You could use least square approximation - the normal equations. You also could treat it as a non-linear root finding problem - Newton-Raphson method.

Dear Dashty T. Akrawy ,

    Your problem can be linearized and solved as shown in the attached files.

Best Luck

Khaled

Be careful when doing transformations, the solution given above gives the coefficients for the line closest to Y= aX+lnb, which does not necessarily give the function with the smallest error in F for the stated form of F. Squared error sum in F for the given points in this solution is >100000, closer solutions can be readily found manually. a=-26, b=16 is pretty close; sumsq = 10950,4.

Sorry, I am no MATLAB expert, but defining the sum of the error squared from the four arrays of data should not be very difficult, it's easy in EXCEL, finding the (a,b) point that minimizes this value is probably just some solver. fminunc looks like a good candidate.

Best wishes.

Olof 

http://se.mathworks.com/help/optim/ug/fminunc.html

Dear Dashty,

Although  I rarely use Matlab because I usually use Mathematica, but I hope the following video to has helpful examples for you.

Follow the second example technique in this video, I think It will help you to solve your problem.

The second video also has detailed data about fitting curves in Matlab.

With Best Wishes

https://www.youtube.com/watch?v=AQTuJpNXgQ0

https://www.youtube.com/watch?v=NsT5BAofRN0

You can use Genetic algorithm or other optimization method such as PSO or simulated annealing, By choosing a and b as your optimization variable and optimizing the difference between new generated path and the desired one (F) to zero.

You can try "fsolve" in Matlab (a built-in optimization based on the Newton-Rhapson iteration method).