Math Is Fun Forum

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Inverse of Sum of Matrices

Hi!

I come across a problem when comtemplating an econometric problem

just think dividing a sample into two parts before applying regression.

and suppose the coefficients are different in the two divisions although the same linear model

like
Y1=X1b1+e1
Y2=X2b2+e2

and then I run the regression on whole, and it will yield

b=(X1'X1+X2'X2)[sup]-1[/sup](X1'Y1+X2'Y2)

Now does anyone have an idea on how to solve the

(X1'X1+X2'X2)[sup]-1[/sup]

into something without bracket?

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X'(y-Xβ)=0