How Does Standard deviation of residuals or Root-mean-square error (RMSD) Work?

Standard deviation of residuals or Root-mean-square error (RMSD) tells us how close our predictions are to the real values, like knowing if your guess about how many jellybeans are in a jar is really close or way off.

Imagine you and your friend are playing a game where you both try to guess the number of marbles in a bag. After everyone guesses, you count the marbles and see who was closest. RMSD is like calculating how far off all the guesses were on average, not just yours or your friend's.

Think of each guess as a step away from the real number of marbles. The standard deviation measures how much these steps vary, if most people are really close, but one person is way off, that affects the total.

RMSD takes all those steps (guesses), squares them to make sure big mistakes don't get ignored, then averages and finds the square root. It gives you a single number that shows how good your predictions are overall, like getting a score on a guessing game that reflects everyone's performance.