Root Mean Square Error
What is rmse ? :-The error of a model in predicting quantitative data is often measured using the Root Mean Square Error (RMSE). Let's try to investigate the mathematical justification for this measure of inaccuracy. The first thing we can see is a similarity to the formula for the Euclidean distance between two vectors in Rn, ignoring the division by n beneath the square root: Heuristically, this suggests that RMSE may be seen as a distance between the vector of expected values and the vector of observed values. But why are we doing this division by n here under the square root? The Euclidean distance is only scaled down by a factor of (1/n) if we maintain n (the number of observations) constant. It's a little difficult to see why this is the appropriate course of action, so let's go a little more. Imagine that the following happens when we add random "errors" to each of the predicted values to create our observed values: Considered random variables, these mist