Distance is associated with both the type of bike and commute time, so if we are really interested in which type of bike is faster, we should account for the confounding variable Distance. Output regressing Minutes on both BikeSteel and Distance (measured in miles) is shown below.

Residual standard error: 5.133 on 53 degrees of freedom

Multiple R-squared: 0.161, Adjusted R-squared: 0.1294

F-statistic: 5.087 on 2 and 53 DF, p-value: 0.00953

(a) Interpret the coefficient of BikeSteel.
(b) Interpret the coefficient of Distance.
(c) What is the predicted commute time for a 27 mile commute on the steel bike? On the carbon bike?

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.

Exercise C.72 on page 456

Dr. Jeremy Groves, a British anaesthetist, often uses a bicycle for his 27-mile round-trip commute to work. He bought an expensive, lightweight, carbon bike but also had an older, heavier, steel bike€”so he decided to do an experiment. On each day he biked to work he flipped a coin to determine which bike he would ride. He used a bicycle computer to accurately record the commute time each day as well as his maximum and average speed for the day. His data for 56 days are stored in BikeCommute. The type of bicycle (carbon or steel) is in the Bike variable and his time (in minutes) is stored in Minutes. Do the data provide evidence that mean commute time differs between the two types of bikes?

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Response: Minutes Coefficients: Estimate Std. Error 90.065 1.895 3.290 Pr(> It|) t value -1.961 1.884 |(Intercept) -176.620 BikeSteel Distance 0.05514 3.571 0.06500 0.00258 ** 10.410 3.164