Accuracy Assessment
1. **Problem statement:** We want to assess the accuracy of predicted values for national average access to basic water services based on Annual Rates of Change (ARC) using the given error metrics: MAE = 9.67, MSE = 187.03, RMSE = 13.68.
2. **Definitions:**
- MAE (Mean Absolute Error) measures the average magnitude of errors in predictions, without considering their direction. It is in the same units as the target variable.
- MSE (Mean Squared Error) measures the average of the squares of the errors, giving more weight to larger errors.
- RMSE (Root Mean Squared Error) is the square root of MSE, also in the same units as the target variable.
3. **Interpretation:**
- Since the target variable is "Average access to basic water services (%)", the errors (MAE, RMSE) are in percentage points.
- MAE = 9.67 means on average, predictions deviate from actual values by about 9.67 percentage points.
- RMSE = 13.68 is higher than MAE, indicating some larger errors exist.
4. **Evaluating the statements:**
- Statement 1 claims the measures are not expressed as percentages and do not account for units. This is false because errors are in percentage points, matching the target variable units.
- Statement 2 says the predicted values are generally inaccurate with an average error of about 9.67 percentage points, which aligns with the MAE interpretation.
- Statement 3 claims MAE and RMSE are relatively low, indicating good accuracy. However, an average error near 10 percentage points in a percentage-based variable may not be considered low depending on context, and the RMSE being higher suggests notable variation.
- Statement 4 is "None of the above".
5. **Conclusion:** The most accurate statement is Statement 2: The measures suggest that the predicted values are generally inaccurate, with an average error of approximately 9.67 percentage points from the actual values, as indicated by the MAE.
**Final answer:** Statement 2 is true.