What does mean squared error (MSE) quantify?

Mean squared error (MSE) specifically quantifies the average of the squares of the errors—where an error is the difference between the predicted value and the actual value. By squaring each of the individual forecast errors, MSE ensures that positive and negative errors do not cancel each other out and gives more weight to larger errors, thus providing a robust measure of forecast accuracy. This focus on squaring the errors is what distinguishes MSE and makes it a commonly used statistic in regression analysis and other predictive modeling contexts.

The average component indicates that MSE takes the collective error over all predictions and divides by the number of observations, providing a single measure that expresses the average level of error in the forecasts in terms of squared units. This highlights how much the predicted values deviate from the actual values on average, which is critical for assessing the performance of predictive models.