Programmatic polynomial fitting with mutliple measurements and known parameters

If I understand this correctly, you want model something as y = f(x1,x2,x3,x4), where f is a polynomial of some sort.

You have 70 data points, and if we call your 7x10 response matrix y, then it is arranged like this:

f(1.92, 275, 0, 100) -> y(1,1)
f(1.92, 275, 0, 90) -> y(1,2)
f(1.92, 275, 0, 80) -> y(1,3)
.
.
f(1.82, 160, 22, 100] -> y(2,1)
f(1.82, 160, 22, 90] -> y(2,2)
f(1.82, 160, 22, 80] -> y(2,3)
.
.
f(1.84, 107, 100, 10) -> y(7,10)

In that case, the first step is to put your x's into a 70x4 matrix like this.

x1=[ 1.92683450920000 1.82794091830000 2.01642468230000 1.75600069780000  1.75466924060000 1.83419721490000 1.84217366130000];
x2=[275 160 26 76 30 133 107];
x3=[ 0 22 42 40 67 80 100];
x4=[ 100 90 80 70 60 50 40 30 20 10];

X = []; 

for n = 1:7; 
X = [X; repmat([x1(n) x2(n) x3(n)],10,1)]; 
end; 
X(:,4) = repmat(x4',7,1);

Now X is a 70x4 matrix representing your inputs.

Next turn your 7x10 matrix y into a 70x1 column vector representing your results.

Y = y(:);

Now there are many ways to fit depending of what form of f you want to use. If you have the latest release of MATLAB along with the Statistics Toolbox installed, a simple first order linear model could be solved like this:

LinearModel.fit(X,Y)

This yields a model of the form y = A*x1 + B*x2 + C*x3 + D*x4 + E

For higher order polynomials, see the help for LinearModel.fit.

You have very little information here in terms of combinations of x1, x2, x3. Essentially you will be able to estimate no more than a linear model in those parameters. Do not try to go higher than that, although you do have sufficient information to try something more complex in x4.