12. Regression

"Height versus Head Circumference Use the results of Problem 13 from Section 12.3 to answer the following questions:

a. Predict the mean head circumference of children who are 25.75 inches tall."

"Height versus Head Circumference Use the results of Problem 13 from Section 12.3 to answer the following questions:

c. Predict the head circumference of a randomly selected child who is 25.75 inches tall"

Variation and Prediction Intervals

In Exercises 17–20, find the (a) explained variation, (b) unexplained variation, and (c) indicated prediction interval. In each case, there is sufficient evidence to support a claim of a linear correlation, so it is reasonable to use the regression equation when making predictions.

Altitude and Temperature Listed below are altitudes (thousands of feet) and outside air temperatures (°F) recorded by the author during Delta Flight 1053 from New Orleans to Atlanta. For the prediction interval, use a 95% confidence level with the altitude of 6327 ft (or 6.327 thousand feet).

[DATA] Apartments The following data represent the square footage and rents for apartments in Queens, New York and Nassau County, New York. For this problem, only consider the Queens data.

i. Construct a 90% prediction interval for the rent of a particular 900-square-foot apartment in Queens.

"An Unhealthy Commute Use the results of Problem 11 from Section 12.3 to answer the following questions:

c. Predict the well-being index composite score of Jane, whose commute time is 20 minutes."

American Black Bears Use the results of Problem 18 from Section 12.3 to answer the following questions:

d. Construct a 95% prediction interval for the weight of an American black bear that is 154.5 cm long.

"In Exercises 19-24, construct the indicated prediction interval and interpret the results.

20. Construct a 90% prediction interval for the average time adults ages 35 to 44 spend per day watching television in Exercise 10 when the average time adults ages 25 to 34 spend per day watching television is 2.25 hours."

Invest in Education Use the results of Problem 17 in Section 12.3 to answer the following questions:

b. Construct a 95% confidence interval for the mean annual ROI found in part (a).

"In Exercises 19-24, construct the indicated prediction interval and interpret the results.

21. Construct a 95% prediction interval for the number of hours of sleep for an adult in Exercise 11 who is 45 years old."

Finding a Prediction Interval

In Exercises 13–16, use the following paired data consisting of weights of large cars (pounds) and highway fuel consumption (mi/gal) from Data Set 35 “Car Data” in Appendix B. (These are the same data used in Exercises 9-12.) Let x represent the weight of the car and let y represent the corresponding highway fuel consumption. Use the given weight and the given confidence level to construct a prediction interval estimate of highway fuel consumption.

Cars Use x = 3800 pounds with a 99% confidence level.

Interpreting a Computer Display

In Exercises 9–12, refer to the display obtained by using the paired data consisting of weights (pounds) and highway fuel consumption amounts (mi/gal) of the large cars included in Data Set 35 “Car Data” in Appendix B. Along with the paired weights and fuel consumption amounts, StatCrunch was also given the value of 4000 pounds to be used for predicting highway fuel consumption.

Finding a Prediction Interval For a car weighing 4000 pounds (x = 4000) identify the 95% prediction interval estimate of the highway fuel consumption. Write a statement interpreting that interval.

Credit Scores Use the results of Problem 12 from Section 12.3 to answer the following questions:

d. Construct a 90% prediction interval for the interest rate of Kaleigh, whose credit score is 730.

"In Exercises 19-24, construct the indicated prediction interval and interpret the results.

24. Construct a 99% prediction interval for the price of a gas grill in Exercise 18 with a usable cooking area of 900 square inches."

Hurricanes Use the results of Problem 14 in Section 12.3 to answer the following questions:

b. Construct a 95% confidence interval for the mean wind speed found in part (a).

CEO Performance Using the results of Problem 19 from Section 12.3, explain why it does not make sense to construct confidence or prediction intervals based on the least-squares regression equation.