# Estimating multiple parameters from a regression

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ektor on 24 May 2019
Commented: Star Strider on 24 May 2019
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?

Star Strider on 24 May 2019
That is a simple linear regression.
Try this:
B = [x1 x2 u] \ fy;
a = B(1)
b = B(2)
c = B(3)

ektor on 24 May 2019
Does it make sense to minimize the sum of squared residuals?
Star Strider on 24 May 2019
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.