The sum-of-squares error function for regression (Eqn. 3.12 in PRML) treats every training data point equally. In some instances, we may wish to place different weights on different training data points. This could arise if we have confidence estimates of the accuracy of each training data point.

Consider the weighted sum-of-squares error function:

()= 1/2n=1{()}2

with weights > 0 on each training data point.

Derive the optimal weights w given this weighted sum-of-squares error function.