Estimation of errors from solving A\B=X

I have a few vectors which by a linear combination fits a different vector quite nice. E.g. I solve the equation

[vec1 vec2 vec3 vec4]*X=vec_dat.

Now I would like to get a feeling of the confidence level on the coefficients returned by matlab.

One thing I have tried is

c=coef(1)
l=linspace(c-c/5,c+c/5,20);
for i=1:length(l)
  l(i);
  sim=l(i).*a+coef(2).*b+coef(3).*g+coef(4).*d;
  RMSa(i)=sum(sqrt((dat-sim).^2));
end

I observe parabolas with different 2nd derivatives for each of the coefficients i test. Obviously the 2nd derivative of such a parabola must be related to the confidence of the given coefficient tested?

Any one know how to extract it?