Suppose we are fitting a regression model y = x B + vile estimating the coefficients Band v ). We are considering an alternative regression model where we augment the feature vector x with a new feature that is the average avg(x) of the original features. The new model is y = x B+ avg(x)y + v , and we wish to estimate the coefficients P, y and v. Do you think it is a good idea? Justify your answer in terms of the predictive power of the model and the estimation procedure