Question: Using the context of the previous exercise, explain the difference between the purpose of a 95% prediction interval (PI) for an observation and a 95%

Using the context of the previous exercise, explain the difference between the purpose of a 95% prediction interval (PI) for an observation and a 95% confidence interval (CI) for the mean of y at a given value of x. Why would you expect the PI to be wider than the CI?
Previous exercise
For a random sample of children from a school district in South Carolina, a regression analysis is conducted of y = amount spent on clothes in the past year (dollars) and x = year in school. MINITAB reports the tabulated results for observations at x = 12.

Predicted Values for New Observations NewObs Fit SEFit 95% CI 95% PI 448.0 10.6 (427, 469) (101,795)

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