Please answer both questions thoroughly and show work! Much appreciated!!

5) For any predictor variable X and response Y, explain what of interest the equation E[(f(X) - Y)2] = E[(f(X) - E[Y|X1)2] + E[(Y - E[Y|X])2]. which holds for any suitable function f, may imply concerning regression analysis. 6) Solve the least squares optimization (minimization) problem . . . 2 (.30! Bl) = arg m1n(ao,a1)eimz 2L1 (Yn (a0 + 0'1an for the numerical values 5'0 \"631 for the particular case of the three specific data points (0,1), (1,0), and (1,1) (so in this case N = 3), without explicitly appealing to the general solution formulas given in the course slides. Show your reasoning/computations, and give reasoning as to why the solution found really is in fact a (local) minimum. (Hint: Use calculus.)