Simple Explanation about Logistic Regression Plot

Question

I was reading an article about logistic regression and I got confused by one of the pictures:

https://towardsdatascience.com/introduction-to-logistic-regression-66248243c148

First animated gif from Uni of Toronto. What is depicted there? What is y-axis and x-axis (from 0 to 1)? How is it related to logistic regression?

UPD: this post is not of the best quality - but I don't ask about the post, but about the picture. I've seen this picture multiple times and once I've seen a senior statistician laughing at this picture on twitter - however, no explanation followed why it is funny.

UPD1: here is another example of this plot:

https://www.datasciencecentral.com/profiles/blogs/why-logistic-regression-should-be-the-last-thing-you-learn-when-b

Answer 1

X and Y are different explanatory variables, while the output appears coded as blue / red dot. The decision boundary is what you should get after calibrating your model and selecting a threshold for classification, here it appears plotted trough the calibration process.

It is misleading for a least two reasons :

• y is traditionaly used to denote the output. Axes should be $X_1$ and $X_2$, two explanatory variables, and the output, y, should appear in the legend (red : y = 1, blue y = 0).

• The exemple does not really provide an explanation as to why logistic regression is better, or how the model is calibrated. Evolving boundaries would better illustrate the functionning of a SVM for exemple.