How to do 4-D Equivalent of 3-D surface fitting ?

I have 3 independent parameters and 1 dependent parameter. I would like to find a equation for the best fit of the data. Something similar to curve fitting but which takes 4 varriables.

For example,

Y=[3, 9, 2, -3, -3, -1, 0, 4, 3, -4, 2, 3, 3, 5, 5, -2, 6, 5, 2, 7, 4, 4, 3, 4, 8];

a=[59.76169, 48.94491, 109.2504, 41.13384, 119.1513, 128.789, 72.16298, 134.1063, 103.9212, 151.3553, 114.1976, 105.0117, 87.97976, 85.17248, 157.5749, 144.1309, 102.5106, 118.2031, 90.04979, 73.26943, 51.56135, 113.2476, 90.25419, 52.70711, 65.29004];

b=[34.03245, 62.00777, 65.26073, 35.14924, 60.43905, 13.2536, 81.35409, 42.96087, 20.11143, 51.95549, 48.69367, 103.4722, 86.34748, 36.3594, 34.22509, 29.06005, 66.28552, 50.34202, 68.52923, 13.37169, 79.57046, 16.90741, 19.23409, 10.61589, 56.88702];

c=[162.0816, 79.415, 83.82825, 27.93687, 40.62826, 82.24879, 138.5984, 90.97681, 99.80004, 67.54529, 94.40013, 122.3847, 111.1037, 73.3585, 97.30746, 122.7819, 173.2984, 123.2553, 70.9507, 124.8281, 109.5493, 107.5167, 104.1119, 100.0313, 98.01023];

How to make a equation or model which can give a output Y for input a,b,c ?

Answer 1

[Matt J]

You can lsqcurvefit if you have Optimization Toolbox.

If not, then you might be able to use fminsearch, if you have only a small number of model parameters.