Suppose we are making predictions of the dependent variable y for specific value

Question

Suppose we are making predictions of the dependent variable y for specific values of the independent variable x using a simple linear regression model holding the confidence level constant. Let Width (C.I) = the width of the confidence interval for the average value y for a given value of x, and Width (P.I) = the width of the prediction interval for a single value y for a given value of x.

Which of the following statements is true?

(A) Width (C.I) = 0.5 Width (P.I)

(B) Width (C.I) < Width (P.I)

(C) Width (C.I) > Width (P.I)

(D) Width (C.I) = Width (P.I)

Explanation / Answer

Answer:

Suppose we are making predictions of the dependent variable y for specific values of the independent variable x using a simple linear regression model holding the confidence level constant. Let Width (C.I) = the width of the confidence interval for the average value y for a given value of x, and Width (P.I) = the width of the prediction interval for a single value y for a given value of x.

Which of the following statements is true?

(A) Width (C.I) = 0.5 Width (P.I)

Answer: (B) Width (C.I) < Width (P.I)

(C) Width (C.I) > Width (P.I)

(D) Width (C.I) = Width (P.I)

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

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