# How much does the value of a car depreciate due to time (only), and mileage (only)?

I have a database of second hand cars. It contains (among other things) the asking price, the mileage, the fuel consumption and the year it was built.

I would like to know how much the value depreciates due to time (only), and due to mileage (only).

So for car model X, I'd like to know: - how much value the car loses with each year - how much value the car loses with each mile

My dated statistical knowledge from college tells me that I can do an OLS regression with price as dependent variable and year as independent variable, controlling for mileage. And a regression analysis with price as dependent variable and mileage as independent variable, controlling for year.

Would this work? How much observations would I need per car model? Year seems to have an exponential effect on value, and is it an ordinal variable that creates problems in such a model? Are there any other solutions?

Any help would be greatly appreciated.

• What do you mean when you say fit a model with one independent variable, controlling for the other -- as opposed to fitting a multiple regression model with both of them as predictors? Including model would help explain a lot of variation, so it should be included. How big is your database? Wouldn't you want to just use all the data -- or all the data for a certain range of model years? – rvl Sep 6 '14 at 17:49
• A thing to consider is centring your predictors to have mean $0$. This makes the model's intercept interpretable as the expected $y$ when the predictor variables are set to their means. Otherwise, the intercept is interpreted as the expected $y$ when the predictors are set to 0 (which can be unrealistic - eg. no cars were made in year $0$ :D) Finally, as pointed by @RussLenth (+1), do you have a reason for not utilizing a multiple regression model? – usεr11852 Sep 6 '14 at 21:39