linear least square method to fit the log data

This is what I have so far. Im trying to fit the line (yp) to the data points plotted. Any suggestions of what Im doing wrong? Thanks!

function LogModel()

    t=[1:1:48]';	%% data for time   : column vector
    y=[1.7039;5.9098;10.6923;15.6497;19.0261;23.1650;25.8011;26.2864;28.0410; 28.0070;28.8502;27.0665;27.4650;
        25.9110; 23.3441;21.9954;20.7284;19.1973;17.3139;15.5076;13.7446;12.5922;11.4729;
        10.4418;9.1933;7.6495;7.2157; 6.0907; 5.3670;4.6935;4.3370;3.6142; 3.1584;2.8272;
        2.4244;2.0813; 1.8584; 1.5881; 1.4892;1.2528;1.1232; 1.0128;0.7994;0.7104;0.6527;0.4646;
        0.4801;0.4537];   %% data for auto supply
    n = length(t);

    yln=log(y);
    A=[ones(n,2),t, yln];	%% matrix formed by basis function 1, t at all time data
    coef=inv(A'*A).*(A'*yln);   %% least square solution
    c1=exp(coef(1)); c2=exp(coef(2)); c3=coef(3);    
    tp=[0:0.01:50];		    %% for plotting the model functiona f(t)
    yp=c1.*tp.^(c2).*exp(c3.*tp);
    m=1:n;
    RMSE=norm((1./m).*sum(abs(y-yln).^2)).^(0.5);
    fprintf('RMSE for log model = %12.5e\n', RMSE);

    plot(t,y,'o', tp, yp, '-');

[Jon]

Please use the code button in the MATLAB answers toolbar to copy and paste your code rather than using a screen shot. The screen shot is not clear enough to read, and also it can't be copied and pasted to try running it

[AJM]

Thanks for the suggestion!

Answer 1

[Star Strider]

Are you required to use a log fit for those data?

If not, try this:

objfcn = @(b,x) b(1).*x.*exp(b(2).*x) + b(3).*x.*exp(b(4).*x);

[B,resnrm] = fminsearch(@(b) norm(y - objfcn(b,t)), rand(4,1))

figure
plot(t, y, '.')
hold on
plot(t, objfcn(B,t), '-r')
hold off
grid

This parameter set provided an acceptable fit:

B =
 -22.028821282813610
  -0.268737534521761
  21.509885470995002
  -0.159842817422680

.