Q1.7: Random errors and prediction – Applied Regression Modeling, 3rd edition

Answer the following questions based on Section 1.7: Random errors and prediction.

Suppose we have sampled 25 observations of Y and our sample mean is 5.8 and our sample standard deviation is 2.5. Note that the 95^th percentile of a t-distribution with 24 degrees of freedom is 1.711, and the 97.5^th percentile is 2.064. Use this information to answer the following questions.

1.

Calculate the upper bound of a 95% prediction interval for an individual Y-value. Write a number rounded to three decimal places.

2.

Calculate the lower bound of a 95% prediction interval for an individual Y-value. Write a number rounded to three decimal places.

3.

Calculate the confidence level of a prediction interval for an individual Y-value that is between 1.4378 and 10.1622. Express as a percentage by writing a whole number.

4.

Which of the following is the correct interpretation of a 95% prediction interval for an individual Y-value that goes from 0.538 to 11.062?

Under repeated sampling, the individual Y-value would be between 0.538 and 11.062 95% of the time

Under repeated sampling, 95% of such confidence intervals would contain the individual Y-value.

The probability that the individual Y-value is between 0.538 and 11.062 is 0.95.

The probability that the sample mean is between 0.538 and 11.062 is 0.95.

5.

Which of the following will result in a wider prediction interval for an individual Y-value? Select all that apply.

Increased level of confidence.

Increased sample mean.

Increased sample standard deviation.

Increased sample size.

Applied Regression Modeling

3rd edition

Iain Pardoe