How can I make an exponential fit using two points of my data.

I have a data that I try to fit which and I get this plot using curve fitting tool box.

x = (length_wg0*10e5)'
y = T_forward_10nm
f = fit (x, y, 'exp1' )    
plot (f, x, y)
set(gca, 'YDir','reverse')

but what I want to get is the curve that passes from the first point. Shown in the graph below.

How can I do it?

[Alex Sha]

if take your data as:

x=[0.253629,16.3269,31.0374,58.454,116.959,175.756,231.876,289.34];

y=1.0033,0.969485,0.959453,0.939367,0.00178676,0.00245301,0.00648837,0.00374009];

The fitting function may be taken as:

y=Vmax*x^n/(k^n+x^n)

by adding the constrained condition of passing first point, the results will be:

Root of Mean Square Error (RMSE): 0.0197683134500478
Sum of Squared Residual: 0.00312628973327472
Correlation Coef. (R): 0.999589835353114
R-Square: 0.999179838941266

Parameter	Best Estimate
----------	-------------
vmax	1.00329999999224
n	-12.6896697136722
k	72.238637792372

Answer 1

[the cyclist]

You can use the 'Weights' Name-Value pair, and heavily weight the first point. Here is a made-up example. Notice how f2 passes through the first point.

x = [0 20 40 60 100 120 140 160]';
y = [1 2 3 4 10 11 12 13]';

f1 = fit (x, y, 'exp1' );
f2 = fit (x, y, 'exp1', 'Weights',[1000 1 1 1 1 1 1 1] );

figure
plot (f1, x, y)

figure
plot (f2, x, y)

[Vahram Voskerchyan]

Thanks a lot for the answer, this worked for my case also. Can you elaborate a little bit what are these [1000 1 1 1 1 1 1 1] if possible?

[the cyclist]

I suggest you read the documentation for the fit function. Scroll down to "Input Arguments -- Name-Value Pair Arguments".

That is a vector of weights, indicating that the error in the first point should be weighted more heavily (by a factor of 1000) than all the other points (which are weighted equally).