Fitting exponent with gnuplot -


I am trying to fit the data under the form - I am most interested in 'C' (I know That C ≈ 1/8, B ≈ 3) but want to remove all these values ​​from the data.

Formula: 

  y = a * (xb) ** c

Values.txt: 

  # "values.txt" 2.000000e + 00 6.058411e-04 2.200000e + 00 5.335520e-04 2.400000e + 00 3.509583e-03 2.600000e + 00 1.655943e-03 2.800000e + 00 1.995418e-03 3.000000e + 00 9.437851e-04 3.200000e + 00 5.51615 9-04 3.400000e + 00 6.765981e-04 3.600000e + 00 3.860859e -04 3.800000e + 00 2.942881e-04 4.000000e + 00 5.039975e-04 4.200000e + 00 3.962199e-04 4.400000e + 00 4.659717e-04 4.600000e + 00 2.892683e-04 4.800000e + 00 2.248839e-04 5.000000e + 00 2.536980e-04

I I tried to use the following commands in gnuplot, but i am not having a meaningful result 

  f (x) = a * (xb) ** cb = 3 c = 1/8 fit f (X) "values.txt" by a, b, c

what to do These values, know the best way to remove? I will not provide initial estimates for 'B' & amp; nbsp; If possible, then 'C'.

Thank you, J

Fitting your problem to function b getting you can express your equation as a linear function in log (xb) , after which the fittings are trivial: 

  b = 3f (x) = c0 + c1 * x ft f (x) "values.txt" (log ($ 1-b)) :( log ($ 2)) through c0, c1a = xp (c ) C = C1

As you see, you will have to provide b , but for the other parameters, Does not require Uman because it is a trivial linear fit.

Now, I will suggest that how well you check a series of values ​​of b and the fitting for each value. Gnuplot gives you an error in the fitting parameter. You can then look at the whole code ( error_c0 + error_c1 ) as the function of b and find that the b error is minimal About the optimum b curve error_c0 + error_c1 versus b can be quadratic and be less than b_opt . After this, from the above code, b = b_opt and "/ html>

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