Studentized residual

Imagine you are counting marbles in a jar and you want to know if you made any mistakes. You could take a guess at how many marbles should be in there, but then you'd want to know how close you were. To get an idea of how good your guess was, you'd count the marbles and compare your guess to the actual count.

Sometimes, when we try to guess something or make a prediction, we use math formulas to help us. When we use math formulas, we can get an idea of how accurate our guesses are, which is important!

The studentized residual is a way to tell how accurate our predictions are when we use a certain formula, called a regression formula. It's kind of like counting marbles in a jar! We use the studentized residual to check if our guesses, or predictions, from the regression formula are close to the real data.

When we use the studentized residual, we take our predicted values and compare them to the actual values. If our predictions are really close to the actual data, then our studentized residual will be small. But if our predictions are really far from the actual data, our studentized residual will be large.

Using the studentized residual helps us check if our regression formula is accurate, and if we need to make any adjustments or changes. So, it's like double checking the number of marbles in a jar to make sure we counted right!