11.11 Solve Example 11.1 by using matrix operations. Solution From the data given in Example 11.1, we see that XO X -2 -1 O Y = W - - O O and X = It follows that x'x = 3 181 X'Y =;] (X'x) ' = 0 0 1/ 10 Thus, B = (Xx xx=['s , no][;]-[."] or Bo = 1 and B, = . 7. Thus, y =1+.7x just as in Example 11.1. = Question 11.12 Fit a parabola to the data of Example 11.1, using the model Y = Bot Bix + B2x2 + 8. Solution The X matrix for this example differs from that of Example 11.11 only by the addition of a third column corresponding to x . (Notice that x, = x, X2 = x , and k = 2 in the notation of the general linear model.) Thus, XO X x 2 - O Y = X = (The three variables, Xo, x, and x , are shown above their respective columns in the X matrix.) Thus, for the first measurement, y = 0, xo = 1, x = -2, and x = 4; and for the second measurement, y = 0, xo = 1, x = -1, and x2 = 1. Succeeding rows of the Y and X matrices are obtained in a similar manner