ii. The R output below (given incomplete) summarizes the statistics of fitting the re- gression (4) against the observation data. Give the estimates of B, and B2. Call: lm (formula = y x1 + x2, data = t2.data, model = T, X = T) Coefficients: Estimate (Intercept) 33.9321 x1 2.7848 x2 -0.2644 Std. Error 26.7483 1.2891 0.5123 > anova (t3.out) Analysis of Variance Table Response: Y Df x1 1 x2 1 Residuals 3 Sum sa 3004.41 5.51 62.07 Mean sa 3004.41 5.51 20.69 iii. Define hat matrix H1 = X1(x7x)-'XT and SSR(B1) = y Hy. Show that Hj 2117, where 1 is (n x 1) vector of one, and SSR(B.) = n?. iv. From the data set and R output, find the value of SSR(B2\B ), SSR(B.), SSE = m and SST = yy. Hint: Recall that SSR(B2\B.) +SSR(B1) +SSE = SST. ii. The R output below (given incomplete) summarizes the statistics of fitting the re- gression (4) against the observation data. Give the estimates of B, and B2. Call: lm (formula = y x1 + x2, data = t2.data, model = T, X = T) Coefficients: Estimate (Intercept) 33.9321 x1 2.7848 x2 -0.2644 Std. Error 26.7483 1.2891 0.5123 > anova (t3.out) Analysis of Variance Table Response: Y Df x1 1 x2 1 Residuals 3 Sum sa 3004.41 5.51 62.07 Mean sa 3004.41 5.51 20.69 iii. Define hat matrix H1 = X1(x7x)-'XT and SSR(B1) = y Hy. Show that Hj 2117, where 1 is (n x 1) vector of one, and SSR(B.) = n?. iv. From the data set and R output, find the value of SSR(B2\B ), SSR(B.), SSE = m and SST = yy. Hint: Recall that SSR(B2\B.) +SSR(B1) +SSE = SST