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

Optimized version of the animated gif

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:

enter image description here

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

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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.

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  • $\begingroup$ wow it was fast. Thank you! $\endgroup$ – German Demidov Nov 14 '19 at 14:58

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