Exercise 7.5 Consider Equation (7.1) (page 304), which gives the error of a linear prediction.

(a) Give a formula for the weights that minimize the error for the case where n = 1 (i.e., when there is only one input feature). [Hint: For each weight, differentiate with respect to that weight and set to zero.]

(b) Give a set of equations for the weights that minimize the error for arbitrary n.

(c) Why is it hard to minimize the error analytically when using a sigmoid linear function (i.e., a squashed linear function when the activation function is a sigmoid or logistic function)?