(c) (3 points) Recall that we define the correlation r between two vectors u and v as Tu,v Vi- n Ou (i) Show that in general, for any two non-constant vectors u and v, if uv = 0 and u = 0, then u and v are uncorrelated, i.e. Tu,v = 0. By non-constant, we mean that the coordinates are not all equal to the same value. (ii) Use (i) to conclude that the residuals e = Y - XO are uncorrelated with every non-constant predictor variable X,, as long as the residuals are not constant (i.e. at least one prediction is not perfect), that is, show that re,x, = 0 for all Xj. (d) (3 points) Use the previous part to show that the residuals are also uncorrelated to the fitted values y = XO as long as neither e nor y is a constant vector, that is, show that re,y = 0