Question: Consider a new model of linear regression: p ( y x , w ) = N ( y w T x , f ( x

Consider a new model of linear regression:p(yx,w)=N(ywTx,f(x))

Where f(x)=x. Given a dataset of the form D={(xi,yi)}i=1N, derive the maximum likelihood estimator of w and the maximum a posteriori estimator of w assuming the prior p(w)=N(w0,2I).

Describe what effect this will have on the estimation of w and why. Finally, if you were fitting this model in practice, what, if any, practical or numerical concerns might you have separate from the usual concerns of linear regression?

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