A depreciation slope, used-car value by age

Question

A dealership models a used car's value against its age:

$\widehat{\text{value}} = 18000 - 1500 \cdot (\text{age in years}).$

How much does the model predict the value drops if the car is 4 years older, and what does the slope of -1500 tell you?

Accepted Answer

The slope -1500 means: each extra year of age is associated with about \1{,}500 less predicted value. The negative sign says value falls as age rises, which matches how cars actually behave. Four more years of age multiplies the per-year drop: -1500 	imes 4 = -6000, a predicted decrease of about \6{,}000. The intercept \18{,}000 (the model's guess for a brand-new car, age 0) is not needed for a change, only for a level. One honest caveat: a straight line assumes the same dollar drop every year forever, which cannot be literally true (value cannot go below zero, and old cars often depreciate …

A depreciation slope, used-car value by age

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