What a regression intercept means, the electric bill

Question

A utility models a household's monthly electricity bill against the number of people living there:

$\widehat{\text{bill}} = 30 + 22 \cdot (\text{number of people}).$

What does the model predict for a home with zero people, and is that intercept a meaningful number here?

Accepted Answer

The intercept is the value the line gives when the input is zero. Plug in 0 people: \widehat{	ext{bill}} = 30 + 22 	imes 0 = 30 	ext{ dollars.} So the model predicts a \30 bill for a home with nobody in it. Is that meaningful? Here, yes, and it has a natural reading: it is the fixed part of the bill that does not depend on how many people live there, things like the standing connection charge and always-on appliances (a fridge, a router). Each person then adds \22 on top. The reason it is meaningful in this problem is that zero is a sensible, real input: an empty but connected home genuine…

What a regression intercept means, the electric bill

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