One of the many mysteries of the FED1 (and probably many other models) is how camera and lens serials could be related and if there is some pattern that would allow predicting a certain lens serial range from only the camera and vice versa.
I have a FED-S 'd' with an odd 4-digit serial and wondered if the lens serial could shed some light on this issue.
See here:
http://ussrphoto.com/Forum/topic.asp?TOPIC_ID=2348
My hypothesis was that the No.2570 might mean that the first and last digit went missing, making the true serial "12570x".
Getting bored while working on my PhD thesis, I instead ran some statistical analyses on the correlation between camera serials and lens serials in FED-S cameras listed in the Wiki.
I got 48 samples - 17x FED-'c', 27xFED-'d' and 4x FED-'e'.
If we plot the camera s/n on the x-axis and the lens s/n on the y-axis we get a scatterplot which looks like this:

While there are some datapoints far out in the middle of nowhere, most seem to group pretty nicely in the middle. The orange point would be my #2570 assuming it is #125700. To avoid making things even more complicated I have not included this camera in further statistics.
I have marked the 3 models (FED-S 'c', 'd' and 'e') in different colors so we can distinguish them. They form nice separate groups.
Now for a simple linear regression fit:

The red regression line tries to fit a linear relationship between lens and camera s/n depicted in the formula below, while r² measures how well this model fits our actual datapoints - with 1 being a perfect correlation and 0 no correlation at all. We get r² of 0,78 which is pretty good but not extraordinary. Since many datapoints lie far above or below the line it misses most of them.
Next I did something you should not really do in statistics - I excluded all far off datapoints to see if we could get a better fit and thereby a model that would explain most camera:lens relationships. Of the original 48 camera/lens pairs only 33 remained.
Excluded datapoints are drawn in a darker shade.

The red regression line now crosses most of our datapoints resulting in a r² = 0,994
An excellent correlation!
The corresponding formula to calculate lens-camera s/n relationship would be:
Camera = (Lens - 15459) x 10
Lens = 15459 + camera / 10
Feel free to try it out on the FED-S cameras listed in the wiki
Still we see that the datapoints form more of a slight arc than a straight line so I fit a logarithmic curve to the same
25 datapoints, which resulted of an even better match of r² = 0,998

The corresponding formula would be:
Lens = 25200 x log10(camera)-99708
A bit more difficult, but still easy with a calculator. Again you can try it out on any FED-S camera-lens pair in the wiki to see how good the model fits.
The dotted red line is the 95% confidence interval, meaning that according to the model, 95% of samples should lie within these boundaries. Indeed all but one of the datapoints do, only the excluded ones are outside.
Now what does all of this mean?
I'm afraid not very much…
.) I think there is a general relation between lens and camera s/n even though there are exceptions which don't fit in very well
.) The theory that my camera #2570 is missing first and last digits (#125700) seems possible as there are at least 2 examples with similar lens:camera s/n ratios
.) The amount of cameras which seem to have "younger" lenses than average (above red line) seems to be about the same as the amount of cameras which seem to have "older" lenses than average (below red line)
.) By no means do I claim that this model is suitable to determine "matching" or "wrong" camera-lens pairs, we know virtually nothing about how they were paired in the factory. All we can say is, that at least the 2 points high above (1c #76862 / #27890 and 1d #107723 / #31185 as well as the point far below the regression line (1d #158978 / #24761) seem to be quite unusual.
.) There might be a nonlinear relation between camera and lens s/n indicating that in the beginning more lenses than cameras were produced but this is more than speculative.
.) Finally: all of these results are likely to change with more datapoints.
The 48 camera-lens pairs are a good start but twice as much would be a lot better. If you have a FED-S or know someone who does - please submit the camera and lens s/n to the wiki.
If you don't want to reveal the full s/n for whatever reason you can replace the last digits with "x", this is irrelevant for statistics on this scale.
I'd love to do the same thing for "normal" FED1 but therefore I need you to provide a lot more camera:lens s/n to the wiki, currently there almost none listed.
Regards,
Christian
[EDIT]
I managed to restore the images but only from May 23rd 2013 onwards. Therefore the graphs above already contain seven cam/lens pairs which were added by the posters below.




