Non linear Model Fit (surface energy)

Question

data = {{45.65, 38.9}, {66.87, 47.7}, {79.65, 63.4}, {36.03, 
    25.81}, {64.79, 71.99}};

soln = NonlinearModelFit[data, 
(180/pi)*ArcCos (-1 + (2*(s/l)^0.5)*(Exp[-0.0001247 (l - s)^2])),
{s}, {l}, MaxIterations -> 1000]

I think my syntax is ok, but I cannot find my error. I appreciate any help...

Answer 1

In addition to correcting the syntax errors, having some approaching to starting values of parameters will help get desired fit, e.g. (using the definition from Nasser's correction of syntax errors and the data)

Manipulate[
 Plot[f /. s -> p, {L0, 20, 70}, Epilog -> Point@data], {p, 20, 40}]

so fitting:

nlm = NonlinearModelFit[data, {f, s > 0}, {{s, 35}}, {L0}, 
  MaxIterations -> 1000]

You can best fit for single parameter:

nlm["BestFitParameters"]

yields: {s -> 35.094}

You can explore model using nlm["Properties"] and there are a number of excellent answers if you search this site.

Answer 2

syntax errors and not good choice of l as variable name as it looks like 1. Also need a constraint added to avoid complex values errors

Clear[s, L0];
data = {{45.65, 38.9}, {66.87, 47.7}, {79.65, 63.4}, 
   {36.03, 25.81}, {64.79, 71.99}};
f = (180/Pi)*ArcCos [-1 + (2*(s/L0)^0.5)*(Exp[-0.0001247 (L0 - s)^2])];
model = NonlinearModelFit[data, {f, s > 0}, {s}, {L0}, MaxIterations -> 1000]
   // Normal