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 €œIn-Use Emissions 620 CHAPTER 8 Multiple Regression from Heavy-Duty Diesel Vehicles,€ J. Yanowitz, Ph.D. thesis, Colorado School of Mines, 2001.) MINITAB output is presented for the following three models:

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

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NO, = Bo+ B1 Speed + B2 Torque + ɛ NO, = Bo + B, Speed + B, HP + ɛ NO, = Bo + B1 Speed + B2 Torque + B3 HP + ɛ The regression equation is NOx = -321 + 0.378 Speed 0.160 Torque SE Coef 98.14 0.06861 0.06082 Predictor Constant Coef -320.59 0.37820 -3.27 5.51 -2.64 0.003 0.000 0.013 Speed Torque -0.16047 S = 67.13 R-Sq 51.6% R-Sq(adj) = 48.3% The regression equation is NOx = -380 + 0.416 Speed - 0.520 HP %3D Coef -380.1 0.41641 SE Coef 104.8 0.07510 0.1980 Predictor Constant Speed НР -3.63 5.54 -2.63 0.001 0.000 0.014 -0.5198 S = 67.19 R-Sq 51.5% R-Sq(adj) = 48.2% The regression equation is NOx = -302 + 0.366 Speed 0.211 Torque + 0.16 HP Predictor Coef -301.8 Constant Speed Torque SE Coef 347.3 0.2257 0.8884 2.889 -0.87 1.62 -0.24 0.06 0.392 0.3660 -0.2106 0.164 0.116 0.814 0.955 НР S = 68.31 R-Sq 51.6% R-Sq(adj) = 46.4%