Fit an exponential curve

Hi, I have a data set like this

x=[6.5 2.45 2.7 1.85 2.25 1.35 1.4 1 0.7 .475 .66 .475];

y=[0.40 0.80 1 1.40 1.80 2.50 3.00 4.00 6.00 7.00 8.00 9.00];

and I want to fit an exponential curve like this: y=6.5*e^(-a*x) to my data set. Since, the value 6.5 is constant I do not get my desired reslut from cftool. Does anybody know how can I solve this?

Answer 1

[Star Strider]

Try this —

x=[6.5 2.45 2.7 1.85 2.25 1.35 1.4 1 0.7 .475 .66 .475];
y=[0.40 0.80 1 1.40 1.80 2.50 3.00 4.00 6.00 7.00 8.00 9.00];
[fitobject,gof,output] = fit(x(:),y(:),'6.5*exp(-a*x)')

Warning: Start point not provided, choosing random start point.

fitobject = 
     General model:
     fitobject(x) = 6.5*exp(-a*x)
     Coefficients (with 95% confidence bounds):
       a =      0.4585  (0.1848, 0.7323)

gof = struct with fields:
           sse: 35.1246
       rsquare: 0.6496
           dfe: 11
    adjrsquare: 0.6496
          rmse: 1.7869

output = struct with fields:
           numobs: 12
         numparam: 1
        residuals: [12×1 double]
         Jacobian: [12×1 double]
         exitflag: 3
    firstorderopt: 0.0109
       iterations: 7
        funcCount: 16
     cgiterations: 0
        algorithm: 'trust-region-reflective'
         stepsize: 2.6832e-04
          message: 'Success, but fitting stopped because change in residuals less than tolerance (TolFun).'

figure
plot(fitobject, x, y, 'p')
grid

.

[Sahar khalili]

Thank you so much. Yes, it works.

[Star Strider]

As always, my pleasure!

.

Answer 2

[Sulaymon Eshkabilov]

1st of all, your data's good fit is not 6.5*exp(a*x) that is why cftool is giving you the best fit that differs from your expected 6.5*exp(-a*x).

If you're aiming to get a fit for 6.5*exp(-a*x) then use "custom equation" option and set it to 6.5*exp(-a*x).