The Texas Transportation Institute (tti.tamu.edu) studies traffic delays. They estimate that in the year 2011, 498 urban areas experienced 5.5 billion vehicle hours of delay, resulting in 2.9 billion gallons of wasted fuel and $121 billion in lost productivity and fuel costs. That€™s about 0.7% of the nation€™s GDP that year. Data the institute published for the year 2001 include information on the Total Delay per Person (hours per year spent delayed by traffic), the Average Arterial Road Speed (mph), the Average Highway Road Speed (mph), and the Size of the city (small, medium, large, very large). The regression model based on these variables looks like this. The variables Small, Large, and Very Large are indicators constructed to be 1 for cities of the named size and 0 otherwise.

a) Why is there no coefficient for Medium?
b) Explain how the coefficients of Small, Large, and Very Large account for the size of the city in this model.

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Dependent variable is: Delay/person R-squared-79.1% R-squared (adjusted)-77.4% S6.474 with 68 6 62 degrees of freedom Source Regression 9808.23 Residua 2598.64 Sum of Squares df Mean Square F-ratio 5 1961.65 62 41.9135 Coeff 139.104 16.69 Variable Intercept HiWay MPIH Arterial MPH -2.04836 0.6672 Smal1 Large Very Large SE(Coeff) t-ratio P-value 8.33 <0.0001 4.34 0.0001 -3.07 0.0032 -1.22 0.2287 2.38 0.0203 1.06 0.2951 1.07347 0.2474 -3.58970 2.953 5.00967 2.104 3.41058 3.230