Midterm Exam - Statistics for Engineering | STAT 4706, Exams of Statistics

Download Midterm Exam - Statistics for Engineering | STAT 4706 and more Exams Statistics in PDF only on Docsity! 3? - gro MIDTERM EXAM STATISTICS 4706 April 9, 2002 Each problem is given equal weight. Show work for partial credit. 1. & 2. a.) Complete the following ANOVA table based on the regression equation: —— Y= fot frait Pore + Bst3 + Bats and 20 observations: / 5 Source ss-/ DP, MS Ms, \E Model 350 | KT MONE BBS 38.25 Error BO | nll) isso) Y/ 7 7 ' Corrected Total 500 Answer the following questions: ~ b.) Is the overall regression significant? c.} Suppose you computed the following sums of squares due to regression: R(A1, 2, Bs) = 300 R(Bi, 82, Bs) = 250 (Bo, Bs, Bs) = 325 R(A1, Bs, Ba) = 340 Fill in the following “computer output” a Fe “ Source _DF. Type IM S$_ _F-value_ salue PR >F ay ' ). 1245 to 3841 3 4 AS .0042 a4 at 0401 d.) If you were using the Backward bh A on Technique, would one of the variables be removed from the regression equation at this stage? If so, which one and why? Use a = .25. Suppose you computed the following sums of squares due to regression: F(A, Pr) = 100 R(B1, Ba} 150 RBs, Bs) = 330 e.) Using the original model based on 21, £2, #3, and 2, test the hypothesis: 4 IL Ao: PB. = 0 and By =0 vs. A: Ho is not true. (in the presence of z3 and x4) f.) Use a partial F test to compare, at a = .05, the two models: Bot Bre, + Bory + Psas + € Bo + Brt1 + Box, + € ee | 3. Consider a one way ANOVA experiment with K = 4 treatments. The observed data are summarized as follows: Treatment a 1 2 3 4 Yi. 10 12 15 di 6 — SO -Y2)" 60 58 42 60 Y,, = 12, Mm = Ng =Ng3 = Ng = 6. The corresponding ANOVA table follows: Source SS” DF MS F. Model 84 3 24 2.18 Error 220 20 li Corrected Total 304 a.) Test Hp : are = pty = 0. b.) Compute $8, for the contrast w = are — Hl. c.) Do all pairwise comparisons among the treatment means using Duncan’s multiple range test at a = .05? What can you say about the experimentwise crror rate for this procedure?