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Linear Model of Prices, 99 Spring

The Data

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.

The Model

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. (For an alternate assumption, see 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 Findings

Size

The size-function is $12.30 for existence, plus $1.14 per inch.


Tabluation of value for each size

$16.87 

$19.16 

$20.31 

$21.45 

$22.02 

$23.74 

$26.03 

$28.31 

$30.60 

$32.89 

$35.18 

$38.61 

4

6

7

8

8.5

10

12

14

16

18

20

23

Condition

The condition function has constant value 1 for poor, fair, good, and very good, that is, condition does not impact price.


The Fit

With these functions, how well can we estimate actual asking prices? The table below gives the estimates for each clamp, and the overall average. The estimation is particularly poor for the low priced clamps, although overall the relative error (est-act)/est is only 8% on the high side.

How Good are the Estimates?

Actual Estimated Rel. Error
$25.00 $23.74 -5%
$20.00 $28.31 29%
$40.00 $35.18 -14%
$20.00 $20.31 2%
$39.00 $30.60 -27%
$20.00 $20.31 2%
$28.00 $20.31 -38%
$5.00 $21.45 77%
$25.00 $22.02 -14%
$25.00 $22.02 -14%
$5.00 $23.74 79%
$15.00 $23.74 37%
$15.00 $23.74 37%
$25.00 $23.74 -5%
$25.00 $23.74 -5%
$25.00 $23.74 -5%
$25.00 $23.74 -5%
$17.00 $26.03 35%
$20.00 $26.03 23%
$25.00 $26.03 4%
$25.00 $26.03 4%
$25.00 $26.03 4%
$25.00 $28.31 12%
$25.00 $32.89 24%
$39.00 $32.89 -19%
$45.00 $32.89 -37%
$22.00 $35.18 37%
$45.00 $38.61 -17%
$25.00 $23.74 -5%
$20.00 $26.03 23%
$25.00 $28.31 12%
$22.00 $32.89 33%
average  average  average 
$24.59 $26.63 8%

last revised and validated

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