You are fitting 5 data points, using a function that has 4 free parameters. Furthermore, fitting with a double-exponential is problematic, because one of your Y values is zero, which means there is going to be a pathological attempt to balance the exponentially decaying functions, neither of which can ever equal zero. (I'm a little surprised that either a or c is not negative.)
Of course the R^2 is going to be extraordinarily close to 1, because that is just a comparison with the baseline model of picking the average Y. It's a pretty meaningless statistic here. It's a meaningless quibble about the precision of R^2, given the precision of your inputs.
Your goal here is unclear to me, but there is a lot to worry about in your approach here.
load("Calibration1.mat","Calibration1_Cond","Calibration1_Ohm");
[f2,gof2] = fit(Calibration1_Ohm,Calibration1_Cond,'exp2')
f2 =
General model Exp2:
f2(x) = a*exp(b*x) + c*exp(d*x)
Coefficients (with 95% confidence bounds):
a = 7123 (7123, 7123)
b = -0.003526 (-0.003526, -0.003526)
c = 739.5 (739.4, 739.5)
d = -0.0001828 (-0.0001828, -0.0001828)
gof2 =
sse: 7.067779991157303e-07
rsquare: 0.999999999999909
dfe: 1
adjrsquare: 0.999999999999637
rmse: 8.407008975347477e-04
