Growth of Japanese beetles. In the Journal of Insect Behavior (Nov. 2001), biologists at Eastern Illinois University published the results of their study on Japanese beetles. The biologists collected beetles over a period of n = 13 summer days in a soybean field. For one portion of the study, the biologists modeled y, the average size (in millimeters) of female beetles as a function of the average daily temperature x1 (degrees) and Julian date x2.

a. Write a first-order model for E(y) as a function of x1 and x2.

b. The model was fit to the data, with the results shown in the accompanying table. Interpret the estimate of β1.

c. Conduct a test to determine whether the average size of female Japanese beetles decreases linearly as the temperature increases. Use α = .05.

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Parameter Estimate t-Value p-Value Variable Intercept 6.51 26.0 <.0001 Temperature (x-.002-0.72 Date (2) 49 3.30 008 一.010