Quantile Regression Quiz

Answers and explanations appear as you take the quiz.

1. A delivery model estimates a conditional 90th percentile. Which interpretation matches the guide for a continuous outcome and a well-estimated model?
   • The estimate is the mean of the slowest 10% of comparable deliveries
   • About 90% of comparable outcomes fall at or below that value
   • The estimate is exactly correct on 90% of individual parcels
   • The model's parameters have a 90% probability of being correct
2. At quantile 0.9, a prediction of 10 is followed by an outcome of 12. Which pinball loss applies?
   • 0.2
   • 2.0
   • 0.9
   • 1.8
3. Why does fitting a high quantile favor a higher estimate than fitting the median?
   • Underprediction receives a larger penalty than equal-sized overprediction
   • All errors receive the same squared penalty
   • The model discards every outcome below the median
   • The target values are multiplied by the quantile
4. Which nominal central interval is formed by the 10th and 90th conditional percentiles?
   • A 90% interval
   • A 10% interval
   • An 80% interval
   • A 100% interval
5. A model's nominal 80% interval covers only 60% of held-out outcomes. Which conclusion follows?
   • The training loss guarantees coverage, so the evaluation must be ignored
   • The observed coverage falls below the nominal target
   • The interval is automatically a confidence interval for the mean
   • A nominal interval should contain every held-out outcome
6. Two separately fitted quantile models predict an upper bound below the lower bound. Which issue has occurred?
   • Perfect calibration
   • Mean regression
   • Overcoverage
   • Quantile crossing
7. At the 50th percentile, how does pinball loss weight equally sized positive and negative residuals?
   • Equally, yielding half the absolute error
   • Positive residuals receive twice the weight
   • Negative residuals receive twice the weight
   • Both are squared before averaging
8. A manager needs a range for future service times. Why might a confidence interval for the estimated mean be inappropriate?
   • It describes the central 80% of future outcomes whenever the sample is large
   • It directly measures variation among individual future service times
   • It concerns uncertainty in an estimated parameter rather than the spread of future outcomes
   • It guarantees the same coverage for every future customer group