6 Carboco puts metal coatings on jet propeller blades. The harder the coating, the higher the quality of the coating. The coating is shot onto the blade using pressurized gas contained in an F-gun. Carboco can control the temperature and gas pressure in the F-gun and can also control the room humidity. To see how gas pressure, temperature, and humidity influence hardness, Carboco engineers have run a regression for which the dependent variable is HARD  hardness of a coating

 and the independent variables are HUMIDI  room humidity TEMP  1 if temperature level is high

 0 if temperature level is low PRESS  1 if gas pressure is high

 0 if gas pressure is low T*P  product of TEMP and PRESS We assume that temperature and gas pressure have only two possible levels, low and high. The relevant data are given in Table 30 (file Temp.xls).

a Ignoring considerations of heteroscedasticity, multicollinearity, and autocorrelation, which equation should be used to predict hardness? Explain.

b What combination of gas pressure and temperature setting will maximize hardness?

c Explain how changing temperature from a low level to a high level affects hardness. Be specific!

TAB L E 29 x y 0 100 1 130 2 170 3 200 4 260 5 300 6 305 7 330 8 380