Chapter 13.3, Problem 15E

Engine emissions: 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 $b_0+b_1$

Speed $+b_2$

Torque.

1. Predict the emissions rate for an engine with speed 1500 and torque 500.
2. 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?
3. Is the model useful for prediction? Explain. Use the $\alpha =0.05$ level.
4. How much of the variation in the emission rate is explained by the model?
5. Let ${\beta }_1$ be the coefficient of speed. Test $H_0{\beta }_2=0$ versus $H_1{\beta }_2\ne 0$ at the $\alpha =0.05$ level. What do you conclude?
6. Let ${\beta }_2$ be the coefficient of torque. Test $H_0{\beta }_2=0$ versus $H_1{\beta }_2\ne 0$ at the $\alpha =0.01$ level. What do you conclude?