1. Non-Uniform Weights in Linear Regression: (3 marks) You are given a dataset in which the data points are denoted by ($x_n$, $y_n$), $n = 1, \dots, N$. Each data point is associated with a non-negative weighting factor $\sigma_n > 0$. The error function is thus modified to:
$E_D(\mathbf{w}) = \frac{1}{2} \sum_{n=1}^{N} \sigma_n \left( y_n - \mathbf{w}^T \Phi(x_n) \right)^2$
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where $\Phi(.)$ is any representation of the data. Find an expression for the solution $\mathbf{w}^*$ that minimizes the above error function.
