The management science staff of a grocery products manufacturer is developing a linear programming model for the production and distribution of its cereal products. The model ­requires transportation costs for a very large number of origins and destinations. It is impractical to do the detailed tariff analysis for every possible combination, so a sample of 48 routes is ­selected. For each route, the mileage x and shipping rate y (in dollars per 100 pounds) are found. The data are as follows:

a. Obtain the regression equation and the residual standard deviation.
b. Calculate a 90% confidence interval for the true slope.

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Mileage 50 60 80 90 90 100 100 100 110 10 110 Rate 12.7 13.0 13.7 14.1 14.6 14.1 15.6 149 14.5 15.3 155 15.9 Mileage 120 120 120 120130 130 140 150 170 1 200 230 Rate 164 11 16.0 15.8 16.0 167 172 175 18.6 19.3 204 218 Mileage 260 300 330 340 370 400 440 440 480 510 540 600 Rate 24.7 24.7 180 27.1 28.2 306 318 324 345 35.0 36.3 41.4 Mileage 650 700 720 760 800 810 850 920 960 1050 1,200 1650 Rate 46.4 45.8 46.6 48.0 51.7 502 53.6 57.9 56.1 58.7 758 89.0