How is the mean squared errors measure critically useful?

The mean squared error (MSE) is critically useful because it quantifies how much, on average, the predicted values differ from the actual values in a dataset. MSE is calculated by taking the average of the squared differences between each predicted value and the corresponding actual value. This squaring of differences ensures that larger errors are given more weight than smaller ones, making it particularly sensitive to outliers. By focusing on the average of these squared differences, MSE provides a clear and concise measure of how well a model performs in terms of accuracy. In predictive modeling and regression analysis, understanding MSE is essential for evaluating model performance and making improvements.