Question

For a given set of values for x1, x2, . . . , xk the confidence interval for the conditional mean of Y is

• usually about the same as the prediction interval for the individual Y value.

• wider than the prediction interval for the individual Y value.

• narrower than the prediction interval for the individual Y value.

Answer 1

Confidence intervals tell you about how well you have determined the mean.

Prediction intervals tell you where you can expect to see the next data point sampled.

Prediction intervals must account for both the uncertainty in knowing the value of the population mean, plus data scatter. So a prediction interval is always wider than a confidence interval.

Answer: The confidence interval for the conditional mean of Y is narrower than the prediction interval for the individual Y value.