The width of the confidence interval estimate for the predicted value of y depends on
A)the standard error of the estimate
B)the value of x for which the prediction is being made
C)the sample size
D)All of these choices are true.

Question

Quizplus · Accepted Answer

The width of the confidence interval estimate for the predicted value of y depends on all three factors.

A) The standard error of the estimate: As the standard error of the estimate increases, the width of the confidence interval also increases, indicating less precision in the prediction.

B) The value of x for which the prediction is being made: The width of the confidence interval increases as x moves away from the mean of x, indicating that the prediction is less precise for extreme values of x.

C) The sample size: As the sample size increases, the standard error of the estimate decreases, leading to a narrower confidence interval and increased precision in the prediction.

Therefore, all three factors influence the width of the confidence interval estimate for the predicted value of y, and the correct answer is D.

The Width of the Confidence Interval Estimate for the Predicted