Cumulative distribution function
Understanding the logistic distribution is key to understanding logistic regression. Like the normal (Gaussian) distribution, it is a probability distribution of a single continuous variable. Here you'll visualize the cumulative distribution function (CDF) for the logistic distribution. That is, if you have a logistically distributed variable, x, and a possible value, xval, that x could take, then the CDF gives the probability that x is less than xval.
The logistic distribution's CDF is calculated with the logistic function (hence the name). The plot of this has an S-shape, known as a sigmoid curve. An important property of this function is that it takes an input that can be any number from minus infinity to infinity, and returns a value between zero and one.
ggplot2 is loaded.
This exercise is part of the course
Intermediate Regression in R
Hands-on interactive exercise
Have a go at this exercise by completing this sample code.
logistic_distn_cdf <- tibble(
# Make a seq from -10 to 10 in steps of 0.1
x = ___,
# Transform x with built-in logistic CDF
logistic_x = ___,
# Transform x with manual logistic
logistic_x_man = ___
)
# Check that each logistic function gives the same results
all.equal(
___,
___
)