Top of Site > Clamps as Things > Prices for Clamps > 99 Spring : Fitted Model of Prices
The following is an attempt to explain the prices of clamps, using data gathered at Brimfield, Spring 1999, on the Saturday. There are 35 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. And we achieve a 5% relative error (est-act)/act, compared to 8% for the Linear Model.
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.
The Excel Solver function was set up, and run.
The Size_function is tabulated below:
| $16.87 | $19.16 | $23.29 | $05.00 | $25.09 | $22.84 | $22.46 | $23.57 | $39.13 | $35.44 | $33.75 | $44.59 |
| 4 | 6 | 7 | 8 | 8.5 | 10 | 12 | 14 | 16 | 18 | 20 | 23 |
The condition function has constant value 1 for poor, fair, good, and very good, that is, condition does not impact price.
| Actual | Estimate | Rel. Error |
| $25.00 | $22.84 | -9% |
| $20.00 | $23.57 | 15% |
| $40.00 | $33.75 | -19% |
| $20.00 | $23.29 | 14% |
| $39.00 | $39.13 | 0% |
| $20.00 | $23.29 | 14% |
| $28.00 | $23.29 | -20% |
| $5.00 | $5.00 | 0% |
| $25.00 | $25.09 | 0% |
| $25.00 | $25.09 | 0% |
| $5.00 | $22.84 | 78% |
| $15.00 | $22.84 | 34% |
| $15.00 | $22.84 | 34% |
| $25.00 | $22.84 | -9% |
| $25.00 | $22.84 | -9% |
| $25.00 | $22.84 | -9% |
| $25.00 | $22.84 | -9% |
| $17.00 | $22.46 | 24% |
| $20.00 | $22.46 | 11% |
| $25.00 | $22.46 | -11% |
| $25.00 | $22.46 | -11% |
| $25.00 | $22.46 | -11% |
| $25.00 | $23.57 | -6% |
| $25.00 | $35.44 | 29% |
| $39.00 | $35.44 | -10% |
| $45.00 | $35.44 | -27% |
| $22.00 | $33.75 | 35% |
| $45.00 | $44.59 | -1% |
| $25.00 | $22.84 | -9% |
| $20.00 | $22.46 | 11% |
| $25.00 | $23.57 | -6% |
| $22.00 | $35.44 | 38% |
| average | average | average |
| $24.59 | $25.91 | 5% |
last revised and validated
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