Top of Site > Clamps as Things > Prices for Clamps > 1999 Fall : Linear Model of Prices
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 further assume that the Size_Function is linear, a constant plus so much per inch of jaw. An alternative is explored in the Fitted Model.
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 -$0.13 for existence, plus $1.99 per
inch.
The tabulated value for each size is
| 7.81 | 11.78 | 13.76 | 16.74 | 19.72 | 23.69 | 27.66 | 31.63 | 39.57 |
| 4 | 6 | 7 | 8.5 | 10 | 12 | 14 | 16 | 20 |
The condition function has constant value 1 for poor, fair, good, and very good, that is, condition does not impact price.
| Actual | Estimated | Relative Error |
| $10.00 | $8.19 | 22% |
| $15.00 | $19.22 | -22% |
| $20.00 | $27.50 | -27% |
| $30.00 | $27.50 | 9% |
| $25.00 | $19.72 | 27% |
| $25.00 | $23.69 | 6% |
| $25.00 | $23.69 | 6% |
| $15.00 | $27.66 | -46% |
| $25.00 | $27.66 | -10% |
| $30.00 | $27.66 | 8% |
| $7.00 | $7.81 | -10% |
| $7.00 | $7.81 | -10% |
| $7.00 | $7.81 | -10% |
| $10.00 | $13.76 | -27% |
| $15.00 | $13.76 | 9% |
| $15.00 | $31.63 | -53% |
| $20.00 | $16.74 | 19% |
| $25.00 | $19.72 | 27% |
| $18.00 | $19.72 | -9% |
| $18.00 | $19.72 | -9% |
| average | average | average |
| $18.10 | $19.55 | -5% |
last revised and validated
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