Understanding the fitted regression line. Researchers study the rate of water loss (% body weight per minute) of a tropical bedbug exposed to different combinations of temperature x1 and relative humidity x2. The fitted regression equation for their multiple regression is
y^ = -2.7 + 0.05x1 + 0.04x2
(a) If x1 = 30°C and x2 = 80%, what is the predicted value of y?
(b) For the answer to part (a) to be valid, is it necessary that the values x1 = 30 and x2 = 80 correspond to a case in the data set? Explain why or why not.
(c) If you hold x2 at a fixed value, what is the effect of an increase of 5°C on the predicted value of y?