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Accuracy Assessment

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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.