# Pairs of values - finding their relationship

Discussion in 'Math' started by atferrari, Jul 16, 2010.

1. ### atferrari Thread Starter AAC Fanatic!

Jan 6, 2004
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Given the following pairs of values:

6 - 6,1399
7 - 6,6319
8 - 7,0898
9 - 7,5199
10 - 7,9267

Is there any effective generic procedure to find out the mathematical relationship between values of each pair?

This have been puzzling me for years and if it exists I do not how to Google for it in English.

I am affraid that the answer is maybe almost in front of my eyes.

Just in case please note I have not generated those values but I suspect they all follow the same law.

2. ### hgmjr Moderator

Jan 28, 2005
9,030
215
You might try putting the number pairs in Microsoft Excel and use the trendline feature to obtain a formula for the number pairs.

hgmjr

3. ### Georacer Moderator

Nov 25, 2009
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Jul 7, 2009
1,585
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Always plot the data. Always. Your brain is a powerful pattern recognizer -- and it gets better with practice.

One of the things that seems to be lost today is the willingness of people to sit down with a pencil and a piece of paper and do simple graphing. When the dinosaurs roamed the earth, we didn't have computers to do this stuff for us, so we just grabbed a piece of paper and did a quick plot. 5 or 10 points are pretty quick to do -- 30 to 40 or more start to get a bit tiresome. But the task puts you in touch with the data in a way a computer can't. Line up a ruler to see how good the data fit a straight line. If it curves, replot on log-log or semilog paper and see if you get a better fit there. If so, you've got a power or exponential/log relationship.

That said, hgmjr's suggestion of a spreadsheet is a good one because most people have one handy (use Open Office if you don't have one). My personal favorite tools are python and matplotlib (I used to use gnuplot, but like matplotlib better).

5. ### atferrari Thread Starter AAC Fanatic!

Jan 6, 2004
2,830
928
THanks for the answers. This is my first time in this subject.

All this started when reading about inductors and using the formulas to calculate dimensions, number of turns, final L, etc.

Those formulas are usually quite complex and include factors of some kind.

People doing that "empirical" thing, do they measure hundred of different inductors and then try to find a formula that relates all variables? If so, how they do obtain the "factors"?

Maybe I am quite far from how this is actually done.

Last edited: Jul 18, 2010