11.84 The recent expansion of U.S. grain exports has intensified the importance of the linkage between the domestic grain transportation system and international transportation. As a first step in evaluating the economies of this interface, Martin and Clement (Transportation Journal, 1982) used multiple regression to estimate ocean transport rates for grain shipped from the Lower Columbia River international ports. These ports include Portland, Oregon; and Vancouver, Longview, and Kalama, Washington. Rates per long ton Y were modeled as a function of the following independent variables:

X shipment size in long tons = x2 = distance to destination port in miles X3 = x4 = bunker fuel price in dollars per barrel 1 if American flagship 0 if foreign flagship X5 = size of the port as measured by the U.S. Defense Mapping Agency's Standards X6 = quantity of grain exported from the region during the year of interest The method of least squares was used to fit the model to 140 observations from the period 1978 through 1980. The following results were obtained:

R=0.8979 F = 130.665 a Using a = 0.01, test Ho: B1 B2 B3 B4 B5 B6 B7 = 0. Interpret the results of your test in the context of the problem.

b Binkley and Harrer (American Journal of Agricultural Economics, 1979) estimated a similar rate function by using multiple regression, but they used different independent variables.
The coefficient of determination for their model was 0.46. Compare the explanatory power of the Binkley and Harrer model with that of Martin and Clement.
c According to the least-squares model, do freight charges increase with distance? Do they increase at an increasing rate? Explain.

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t-statistic for i B testing B = 0 Bi 01234567 0 -18.469 -2.76 -0.367 -5.62 2 6.434 3.64 -0.269 -2.25 1.799 12.96 5 50.292 19.14 2.275 1.17 -0.018 -2.69