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Chapter 14: Q 14.110 (page 580)

Refer to the confidence interval and prediction interval formulas in Procedures 14.3 and 14.4, respectively.

a. Explain why, for a fixed confidence level, the margin of error for the estimate of the conditional mean of the response variable increases as the value of the predictor variable moves farther from the mean of the observed values of the predictor variable.

b. Explain why, for a fixed prediction level, the margin of error for the estimate of the predicted value of the response variable increases as the value of the predictor variable moves farther from the mean of the observed values of the predictor variable.

Short Answer

Expert verified

Part (a)Is due only to the fact that population regression line is estimated by a sample regression line.

Part (b)The error in prediction of all values of response variable is more than predicting the single value of response variable

Step by step solution

01

Step 1:Given information

The confidence interval and prediction interval formulas in Procedures 14.3 and 14.4, respectively.

02

Step 2:Explaination Part a)

The error in the estimate of conditional mean for response variable is due only to the fact that population regression line is estimated by a sample regression line.

Because of this, the margin of error for the estimate of the conditional mean of the response variable increases as the value of the predictor variable moves farther from the mean of the observed values of the predictor variable.

03

Step 2:Explaination Part b)

The error in prediction of all values of response variable is more than predicting the single value of response variable. Therefore, for a fixed prediction level, the margin of error for the estimate of the predicted value of the response variable increases as the value of the predictor variable moves farther from the mean of the observed value sof the predictor variable.

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