1. In investigating growth of Japanese beetles, biologists predicted the size (in millimeters) of female beetles from daily temperature (in degrees) and age (in days).

The regression equation is: size(hat) = 6.51 -0.002temperature -0.01age
Which is correct?

a. The estimated size of female beetles is expected to decrease by 0.002 when daily temperature increases by 1 degree, for beetles of the same age (in days).
b. Holding temperature constant and controlling for age, the estimated size of female beetles is 6.51 millimeters.
c. Holding other predictors constant, the estimated size of female beetles is 6.51 millimeters.
d. The size of female beetles is expected to decrease by 0.002 when allowing for temperature.

The correct statement based on the regression equation is:

a. The estimated size of female beetles is expected to decrease by 0.002 when daily temperature increases by 1 degree, for beetles of the same age (in days).

Explanation:

To understand this, let's break down the regression equation:

size(hat) = 6.51 - 0.002temperature - 0.01age

In this equation, "size(hat)" represents the estimated size of female beetles. The coefficient in front of the "temperature" variable is -0.002, indicating that for every 1-degree increase in temperature, the estimated size of female beetles is expected to decrease by 0.002 millimeters, given that all other variables are held constant (in this case, age).

Therefore, option a is the correct statement.