Which metric measures how wrong predictions are overall?

Which metric measures how wrong predictions are overall?

• A. Residual Sum of Squares (RSS)
• B. Mean Squared Error (MSE)
• C. Root Mean Squared Error (RMSE)
• D. Mean Absolute Error (MAE)

Answer: (A)

Residual Sum of Squares sums up the squared differences between what was observed and what the model predicted across every data point, giving the total amount of squared error the model makes. This captures the overall misfit of the predictions for the entire dataset, not averaged per observation. The squaring emphasizes larger errors, and in least squares fitting, minimizing this total helps produce the best overall agreement between predictions and actual values. By contrast, the other metrics either average the errors (mean squared error, which is the average squared residual; root mean squared error, which is the square root of that average; mean absolute error, which averages the absolute residuals). These provide per-point or per-observation error levels, not the total misfit across all data points. So when the goal is to express how wrong the predictions are overall, the total sum of squared errors—residual sum of squares—is the best fit.

Residual Sum of Squares sums up the squared differences between what was observed and what the model predicted across every data point, giving the total amount of squared error the model makes. This captures the overall misfit of the predictions for the entire dataset, not averaged per observation. The squaring emphasizes larger errors, and in least squares fitting, minimizing this total helps produce the best overall agreement between predictions and actual values.

By contrast, the other metrics either average the errors (mean squared error, which is the average squared residual; root mean squared error, which is the square root of that average; mean absolute error, which averages the absolute residuals). These provide per-point or per-observation error levels, not the total misfit across all data points. So when the goal is to express how wrong the predictions are overall, the total sum of squared errors—residual sum of squares—is the best fit.