The commute is about 27 miles round trip, but actual biking distances, Distance, ranged from 25.86 to 27.52 miles. Output regressing Distance on BikeSteel is given below. Is the predicted distance higher for the carbon or the steel bike? By how much? Is this difference significant?

Residual standard error: 0.2123 on 54 degrees of freedom

Multiple R-squared: 0.473, Adjusted R-squared: 0.4633

F-statistic: 48.48 on 1 and 54 DF, p-value: 4.741e-09

Refer to data introduced in Exercise C.72 on page 456 from an experiment in which Dr. Jeremy Groves flipped a coin each day to randomly decide whether to ride his 20.9 lb (9.5 kg) carbon bike or his 29.75 lb (13.5 kg) steel bike for his 27 mile round trip commute. His data for 56 days are stored in BikeCommute. The type of bicycle (carbon or steel) is the Bike variable and his time (in minutes) is stored in Minutes. We€™ve created a new variable BikeSteel, which is 1 if the ride is on a steel bike and 0 if the ride is on a carbon bike.

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Response: Distance Coefficients: t value 657.363 -6.962 Std. Error 0.04164 0.05689 Estimate 27.37446 -0.39613 Pr(> It)) < 2e-16 *** 4.74e-09 *** |(Intercept) BikeSteel