In the context of a statistical model, which measure best represents the typical size of a prediction error for this model?

• A. $\text{Sum of squared errors}$
• B. $\text{Mean of the observed values}$
• C. $\text{Median of the predictor variable}$
• D. $\text{Standard deviation of the residuals}$

Answer: (D)

Verified step by step guidance

1. Understand that prediction errors in a statistical model are the differences between observed values and predicted values, often called residuals.
2. Recognize that the 'sum of squared errors' aggregates the squared residuals but does not provide a typical size of the error; it is a total measure rather than an average or typical measure.
3. Recall that the 'mean of the observed values' and the 'median of the predictor variable' are descriptive statistics unrelated to measuring prediction error size.
4. Identify that the 'standard deviation of the residuals' quantifies the typical magnitude of prediction errors by measuring the spread or variability of residuals around their mean (which is usually zero).
5. Conclude that the standard deviation of the residuals is the best measure to represent the typical size of prediction errors because it provides an average scale of how far predictions deviate from actual observations.