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An economist wanted to analyze the relationship between the speed of a car (x) and its gas mileage (y). As an experiment a car is operated at several different speeds and for each speed the gas mileage is measured. These data are shown below.
Speed 25 35 45 50 60 65 70
Gas Mileage 40 39 37 33 30 27 25
(a) Determine the least squares regression line.
(b) Estimate the gas mileage of a car traveling 70 mph.
(1) Does this data provide sufficient evidence at the 5% significance level to infer that a linear relationship exists between speed and gas mileage?(Use test for ? )
(2) Predict with 99% confidence the gas mileage of a car traveling 55 mph.
(3) Calculate the coefficient of determination and interpret its value.
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