STAT 235 Final, Spring 2002

AMERICAN UNIVERSITY OF BEIRUT STATISTICS 235, Final Exam June 19, 2002 Time = 1 Hour and 30 Minutes You are allowed to use a calculator. 1. (Any simple linear regression problem can be converted to a simple lincar regression problem with no intercept.) To seo this, eansider the usual simple linear regressiou problem: ¥; = Bo + ON; + €;, (1) where « = 1,...,1. J) and 3; are unknown parameters, ¢; are iid N(O, o°), and o? is an unkuown constant. Show that, if we let 15* = ¥; — Y and Aj = X; — X, then model (1) becomes Y~* = BX} + ;. (10 pts) A simple linear regression was run on a set of data using an intercept and one independent variable. You are given the following information from the S-PLUS output: (a) i Y= lt - 15, u. The t-test for Ho : 3; = 0 was not significant at aw = 0.05 level. A computed t-value of -4.087 was compared to ta = 0.05, df = 2) = 4.183 which was read from the t-table. iti. The estimate of o? was s* = 1.75 (b) Complete the ANOVA table using the above results. (10 pts) (c) Compute and interpret the coefficient of determination R?. (5 pts) 3. You ave given the following matrices computed to a multiple regression problem: 9 136 269 260 , 136 2114 4176 3583 XX = 269 4176 8257 7104 200 3583 7104 12276 9.6109 0086 —.2792 —.0445 finn-t | O86 5100 —.2589 0008 x) ~ | ~.2792 —.2589 1395 0007 —.0445 0008 = 0007 .0N04 NY =[45, 648, 1283, 1821), B= [- 1.1635, 0.1353, 0.0199, 0.1220)’ and YY = 285. (a) Using the above results, compute the ANOVA table. (Hint: try to generalize for this problem the following fact of simple linear regression that states: SSR=Ay TUX — X)*]. (10pts) (b) Give the computed regression eqnation and the standard errors of the regression coefficients. (8 pts) (c) show how you would test the ca composite hypothesis: Bo = 0. By = Bs. and Be = 0 (7 prs) Geek Dd 2