The intercept as a base fare in a taxi model

Question

A ride-hailing app models a trip's fare against its distance:

$\widehat{\text{fare}} = 3.5 + 2.1 \cdot (\text{miles traveled}).$

What fare does the model predict for a zero-mile trip, and what does that intercept represent in everyday terms?

Accepted Answer

Put distance at zero miles: \widehat{	ext{fare}} = 3.5 + 2.1 	imes 0 = 3.5 	ext{ dollars.} The intercept \3.50 is the fare before you have gone anywhere: the base charge, often called the flag-fall, that you pay just for the ride starting. The slope \2.10 is then the per-mile rate added on top. This intercept is meaningful because a very short trip is realistic, and fare structures really do include a fixed starting charge. So the split is natural: total fare equals a fixed base (intercept) plus a per-mile amount (slope) times the distance. Reading a fitted line this way, fixed part plus r…

The intercept as a base fare in a taxi model

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