(Solved): Non-Uniform Weights in Linear Regression: (6 marks) You are given a dataset in which the data poin ...

Non-Uniform Weights in Linear Regression: (6 marks) You are given a dataset in which the data points are denoted by (Xn, tn), n = 1, ... ,N. Each data point is associated with a non-negative weighting factor 9n > 0. The error function is thus modified to: N Ep(w) 9n(tn (tu – w*x.)) ?() n=1 where 0 (-) is any representation of the data. 1 error (a) (3 marks) Find an expression for the solution w* that minimizes the above err function. (b) (3 marks) Give two alternative interpretations of the above weighted sum-of-squares error function in terms of: (i) data-dependent noise variance and (ii) replicated data points.