Carboco puts metal coatings on jet propeller blades. Theharder the coating, the higher the quality of the coating. Thecoating is shot onto the blade using pressurized gascontained in an F-gun. Carboco can control the temperatureand gas pressure in the F-gun and can also control the roomhumidity. To see how gas pressure, temperature, andhumidity influence hardness, Carboco engineers have run aregression for which the dependent variable isHARD hardness of a coatingand the independent variables areHUMIDI room humidityTEMP 1 if temperature level is high0 if temperature level is lowPRESS 1 if gas pressure is high0 if gas pressure is lowT*P product of TEMP and PRESSWe assume that temperature and gas pressure have only twopossible levels, low and high. The relevant data are given inTable 30 (file Temp.xls). a Ignoring considerations of heteroscedasticity, multi-collinearity, and autocorrelation, which equation should be used to predict hardness? Explain.b What combination of gas pressure and temperaturesetting will maximize hardness?c Explain how changing temperature from a low levelto a high level affects hardness. Be specific! Humidi Temp Press Hard40 1 0 14860 1 0 20950 1 0 17770 1 0 20880 1 0 26260 1 1 24865 1 1 25370 1 1 26335 1 1 18445 1 1 22070 0 0 12928 0 0 5349 0 0 9889 0 0 17090 0 0 17234 0 1 8056 0 1 9077 0 1 15123 0 1 5856 0 1 107

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, multi-
collinearity, 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!

Humidi Temp Press Hard
40 1 0 148
60 1 0 209
50 1 0 177
70 1 0 208
80 1 0 262
60 1 1 248
65 1 1 253
70 1 1 263
35 1 1 184
45 1 1 220
70 0 0 129
28 0 0 53
49 0 0 98
89 0 0 170
90 0 0 172
34 0 1 80
56 0 1 90
77 0 1 151
23 0 1 58
56 0 1 107