12. Regression

"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"

"Concrete Use the results of Problem 15 from Section 12.3 to answer the following questions:

c. Predict the 28-day strength of concrete whose 7-day strength is 2550 psi."

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.

[DATA] Seat Choice and GPA A biology professor wants to investigate the relation between the seat location chosen by a student on the first day of class and their cumulative grade point average (GPA). He randomly selected an introductory biology class and obtained the following information for the 38 students in the class.

i. Construct a 95% prediction interval for the GPA found in part (h).

[DATA] Crickets make a chirping noise by sliding their wings rapidly over each other. Perhaps you have noticed that the number of chirps seems to increase with the temperature. The following table lists the temperature (in degrees Fahrenheit, °F) and the number of chirps per second for the striped ground cricket.

b. Compute the standard error of the estimate, Sₑ.

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).

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.

Weighing Seals with a Camera The table below lists overhead widths (cm) of seals measured from photographs and the weights (kg) of the seals (based on “Mass Estimation of Weddell Seals Using Techniques of Photogrammetry,” by R. Garrott of Montana State University). For the prediction interval, use a 99% confidence level with an overhead width of 9.0 cm.