Prediction interval vs. confidence interval

[tiger]

Which of these intervals based on the same estimated regression equation with fixed values of the explanatory variables would be wider: (i) a 95% prediction interval for an individual value of Y or (ii) a 95% confidence interval for the mean value of Y? Explain your answer. How would you interpret the wider of these two intervals in words?

[vicki]

Individual value of Y varies more than the mean of Y. (From the formula, the difference is the addition of a single value "1" under the square root sign.) Thus the 95% prediction interval for an individual value of Y is wider.

Interpretation:
Given x, we are 95% confident that the interval contains the individual value of Y.

we can also say the following:
If we repeat sampling for 100 times, and compute the 95% prediction interval for an individual value of Y for each sample, 95 of the prediction intervals will contain the true individual value of Y given X.