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 $95\%$ confident that a single weekly revenue value with \$200 in ad spending will fall between \$520 and \$610.
• D. We are $95\%$ confident the mean revenue from \$200 in ad spending is between \$520 and \$610.

Answer: (C)

Verified step by step guidance

1. Understand the context: The problem involves interpreting a prediction interval in a linear regression model. A prediction interval provides a range where we expect a single observation (in this case, weekly revenue) to fall, given a specific value of the independent variable (ad spending).
2. Clarify the difference between prediction intervals and confidence intervals: A prediction interval is used to estimate the range for a single observation, while a confidence interval estimates the range for the mean of the dependent variable. This distinction is crucial for selecting the correct interpretation.
3. Analyze the given interval: The prediction interval for \$200 in ad spending is (\$520, \$610). This means that the model predicts a single weekly revenue value to fall within this range with a certain level of confidence (typically 95%).
4. Evaluate the provided options: The first option ('The model will generate at least \$520 in revenue') is incorrect because a prediction interval does not guarantee a minimum value; it only provides a range with a certain confidence level. The second option ('The average revenue for \$200 in ad spending is exactly \$565') is also incorrect because the interval does not describe the mean revenue. The fourth option ('We are 95% confident the mean revenue from \$200 in ad spending is between \$520 and \$610') is incorrect because the interval is a prediction interval, not a confidence interval for the mean.
5. Select the correct answer: The third option ('We are 95% confident that a single weekly revenue value with \$200 in ad spending will fall between \$520 and \$610') is correct because it accurately describes the purpose of a prediction interval in this context.