Not a very well structured article. The animated graphic (which is cool) comes before the lambda parameter is even introduced. That animation should have been put at the end.
It's also not doing a good job at explaining when regularization should be used. The dot cloud in the article is self serving because these points are roughly aligned but they also have a vague cubic form, which explains why the cubic model works better.
The hard part is knowing when you should be using regularization, and that graph doesn't help because it doesn't show further points, therefore not explaining why a certain regression is better than another.
It's also not doing a good job at explaining when regularization should be used. The dot cloud in the article is self serving because these points are roughly aligned but they also have a vague cubic form, which explains why the cubic model works better.
The hard part is knowing when you should be using regularization, and that graph doesn't help because it doesn't show further points, therefore not explaining why a certain regression is better than another.