Problem fitting with lsqcurvefit

im getting the following error while executing the code "Index exceeds the number of array elements (2)", the goal is to fit a curve to points using a certain Formula:

[name,path]=uigetfile({'*.xlsx'});

Error using matlab.internal.lang.capability.Capability.require
Support for Java user interfaces is required, which is not available on this platform.

Error in uigetfile (line 117)
Capability.require(Capability.Swing);

filename = [path name];
opts = detectImportOptions(filename);
preview(filename,opts);
newtable = readtable(filename);
x = newtable{:,1};
y = newtable{:,2};
fun = @(w,x) sqrt(w(1)^2+w(2)^2*(x-w(3))^2)
x0 = [1 1];
w = lsqcurvefit(fun,x0,x,y)

Answer 1

[Torsten]

M = [26	93
    27	67.9
    28	54.5
    29	20.5
    29.1	20.6
    29.2	17.6
    29.3	15.7
    29.4	13
    29.5	12
    29.6	9.2
    29.7	8.7
    29.8	6
    29.9	5.4
    30	6.3
    30.1	7.2
    30.2	8.3
    30.3	12.3
    30.4	12.4
    30.5	16.4
    30.6	18.3
    30.7	21.5
    30.8	23.7
    30.9	27.6
    31	28.7
    31.1	32.1
    31.2	34.6
    31.3	36.3
    31.4	39.1
    31.5	40.6
    31.6	44.2
    31.7	48.2
    31.8	50.5
    31.9	53.8
    32	55.9
    33	77.1];
x = M(:,1);
y = M(:,2);
fun = @(w) sqrt(w(1)^2+w(2)^2*(x-w(3)).^2);
fun2 = @(w)fun(w)-y;
w0 = [1 1 1];
w = lsqnonlin(fun2,w0)

Local minimum possible.

lsqnonlin stopped because the final change in the sum of squares relative to 
its initial value is less than the value of the function tolerance.

w = 1×3

5.7432 24.9821 29.8623

hold on
plot(x,y,'o')
plot(x,fun(w))
hold off

[Hussam Saddour]

thanx!

Answer 2

[Matt J]

Your model has 3 unknowns w(1), w(2), and w(3). However, you are only providing initial guesses x0 for 2 of these variables.