In a laboratory test of a new automobile engine design carried out at the Colorado School of Mines, the emission rate (in milligrams per second) of oxides of nitrogen was measured for 32 engines at various engine speeds (in rpm) and engine torque (in foot-pounds). The following MINITAB output presents the multiple regression equation Emission rate = b0 + b1 Speed + b2 Torque.

a. Predict the emissions rate for an engine with speed 1500 and torque 500.

b. Two engines are run at the same torque, but their speeds differ by 300 rpm. By how much should we predict their emissions rates to differ?

c. Is the model useful for prediction? Explain. Use the α = 0.05 level.

d. How much of the variation in the emission rate is explained by the model?

e. Let β1 be the coefficient of speed. Test H0: β1 = 0 versus H1: β1 ≠ 0 at the α = 0.05 level. What do you conclude?

f. Let β2 be the coefficient of torque. Test H0: β2 = 0 versus H1: β2 ≠ 0 at the α = 0.01 level. What do you conclude?

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The regression equation is Emission rate = -321 +0.378 Speed - 0.160 Torque Predictor Coef StDev T P Constant -320.59 98.14 -3.27 0.003 Speed 0.37820 0.06861 5.51 0.000 Torque -0.16047 0.06082 -2.64 0.013 S = 67.13 R-Sq = 51.6% R-Sq (adj) = 48.3% Analysis of Variance Source DF SS MS F P Regression 2 139419.6 69079.8 15.469 0.000 Residual Error 29 130685.2 4506.4 Total 31 270104.8