Estimating multiple parameters from a regression

Dear all,

I have this regression model

fy=randn(1000,1);
x1=randn(1000,1);
x2=randn(1000,1);
u=randn(1000,1);
fy=a*x1+b*x2+c*u; %regression model

where fy is the dependent variable,

x1 and x2 are the independent variables,

u is the error term which is standard normally distributed,

a and b are the coefficients

and c is the square root of the variance.

My goal is to estimate the scalars a,b and c. Is there a way to do that?

Answer 1

[Star Strider]

That is a simple linear regression.

Try this:

B = [x1 x2 u] \ fy;
a = B(1)
b = B(2)
c = B(3)

[ektor]

Does it make sense to minimize the sum of squared residuals?

[Star Strider]

Yes. However to do that you likely have to introduce an intercept term as well:

B = [x1 x2 u ones(size(u))] \ fy;
a = B(1)
b = B(2)
c = B(3)
I = B(4)

It just depends on what you want to do with your model.