Hat matrix

Imagine you have a group of friends playing a game where they have to jump as high as they can. You, as a grown-up, are trying to figure out who jumps the highest and what factors help them jump higher.

To do that, you measure their height, weight, and the distance they jump. Then you use a special formula called "regression" to find out how the factors of height and weight impact their jumping distance.

But wait – there's a problem. Some friends might have taken a longer run-up than others, which could affect how far they jump. To eliminate that difference, you need to factor in the distance each friend ran before jumping.

So, you use a special tool called the Hat Matrix, which takes into account the distance each friend ran before jumping. Hat Matrix is like wearing a magician's hat that tells you the correct distance they jumped relative to the distance they ran.

By using the Hat Matrix and regression formula, you find out that height has a greater role in jumping distance than weight. Also, the distance each friend ran before jumping didn't affect their jumping distance, after all. Now you can use this knowledge to bet on your friend who is taller and see who wins the game!