Least-absolute-deviations regression

Okay kiddo, let me try to explain least-absolute-deviations regression to you in the simplest way possible.

You know how sometimes when you're trying to draw a line through a set of points on a graph, it's hard to decide where exactly to put the line, right?

Well, that's where least-absolute-deviations regression comes in. It's like a wizard that can magically find the best line that goes through all the points.

But how does it do that?

Well, let's say we have a bunch of points on a graph that look like they make a line, but some of them are a little bit off. Like if you were trying to draw a line through a set of dots and one of the dots was way up high, like on the ceiling, it would be hard to make the line go through that dot, right?

Least-absolute-deviations regression looks at all the points and tries to find the line that's the closest to all of them combined, but it doesn't care about any one point being off. It cares about the total distance between the line and all the points. It tries to make that distance as small as possible, by moving the line up or down, left or right, until it's in the right spot.

And instead of measuring the distance between the line and the points using a straight line like regular regression, least-absolute-deviations regression measures it using an L-shape. So it's like going from one point to the line, and then going straight up or down to the line.

This method can be really useful in situations where there are outliers, or points that are really different from all the others. It can help find the line that fits the data best, even if there are a few weird points that stick out.

So that's least-absolute-deviations regression in a nutshell, kiddo. It's like a wizard that finds the best line to draw through a bunch of dots on a graph, by making the total distance between the line and the dots as small as possible, using an L-shape. Cool right?