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Postby ankuragrawal.nit » Tue Jan 10, 2012 12:43 am

Hi Deven,
firstly the subject is kind of misleading in that it should read 'linear regression' instead of OLS.

That said, If you roughly plot the data on an x-y plane you ll clearly trace a parabola of the form Y^2=4*a*X (Notice that it passes through (0,0) )
where 'a' is a constant depending on shape of parabola.

Now linear regression is linear w.r.t. parameters
i.e. If I have a general linear regression of the form X= A + B*Y + independent error term
where variables are X and Y
slope coefficient being "B" and intercept coefficient "A".i.e. expected value of X when Y is zero
note that when Y is zero , X is also zero
so intercept coefficient is zero.
Also independent error term is zero.

Being linear wrt parameters imply tht "A" and "B" should be linear in nature or to say more perfectly the relnship between X and Y must be linear wrt parameters and not variables
So variables can assume any "degree" or "power" (in option b this being '2' )
however , if the regression would have been of the form A^2 + some Y^exp(Deven) * B
then u see tht A is no more linear in the relnship so this cannot be called a linear regression wrt FRM curriculum :P

Hope that helps :)

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