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Chapter 13: Problem 25

A student who has been accepted by two colleges wants to estimate what GPA he might get at the two colleges. His data consist of SAT scores and GPAs from random samples of recent graduates at each college. He wishes to predict his GPA at each school, using separate linear regression models for the two colleges. Should he use prediction intervals or confidence intervals for the prediction of his own GPA? Explain.

Short Answer

Expert verified
The student should use prediction intervals as he is interested in estimating his own GPA, not the average GPA of others with similar SAT scores.

Step by step solution

01

- Understand Confidence Intervals

A confidence interval provides a range of values for a parameter (like a mean or an average) within which the true value is likely to fall. For the question, this would mean what the average GPA of all students similar to him might be.
02

- Understand Prediction Intervals

A prediction interval, on the other hand, furnishes a range within which a single future observation is likely to fall. For the question, this would mean what his own GPA will most likely be.
03

- Relate to the Problem

In this case, the student is interested in predicting his own GPA i.e., a single future observation. Hence, it is appropriate to use a prediction interval rather than a confidence interval.

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