Mean squared error

The mean squared error (MSE) is a measure of the average squared difference between estimated values (ŷ_i) and true values (y_i). It quantifies the accuracy of an estimator by calculating the squared errors, summing them up, and then averaging them over the number of observations (n).

MSE incorporates both the variance and bias of an estimator. Variance refers to the spread of the estimates across different data samples, while bias refers to the systematic error that occurs when the estimator consistently deviates from the true value. By squaring the errors, MSE ensures that all deviations are positive and emphasizes larger errors more significantly.

The MSE formula is crucial in fields like machine learning and statistics, where it serves as a risk function. It helps in evaluating and comparing different estimators by providing a single metric that reflects both variance and bias. A lower MSE indicates a better estimator that produces estimates closer to the true values.