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Linear Model of Prices, Spring 98

The Data

The following is an attempt to explain the prices of clamps, using data gathered at Brimfield, Spring 1998, on the Saturday. Please note the special nature of the sample, and do not over-generalize the findings.

This analysis of asking prices is based on thirty examples seen at Brimfield in May 1998.  They ranged from 5 inches to 24 inches in length, from unusable to spiffy in condition, from blah to exciting in collector appeal, and from 5$ to 35$ in price.  Most were close to average condition, and many jaw lengths were in the range 10 to 14 inches. Several dealers had multiple examples of the same clamp at a price (I wondered how this happened);  this was taken as a single datum point, and not given multiple weights.  The idea was to analyse "What does a dealer ask for a given clamp?"

The Model

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

Price = Size_Function + Condition_Function

(Notice the use of an additive model, not a multiplicative, for this data.)

I further assume that the Size_Function is linear, a constant plus so much per inch of jaw.

The condition points are defined to be 1 for absolutely useless, 5 for average, and 9 for spiffy. The Condition Function is assumed to be so much per point.

Results

The first analysis is in terms of jaw length alone.  It explains about 58% of the variation in price.  The stating price for a clamp is 6.84$.  Add 1.14$ per inch of jaw length.  

The next analysis is in terms of jaw length, and condition.  It explains about 60% (yes, that is not much improvement) of the variation in price.  The starting price for a clamp is 1.91$.  Add 1.14$ per inch of jaw length.  Add 0.89$ per condition point.  (You can round all these to the nearest dollar, and not lose much. ) 

Collector appeal (based on single sources or non-married items, spindle lengths matched to jaw lengths, rarity of maker) added no explanatory power.  

The predicted value should then be rounded to the nearest 5$ value.  The result will under-estimate expensive clamps, and over-estimate cheap ones.  

Compared to the analysis of September 1997, several things are worthy of note.

  1. The base price is a bit higher.
  2. The value of an added inch is much less, closer to 1$ than 2$.
  3. The round off is to the nearest 5$, not to the higher 5$.  
  4. There seems to be more unexplained variation.  

last revised and validated

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