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Simply determined

I have seen many derivations of the coefficients for linear regression using calculus to minimize error, using linear algebra to project the target vector onto the solution space (a particularly neat derivation):

A x=b

A^TAx=A^Tb

\hat{x}=(A^TA)^{-1}(A^Tb)

with assumptions that the system is not overdetermined and providing insights (via eigenvalues) into collinearity etc.

Professor Blitzstein’s ‘look ahead’ provided the succinct frame of reference of modelling the relationship between X and Y…the whole point perhaps.

In that spirit,

There was a lot of food for thought in STAT110. If time permits I hope to think about Gambler’s ruin and other insights from these lectures.

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Categories: Mathematics
  1. March 4, 2012 at 9:14 pm
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