What statistical measure is fundamental for assessing model performance by averaging squared differences?

The statistical measure fundamental for assessing model performance by averaging squared differences is the Average Squared Error. This measure is crucial in understanding how well a model predicts observed values by specifically quantifying the errors between predicted and actual results.

When evaluating predictive models, it's important to minimize deviation from the true values, and Average Squared Error achieves this by calculating the squares of errors (the differences between predicted values and actual values), ensuring that positive and negative errors do not cancel each other out. By taking the average of these squared differences, practitioners obtain a clear numerical representation of the model's performance that reflects variability around the mean.

In contrast, while measures like Mean Absolute Error and Root Mean Square Error relate to squared differences, they are parts of different metrics or formulations that provide insights into model performance but do not align directly with the basic concept of averaging squared differences. The Coefficient of Determination, on the other hand, is a different statistical concept that serves to explain the proportion of variance in the dependent variable that is predictable from the independent variables, and it does not involve direct averaging of squared errors. Thus, the focus on averaging squared differences definitively points to Average Squared Error as the correct measure for this particular question.