14.19 Data from a sample of n 5 150 quail eggs were used to fit a multiple regression model relating y 5 eggshell surface area (mm2)

x1 5 egg weight (g)

x2 5 egg width (mm)

x3 5 egg length (mm)

(“Predicting Yolk Height, Yolk Width, Albumen Length, Eggshell Weight, Egg Shape Index, Eggshell Thickness, Egg Surface Area of Japanese Quails Using Various Egg Traits as Regressors,” International Journal of Poultry Science

[2008]: 85–88).

The resulting estimated regression function was 10.561 1 1.535x1 2 0.178x2 2 0.045x3 and R2 5 .996.

a. Carry out a model utility test to determine if this multiple regression model is useful. (Hint: See Example 14.10.)

b. A simple linear regression model was also used to describe the relationship between y and x1,

resulting in the estimated regression function 6.254 1 1.387x1. The P-value for the associated model utility test was reported to be less than .01, and r2 5 .994. Is the linear model useful? Explain.
(Hint: See Example 14.11.)

c. Based on your answers to Parts

(a) and (b), which of the two models would you recommend for predicting eggshell surface area? Explain the rationale for your choice.