Weighted Regression:

In weighted least-squares linear regression, we have a weight ri corresponding to each data measurement.

Our goal is to fit the data points in proportion to their weights by minimizing the following objective function:

E(w) = sum from i=1 to m [r(i) (y(i) - (wx(i) + b))2]

where w and b are the model parameters, the training data are pairs {x(i), y(i)}, i = 1, …, m.

Derive a closed-form expression for the estimates of w and b that minimize the objective function.

In weighted least-squares linear regression, we have a weight ri corresponding to each data measurement.

Our goal is to fit the data points in proportion to their weights by minimizing the following objective function:

E(w) = sum from i=1 to m [r(i) (y(i) - (wx(i) + b))2]

where w and b are the model parameters, the training data are pairs {x(i), y(i)}, i = 1, …, m.

Derive a closed-form expression for the estimates of w and b that minimize the objective function.