Textbook Question
"Concrete Use the results of Problem 15 from Section 12.3 to answer the following questions:
c. Predict the 28-day strength of concrete whose 7-day strength is 2550 psi."
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12. Regression
Prediction Intervals
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A linear regression model predicts weekly revenue from ad spending. You find the prediction interval for exactly \$200 in ad spending is (\$520, \$610). Choose the answer that best describes what this interval means.
A
The model will generate at least \$520 in revenue.
B
The average revenue for \$200 in ad spending is exactly \$565.
C
We are confident that a single weekly revenue value with \$200 in ad spending will fall between \$520 and \$610.
D
We are confident the mean revenue from \$200 in ad spending is between \$520 and \$610.
Verified step by step guidance1
Step 1: Understand the concept of a prediction interval. A prediction interval provides a range within which we expect a single observation (e.g., weekly revenue) to fall, given a certain level of confidence (e.g., 95%). It is different from a confidence interval, which estimates the range for the mean of the population.
Step 2: Analyze the given interval (\$520, \$610). This interval represents the range of possible weekly revenue values for \$200 in ad spending, with a 95% confidence level.
Step 3: Clarify the distinction between the mean and individual observations. The prediction interval applies to individual weekly revenue values, not the average revenue. The average revenue would be addressed by a confidence interval.
Step 4: Evaluate the provided options. The correct interpretation of the prediction interval is: 'We are 95% confident that a single weekly revenue value with \$200 in ad spending will fall between \$520 and \$610.'
Step 5: Reject incorrect options. For example, 'The model will generate at least \$520 in revenue' is incorrect because the prediction interval does not guarantee a minimum revenue. Similarly, 'The average revenue for \$200 in ad spending is exactly \$565' is incorrect because the interval does not specify the exact mean revenue.
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