MATLAB: Derive equation from dataset

Question

Hello!

I have the following four sets of data:

x11=[0  8  32  35  38  46  50  62];
y11=[288  288  224  183  155  29  23  0];
x12=[0  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  26  35  36  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60  61  71];
y12=[1830  1830  1830  1779  1779  1779  1779  1481  1481  1225  1225  1128  1128  995  995  707  707  682  682  661  661  607  515  511  344  344  344  339  339  339  332  332  332  319  319  319  305  305  305  261  261  261  249];
x21=[0  12  18  20  22  23  24  26  31  32  35  37  38  39  48  50  54  57];
y21=[715  715  670  643  639  616  612  581  521  466  421  369  318  326  109  55  7  0];
x22=[0  5  6  9  16  21  22  23  24  35  37  38  40  44  48  58  72  73  77];
y22=[6833  6833  6776  5704  2497  1893  1779  1706  1741  1444  1335  1256  1217  967  947  812  649  593  551];

All x-y pairs have quite the similar shape, with the curve decaying rapidly in the first half and then slowly in the second one.

The goal is to interpolate each x-y pair to derive an equation that will represent the phenomenon.

I tried interp1 and lsqcurvefit but they don't give good enough results. Could someone suggest an alternative way to interpolate these data?

Thank you!

Answer 1

Since you do not know what could be the best function to fit your data with try out the Curve Fitting App with cftool. It lets you fit data using a wide range of functions, apply bounds, weights, etc. You even have the option of making your own equation to fit it with.