Roads in Egypt are notoriously haphazard, often lacking proper engineering consideration. The article “Effect of Speed Hump Characteristics on Pavement Condition” (J. Traffic Transp. Engr. 2017: 103–110) reports a study by two Egyptian civil engineering faculty of 52 speed bumps on a major road in upper Egypt. They measured each speed bump’s height (x₁), width (x₂), and distance (x₃) from the preceding speed bump (all in meters). They also evaluated each bump using a pavement condition index (PCI), a 0–100 scale with 100 the best condition.
a. With y = PCI, the estimated regression equation reported in the article is y = 59.05 – 243.668x₁ + 11.675x₂ + .012x₃. Interpret the coefficient on x₁. 

b. Estimate the pavement condition index of a speed bump 0.13 m tall, 2.5 m wide, and 666.7 m from the preceding speed bump.
c. The authors report R² = .770 for this three-variable model. Interpret this value, and then carry out the model utility test at the .05 significance level.