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.