In rock blasting, the peak particle velocity (PPV) depends both on the distance from the blast and on the amount of charge. The article ??Prediction of Particle Velocity Caused by Blasting for an Infrastructure Excavation Covering Granite Bedrock?? (A. Kahriman, Mineral Resources Engineering, 2001:205??218) presents data on PPV, scaled distance (which is equal to the distance divided by the square root of the charge), and the amount of charge. The following table presents the values of PPV, scaled distance, and amount of charge for 15 blasts.

a. Fit the model ln PPV = β₀ + β₁ ln Scaled Distance + β₂ ln Charge + ε. Compute the P-value for testing H₀ : β_i = 0 for β₀, β₁, and β₂.

b. The article claims that the model ln PPV = β₀ +β₁ ln Scaled Distance + ε is appropriate. Fit this model. Compute the P-value for testing H₀ : β_i = 0 for β₀, β₁, and β₂.

c. Which model do you prefer? Why?

Scaled Distance Amount of PPV (mm/s) (m/kg5) Charge (kg) 1.4 47.33 4.2 15.7 9.6 92.0 2.54 15.8 40.0 1.14 24.3 48.7 0.889 23.0 95.7 1.65 12.7 67.7 1.4 39.3 13.0 26.8 8.0 70.0 1.02 29.94 13.5 4.57 10.9 41.0 6.6 8.63 108.8 28.64 18.21 33.0 1.02 27.43 3.94 1.4 59.1 11.5 1.4 34.0 175.0