Optimizing Simultaneous Equations for Experimental Data Analysis

[Just some guy]

Hi,

I have the results from an experiment I carried out and basically I have a formula with 2 unknown variables in it, and 6 sets of data. Because this data is from an experiment it isn't perfect and I was wondering about the method that determines the value of the 2 constants that would best fit the data.

(to elaborate, I was plugging an AC waveform into a circuit with an inductor and measuring the current and voltage - from this I got the impedance and the frequency. Since Z^2 = R^2+X^2 where X = inductive reactance, I want to find the best fitting value of R and L with 6 sets of data for Z and the frequency of the oscillator (since X=2pifL)


Cheers,
Zachary.

 

[Just some guy]

ok, to elaborate some more I have these sets of data:

f=496
z=5.99

f=997
z=9.10

f=1410
z=11.3

f=1900
z=13.5

f=2377
z=15.3

f=2800
z=16.8

And the formula Z^2 = R^2 + (2pifL)^2

How do I find which values of R and L which best fit this data?

 

[Ouabache]

Do you have thoughts on how you may approach this question? If you are still stymied, just take an educated guess on the procedure. Then we can help steer you in a successful direction.

 

[0rthodontist]

What does pifL mean? Is that pi * f * L? If so then you could let x = f^2 and y = z^2 and do a linear regression.