Predicting motorcycle prices

I'm in the market for a new motorcycle and have been looking at the BMW R1150GS/R1200GS. Like cars, motorcycles have a lot of depreciation the minute they pull off the lot, and because you're fairly likely to drop your bike anyway, most people I know figure you might as well buy pre-dropped and look for a used model. But once you're buying used you have the problem of figuring out how much you should pay. KBB motorcycles isn't much help here because the market is small and the mileage varies a lot.

An alternate approach is to mine the available data on what people are offering vehicles for and use this to build an analytical model for predicting prices; this lets us figure out what the appropriate asking (which isn't the same as fair; more on this later) price for a new vehicle is and identify outliers in either direction.

Below, you can find the list of the relevant bikes on sale on CL for the past week or so:

	Asking	Model	Year	Mileage
1	7650	1150GS	2002	25000
2	7900	1150GS	2001	54000
3	14500	1200GSA	2006	3700
4	8500	1200GS	2005	54000
5	13700	1200GS	2007	3658
6	7400	1150GSA	2004	60000
7	5500	1100GS	1996	23000
8	11500	1200GS	2005	12000
9	7200	1150GS	2002	40000
10	11950	1200GS	2008	29000
11	9600	1200GS	2005	39000

I used a simple OLS regression model to fit this data, using the model year and mileage for the bike. The result is:

summary(fit2)

Call:
lm(formula = d2$Asking ~ d2$Year + d2$Mileage)

Residuals:
      Min        1Q    Median        3Q       Max 
-1360.040  -353.520  -150.358     2.140  1708.510 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -1.201e+06  1.889e+05  -6.359 0.000218 ***
d2$Year      6.056e+02  9.423e+01   6.426 0.000203 ***
d2$Mileage  -7.631e-02  1.578e-02  -4.836 0.001294 ** 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 975.1 on 8 degrees of freedom
Multiple R-squared: 0.9108,	Adjusted R-squared: 0.8885 
F-statistic: 40.84 on 2 and 8 DF,  p-value: 6.335e-05 

Our model predicts that each year the bike is on the road it loses about $600 in value and that it loses about $76 for each 1000 miles it has. [Note that I'm treating mileage and age as independent variables; it might make more sense to try to estimate "excess" mileage over some base value, but I don't have the baseline data I would need.] In any case, we're doing pretty well here: with only two predictors we are accounting for around 90% of the price variation. We can see this visually by plotting the price points against the best fit plane, as below:

s3d <- scatterplot3d(d2$Asking~d2$Year+d2$Mileage,xlab="Year",ylab="Mileage",zlab="Asking")
orig <- s3d$xyz.convert(d2$Year,d2$Mileage,d2$Asking)
plane <- s3d$xyz.convert(d2$Year,d2$Mileage,fitted(fit))
i.negpos <- 1 + (resid(fit)>0)
segments(orig$x,orig$y, plane$x,plane$y, col=c("blue","red")[i.negpos],lty=(2:1)[i.negpos])
s3d$plane3d(fit)

(code ripped off from here).

Points above the plane (shown with red lines) are likely too expensive and points below (with blue lines) are worth checking out to see if they're good deals.

Obviously, we're excluding a lot of variables here. We haven't captured the condition of the bike, how desperate/motivated the seller is to get rid of it, what accessories it has, etc. Looking more closely at the data, the two most comparatively expensive bikes seem to come with a few more accessories, so this may have led the owners to think they could extract more money (I don't think this is really true, however, since often those items are valuable only to the original owner). For the purposes of selecting good deals, we would also like to know how flexible the seller's price is. It's possible that someone lowballing the price will also be less flexible because they've already built that discount into their price. On the other hand, they could be more motivated, so that could cut in the other direction. It would be interested to get secondary data on how much these bikes actually sell for [you could get some of that information by seeing if repeated postings have lower prices], but while that data is available for houses I don't think it is for bikes.