Chapter 8.2, Problem 3E

In a laboratory test of a new engine design, the emissions rate (in mg/s of oxides of nitrogen, NO_x) was measured as a function of engine speed (in rpm), engine torque (in ft·lb), and total horsepower. (From “In-Use Emissions from Heavy-Duty Diesel Vehicles,” J. Yanowitz, Ph.D. thesis, Colorado School of Mines, 2001.) MINITAB output is presented for the following three models:

$\begin{array}{l}{\text{NO}}_x={\beta }_0+{\beta }_1\text{Speed}+{\beta }_2\text{Torque}+\epsilon \\ {\text{NO}}_x={\beta }_0+{\beta }_1\text{Speed}+{\beta }_2\text{HP}+\epsilon \\ {\text{NO}}_x={\beta }_0+{\beta }_1\text{Speed}+{\beta }_2\text{Torque}+{\beta }_3\text{HP}+\epsilon \end{array}$

Of the variables Speed, Torque, and HP, which two are most nearly collinear? How can you tell?