simplifying to bivariate regression formula

**garymarkhov** · January 17th 2010, 07:26 AM

I want to show that if the number of columns for my matrix of regressors is two and if the first column of my regressors matrix is full of ones then the OLS estimator of the second element of $\beta$ reduces to the bivariate regression formula.

How can I show such a thing? It seems obvious to me that
$<br /> <br /> Y = \left[ \begin{array}{cc} 1 & x_{10} \\ 1 & x_{20} \\ 1 & x_{30} \\ 1 & x_{40} \end{array} \right] \beta + u<br /> <br />$ is the same as something like $y = 1 + Xb + u$ although I'm not sure that's a solid enough "proof". Help!

**matheagle** · January 17th 2010, 07:38 PM

Not sure what you're asking
Though the vector $\beta=(a,b)$
giving you the model $y=a+bx+\epsilon$

**garymarkhov** · January 18th 2010, 04:29 PM

The exact question:

Given that $X$ is fixed and a T x k matrix...

If k=2 and the first element of $X$ is a constant, show that the expression for the OLS estimator of the second element of $\beta$ reduces to the familiar bivariate regression formula.

How do I do this? It's killing me.

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