How does a prediction interval differ from a confidence interval around a regression estimate?
Correct Answer
C) A prediction interval covers a single new observation
Why this is correct: A prediction interval estimates the range in which a single, new individual observation (like a specific property's sale price) is likely to fall. It is wider than a confidence interval because it includes both the uncertainty in estimating the mean and the natural variability of individual observations around that mean. Why the other choices are wrong: A prediction interval is wider, not narrower, than a confidence interval. A confidence interval applies to the mean, not a prediction interval. Both intervals require a standard error for their calculation. Exam tip: Confidence interval: "Where is the average?" Prediction interval: "Where is the next single one?" The prediction interval is always wider.
Why This Is the Correct Answer
Why this is correct: A prediction interval estimates the range in which a single, new individual observation (like a specific property's sale price) is likely to fall. It is wider than a confidence interval because it includes both the uncertainty in estimating the mean and the natural variability of individual observations around that mean. Why the other choices are wrong: A prediction interval is wider, not narrower, than a confidence interval. A confidence interval applies to the mean, not a prediction interval. Both intervals require a standard error for their calculation. Exam tip: Confidence interval: "Where is the average?" Prediction interval: "Where is the next single one?" The prediction interval is always wider.
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