Estimating multiple parameters from a regression

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ektor
ektor 2019-5-24
评论： Star Strider 2019-5-24
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?

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Star Strider
Star Strider 2019-5-24
That is a simple linear regression.
Try this:
B = [x1 x2 u] \ fy;
a = B(1)
b = B(2)
c = B(3)
  2 个评论
ektor
ektor 2019-5-24
Does it make sense to minimize the sum of squared residuals?
Star Strider
Star Strider 2019-5-24
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.

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