Explain what that means using everyday language

Question

Here's a statement about the coefficient of determination from the book:

Approximately 44% of the variation (0.4397 is approximately 0.44) in the final-exam grades can be explained by the variation in the grades on the third exam, using the best-fit regression line.

Explain what that means using everyday language (as if you were explaining it to your bff)?

Answer 1

Imagine you and your BFF are looking at a bunch of balloons floating in the air. Some balloons are flying high, while others are a bit lower. The height of these balloons can represent students' final-exam grades. Now, let's say that how much air you put into each balloon earlier (during the third exam) determines how high they fly now.

If you had a magic magnifying glass that could show you the perfect relationship between the amount of air you put in earlier and the height they're at now, it wouldn't be perfect. Not every balloon would line up exactly. There are other things that can influence the height, like maybe a gust of wind or a tiny hole in the balloon.

The statement from the book is like saying: "Hey, about 44% of the reason these balloons are at their current heights is because of how much air we put in them during the third exam. The other 56%? That's due to other stuff we didn't account for."

So, in simpler terms, while the third exam grades (or the air in the balloons) play a role in the final exam grades (or the height they're floating at), they don't tell the whole story. There are other factors at play that make up the remaining 56%.