Local polynomial regression

Local polynomial regression is like making a guess about something by looking at the things around it. Imagine you have a graph with a bunch of points on it, like a dot-to-dot picture.

So, on this graph, we want to find out what the line would look like if we drew one that goes through all of the dots. But instead of drawing the line straight through all of the dots, it draws a squiggly line that follows the shape of the dots nearby.

Just like instead of looking at everything, you only focus on what's around where you want to make the guess. If you're trying to guess what the line will look like near the dots on the far right side of the graph, you only look at the dots that are close to it.

This can help us make better guesses about data if we think there might be some weird stuff happening in small areas. Local polynomial regression guesses the shape of the line by looking at all the dots nearby, and gives us a nice smooth curve that's a more accurate representation of the data than just one straight line.