Suppose we wish to find a prediction function g(x) that minimizes

MSE = E[(y-g(x))^2]

where x and y are jointly distributed random variables with density function f (x; y).

Suppose we restrict our choices for the function g(x) to linear functions of the form g(x) = a + bx and determine a and b to minimize MSE. Show that a = 1 and b =E(xy)/E(x^2) = 0 and MSE = 3. What do you interpret this to mean?