Root-mean-square error (RMSE)

The root mean squared error (RMSE) is a metric used to evaluate the performance of a regression model. It is defined as the square root of the mean squared error (MSE), which is the average squared difference between the predicted values of the model and the true values of the data.

The RMSE is calculated using the following formula:

RMSE = √((1/n) * Σ(y_i - ŷ_i)^2)

Where n is the number of observations in the data, y_i is the true value of the i-th observation, and ŷ_i is the predicted value of the i-th observation. The capital Greek letter sigma (Σ) indicates the sum of the squared differences, and the square root is taken to scale the error to the same units as the original data.

The RMSE is a measure of the average magnitude of the errors made by the model in its predictions, and is a useful metric for evaluating the performance of a model when the errors are evenly distributed across the data. It is particularly useful when the errors are symmetrically distributed and there are no extreme outliers, since it is not sensitive to the presence of outliers.

The RMSE is easy to interpret and is well-suited for tasks where the goal is to minimize the average error made by the model. It is often used in conjunction with other evaluation metrics, such as the mean absolute error (MAE) or the mean squared error (MSE), to get a more comprehensive evaluation of the model's performance.

Assess the implications and limitations; make judgments about the ideas, works, solutions or methods in relation to selected criteria.

A unit of abstract mathematical system subject to the laws of arithmetic.

Use knowledge and understanding to recognize trends and draw conclusions from given information.