Question: Consider that we are trying to fit a linear model to a set of input-output pairs (x(1),d(1)), (x(2),d(2)),(x(n),d(n)) observed in an interval of n steps,

 Consider that we are trying to fit a linear model to

Consider that we are trying to fit a linear model to a set of input-output pairs (x(1),d(1)), (x(2),d(2)),(x(n),d(n)) observed in an interval of n steps, where input x is m dimensional vector, x=[x1,x2,,xm]T. The linear model takes the following form: y(x)=w1x1+w2x2++wmxm=wTx Derive the formula to calculate the optimal parameter w such that the following cost function J(w) is minimized. J(w)=i=1nr(i)e(i)2=i=1nr(i)(d(i)y(x(i)))2 where r(i)>0 are the weighting factors for each output error e(i)

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