Problem 1 [25 points]: Consider the scatterplot below with data {(X;, y;), i = 1, 2, ..., 24}: 100 80 xx X 60 40 Xx XXX * 20 x XX x 8 10 Suppose the data is fitted to a quadratic regression with mean function E( Y | X =x) = Bo+ Bix+B2-x2 V1 X 1 Bo el In matrix form, Y = XB +e => B1 e 2 X24 e24 Given that x=5.833333, y =56.6275 , Ly, =Y'Y = 89882.2642. 24 140 1164 0.450020 -0.242619 0.020761 1359.06 XX = 140 1164 10568 (XX) = -0.242619 0.167181 - 0.015105 X'Y = 6322.83 1164 10568 98268 0.020761 -0.015105 0.001389 47452.65 (a) [6 points] Compute the OLS estimates for Bo, B,and B2. (b) [5 points] Compute the RSS and show that o =13.99 (12.65 also acceptable). (c) [5 points] Let x* be the optimal value of x which maximizes the response y. What is the point estimate of x*? (d) [6 points] Construct an ANOVA table to test if B2 = B, = 0 [not B. = B, = 0] (No testing procedure is required, only the ANOVA table is sufficed). (e) [3 points] Suppose x is an experimental EV. Before performing the experiment to obtain the response y, it's known that the optimal value of x is somewhere in the middle of the interval [1.0, 10.0]. Briefly comment on whether the current choice of EV values {Xi, i = 1,2, ...,24} is reasonable