A negative slope, rent and distance from downtown

Question

A rental listings model relates monthly rent to how far the apartment sits from the city center:

$\widehat{\text{rent}} = 2200 - 90 \cdot (\text{miles from center}).$

If one apartment is 3 miles farther out than another, what does the model predict about the difference in rent, and what does the slope of -90 mean?

Accepted Answer

A negative slope simply means the output goes down as the input goes up. Here the slope -90 means: each extra mile from the center is associated with about \90 less predicted rent. Move 3 miles farther out and multiply: -90 	imes 3 = -270, so the model predicts about \270 lower rent for the apartment that is 3 miles farther from downtown. The minus sign is the whole point: it tells you the direction of the effect. If you dropped it you would wrongly say rent rises. As always with a difference, the intercept \2200 plays no role. It would matter only if you wanted an actual rent figure at a sp…

A negative slope, rent and distance from downtown

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