How do you interpret a categorical dependent variable in a plot?

Question

I ran a logistic regression on a dataset with two variables. Variable 1 (independent, discrete variable) Variable 2 (dependent, 2-option categorical variable)

I ran this code in R -

    ggplot(dataset, aes(x=ind_variable, y=dependent_variable)) + 
geom_point() + 
      stat_smooth(method="glm", method.args=list(family="binomial"), se=FALSE)

This is what I got -

image_plot

The y axis shows the dependent variable (which has two possible outcomes: 0 and 1). What is the right way to understand the areas between 0 and 1?

My understanding is it is a probability of converting, that when the curve is at .25, then it means that about 50 of the independent variable predicts a 25% change of the outcome occurring.

Is that right?

Answer 1

Logistic regression gives you values in $(0,1)$, only at $\pm \infty $ it reaches $0$ or $1$. Hence, the interpretation is the same as at any other point, i.e., it is the estimated probability of $\{Y=1\}$ given this specific value of $x_0$ (and perhaps some dummy variables).