). With 10 bins it is clear that x correlates with positive.y, but not with positive.z:
ggplot(df,
aes(x = x, fill = positive.y))+
geom_histogram(position = "fill", bins = 10)
ggplot(df,
aes(x = x, fill = positive.z))+
geom_histogram(position = "fill", bins = 10)
Now from this I want two things:
Extract the actual data points to supply them to corr.test() function or something like that.
Add geom_smooth(method = "lm") to plot I have.
I tried to add "bin" column to the df, like this:
df$bin = sapply(df$x,
function(x){
if (x <= 10){1}
else if (x > 10 & <= 20) {20}
else if .......
})
Then using tapply() count number of "Yes" and "No" for each df$bin, and convert it to the %.
But in this case each time I change number of bins at histogram, I have to re-write and re-run this part of code which is tedious and consumes a lot of computer time if dataset is large.
Is there a more straightforward way to achieve the same result?

Answer 1

I don't see a good justification for adding an lm line. Logistic regression is the appropriate model and doesn't require binning:
df$positive.y <- factor(df$positive.y)
mod <- glm(positive.y ~ x, data = df, family = "binomial")
summary(mod)
anova(mod)
library(ggplot2)
ggplot(df,
aes(x = x, fill = positive.y))+
geom_histogram(position = "fill", bins = 10) +
stat_function(fun = function(x) predict(mod, newdata = data.frame(x = x),
type = "response"),
size = 2)
If you need an R² value (why?), there are different pseudo-R² available for GLMs, e.g.,
library(fmsb)
NagelkerkeR2(mod)
#$N
#[1] 101
#
#$R2
#[1] 0.4074274