# Should you use a regression line predicting drop from new car sale price from car age to set the price of a used car?

A regression showed a strong linear relationship between a car's age (measured in months) and a drop in its price from new.

Your friend sees these figures and thinks he can sell his car at a price obtained from this regression analysis. What would you say to him?

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Please mark homework problems with the homework tag. Also, since these are homework problems, please also indicate what you've tried and what, specifically, you are stuck on. Welcome to the site, by the way! – Macro Jun 24 '12 at 5:28
Consider, if it happened to be a Benz-Patent Motorwagen, ca. 1890, I rather suspect the friend who relied on the regression model price of the car of around -\$200,000 to -\$400,000 (i.e. you need to pay someone upward of a quarter of a million dollars to drag it away - I base this on modern cars losing around \\$10-20k value per decade) might be a little miffed to discover that other people think the value of the Motorwagen is in fact positive and large. – Patrick Caldon Jun 25 '12 at 2:42

I would ask your friend: "Would you buy a car if the only thing you knew about it was its age?" I assume he would say no.

Then I would ask him another question: "Would you be interested in the age of a used car before deciding to purchase it?" I assume he'd say yes.

So, while the age of a used car is relevant to determining its value, it is by no means the only factor driving its market price, pardon the pun. Other things are relevant to its price: mileage, make, model, wear and tear, maintenance history, etc. etc. These other factors are probably more important to the value of the car than its simple age.

Importantly, these other relevant factors are likely to be correlated with a car's age AND correlated with its sale price (i.e. relevant). This is important because it means you are likely to have bias on the coefficient estimate on the effect of age on a car's value/sales price, due to these "omitted variables". Google "omitted variable bias" for more information.

In a nutshell, your friend's model is misattributing all changes in a car's price to its age.

So, I would tell your friend that his linear "car price model" is incomplete and misleading. Selling his car based solely on the results of his silly regression would result in him losing money (and selling quickly!) or not selling the car at all because it's overpriced.

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If the linear relationship can be considered to be valid then the price on the regression line corresponding to the age of your car would appear to be a fair price that you might expect to be able to get for it. But it may turn out that you could get more or less for it. There is no guarantee on any particular price.

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