I think you already have enough in the two fits already provided. The last one is like the icing. The third one has been resisting any polynomial or rational fit that I can come up with. From a numerical point of view I am done but it seems that the statisticians have already solved this problem in the general case. I have been reading up on their methods and so far it has been slow going.
I will need more time. Please hold on.
]]>To get a relationship between just the 2 meters and the 90 percentile data seems obvious now but the obvious things are always wrong.
]]>Have run into some problems, a certain piece of software is doing the calculation of the residuals in an unusual way. It is probably not wrong but just not what I expected it to do. This has slowed the work down. A whole day and a half has been wasted. Now I must start again. I am sorry.
Some new relationships have been found.
Where :
f is the fifty percentile data
i1 is instrument or meter 1
i2 is instrument or meter 2
This relation has a maximum error or 4.54.
]]>Will be taking a little break now to rest my eyes. I will resume work on it later. Then we can talk about trying to use effectively, alse seeing whether it has any predictive power...
]]>Please give me lots of time to check the figures. There are undoubtedly typos.
would
you be able to explain to me what you did to get to this point?
It is totally an industrial strength solution. Explaining it is harder than doing it. Lots of computing and lots of guesswork. There is one piece of math in here that is unique.
Long time ago in galaxy far, far away, I happened to discover a method of curve fitting that achieved the much desired minimax fit. It is fairly common for continuous data but I never saw anything like my method for discrete points. I went around for a long time using it and hiding my discovery. I named it ABput and used it to compress an entire poker simulation into several formulas. You can imagine my sorrow when I finally found out that a great numerical analyst named Remez had not only done it first but did it better.
You will be happy to know I used it on your problem.
]]>i1 is the first meter reading.
i2 is the second meter reading.
f is the fifty percentile data.
n is the ninety percentile data.
The equation is:
Where:
This has a maximum error of 15.45 for any particular point. Most are a lot less. It is fairly obvious from the residuals that a better fit is still possible.
Please allow me some time to check out the values. Lots of copying can result in errors.
]]>Sorry, I could not get back to you sooner, but my internet went out for 2 1/2 hours. The largest error I have now is around 35. My predicted value is off by 35 from one of your data values. The rest are close I am still trying to reduce these residuals as they are called down. Please hold on it will take time.
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