Fundamentals of Probability and Statistics for Engineers

Linear Models and Linear Regression 351y(x) l 2E(y) =^α^+ βxα^+ β ^ –x(x) l 1–xxFigure 11.4Confidence band for EfYg ˆ ‡ xAnswer: equation (11.41) gives the desired confidence limits, with n ˆ 14, ˆ 0:05, andEfyg d ˆ^ ‡ ^x ˆ 0:63 ‡ 5:24x;t n 2;=2 ˆ t 12;0:025 ˆ 2:179; from Table A.4;x ˆ 11:11;X niˆ1…x i x† 2 ˆ 546:09;b 2 ˆ 182:10:The observed confidence limits are thus given by " #) l 1; 2 ˆ… 0:63 ‡ 5:24x†2:179 182:10 11=2…x 11:11†2‡ :14 546:09This result is shown graphically in Figure 11.5.11.1.5 SIGNIFICANCE TESTSFollowing the results given above, tests of hypotheses about the values of and can be carried out based upon the approach discussed in Chapter 10. Let usdemonstrate the underlying ideas by testing hypothesis H 0 : ˆ 0 againsthypothesis H 1 : 6ˆ 0 ,where0 is some specified value.TLFeBOOK