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Fitted Model of Prices, Fall 99

The following is an attempt to explain the prices of clamps, using data gathered at Brimfield, Fall 1999, on the Saturday. There are 20 clamps in the raw data. Please note the special nature of the sample, and do not over-generalize the findings.

My basic assumption is that the price of a clamp can be estimated from the product of two functions.

Price = Size_Function * Condition_Function

I assume that each size has an individual value, with no given relation to the value of other sizes. (This is in contrast to the Linear Model, where the value depends linearly upon length of jaw.)  This provides 12 +4 parameters to fit to the data, in contrast to 2 + 4, in the Linear Model.  We would expect much better fit.

However, not all combinations of size and condition are in the data set.  This means that the fitting algorithm can sometimes establish values for the Condition_Function based on lots of data, and then compute the Size_Function for a particular clamp to get a perfect fit, with 0 error.  This means that some results are spuriously accurate.

Also, I constrain the Condition_Function so that "good" is worth 1, and the function is monotonic, that is, better condition must not imply lower prices. The conditions are defined to be poor, fair, good, and very good.

• damaged = portions of handles or jaws cut off - not analysed
• poor = threads stripped, spindles jammed, jaws covered with glue or paint
• fair = threads missing, holes drilled in handles, jaws spattered with glue or paint
• good = threads chipped in few places, dings and scratches of normal wear, dust and grime
• very good = no damage to spindles or jaws, polished patina

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