Trying to apply a general exponential fit to data

Hello

I am using CFtool for fitting an exponential curve to a set of data. However, whenever I try to use the coefficients (A,B,C,D) and apply them back to my data using the biexponential general model (f(x) = a*exp(b*x) + c*exp(d*x) ) the resultant curve is nothing like the results shown in cftool

Here is my data and the resulting coefficients:

X = 0.301 2.301 4.301 6.301 8.301 10.301 12.301 14.301 16.301 18.301

Y = 918.8 448.3 192.9 132.3 93.7 211.3 290.3 257.2 80.8 154.3

General model Exp2:

f(x) = a*exp(b*x) + c*exp(d*x)

where x is normalized by mean 9.301 and std 6.055

Coefficients (with 95% confidence bounds):

a = 5.095 (-22.48, 32.67)

b = -3.391 (-6.88, 0.09925)

c = 160.8 (32.15, 289.4)

d = 0.08843 (-0.7854, 0.9622)

I would greatly appreciate your help.

Best,

Alonso Figueroa

Answer 1

[Torsten]

As written in the output from CFtool: x is normalized by mean 9.301 and std 6.055.

Thus, for x in the equation, you have to insert (x-mean(x))/std(x) to get the expected curve.

X = [0.301	2.301	4.301	6.301	8.301	10.301	12.301	14.301	16.301	18.301].';
Y = [918.8	448.3	192.9	132.3	93.7	211.3	290.3	257.2	80.8	154.3].';
f = fit(X,Y,'exp2','Normalize','on')

f = 
     General model Exp2:
     f(x) = a*exp(b*x) + c*exp(d*x)
       where x is normalized by mean 9.301 and std 6.055
     Coefficients (with 95% confidence bounds):
       a =        5.09  (-22.46, 32.64)
       b =      -3.391  (-6.882, 0.09921)
       c =       160.7  (32.16, 289.3)
       d =     0.08831  (-0.7855, 0.9621)

X_normalized = (X-mean(X))/std(X);
Y_model = f.a*exp(f.b*X_normalized)+f.c*exp(f.d*X_normalized);
hold on
plot(X,Y,'o')
plot(X,Y_model)
hold off

[Luis FigueroaFernandez]

Thank you So much Thorsten, I thought I was going insane over here.

Best,

Alonso Figueroa