It does not happen. IF you pass in exactly the same data (in the same order) into polyfit, calling polyfit the same way each time, it will return exactly the same result, time after time after time.
If you change the data in any way, then of course you will get different results. In fact, even changing the order of the data points is sufficient.
x = randn(100,1);
y = randn(100,1);
P1 =polyfit(x,y,1);
s = randperm(100);
P2 = polyfit(x(s),y(s),1);
P1 == P2
ans =
1×2 logical array
0 0
P1 - P2
ans =
1.7347e-17 6.9389e-17
So all I did was permute the data. Change the order of ANY set of floating point additions, subtracts, multiplies, etc., and you can get a slightly different result.
0.3 - 0.2 - 0.1
ans =
-2.7756e-17
-0.1 - 0.2 + 0.3
ans =
-5.5511e-17
What I have described is NOT due to the accuracy of polyfit, but simply a basic feature of floating point arithmetic. If you are having a different problem, I cannot guess what it is, since you have told us virtually nothing about what you really did. People screw up all sorts of things in all sorts of different ways. So without knowing true specifics, all we can do is make guesses.
