In Exercise 10.66, regressing Minutes on BikeSteel, the coefficient for BikeSteel is negative. In Exercise 10.68, regressing Minutes on BikeSteel and Distance, the coefficient for BikeSteel is positive.

(a) A biker interested in whether carbon or steel bikes are faster is not sure what to make of these seemingly contradictory results. Explain to her why the coefficient can be negative in one model and positive in the other.
(b) If we were to regress the variable AvgSpeed = Distance/Minutes on BikeSteel, would the coefficient for BikeSteel be negative or positive? Explain. (You should not need technology to answer this question.)