Question

We have a dataset with n = 10 pairs of observations (34,9), and ΤΟ 813, Στι = 683, Σν Σ? 47, 405, Στον TE 56, 089, Σμ = 66, 731. i=1 11 What is an approximate 95% prediction interval for the response yo at Xo = 60?

Answer 1

gives n=10. Ixi = 683 Eyi = 813 Exp = 47405, Izeigj - 56089 1 X = 683, T =81.3 I 92=6673) To find, 95.). gespoose prediction interval for Xo = 602 at Here, Find the zegoession en Ý =bot bi x bi = Exy, - Ex. 64 {x? - {x? 56089 - 55527.9 47405- 46648.9 561.1 756.) bi = A' 0.74 21 bo = 7 - bi =81.3 - (0.7421) (G8.3) = 81.3 - 50.68543 = 30. 61457 to = 30.6146 the pegoession) eqa is, = bo +bifo 30.6146 + 0.7421 x (7 put Xo = 66 = 30.6146 +6.742160) (T = 75.1406

SSReg 416.3923 Find, SS, ² (4, - ;)² 2 yi² - ny? A = 66731 = 66731 - 66096.9 SS = 634.1 bisoy 561.1 X 0.7421 10 (81-3)2 SSReg Inow that, SS, SS Reg + SSE. SSE • SS7 SST - SS Reg 634.1 416.3923 217.7077 SSE : MSE SSE - 2147.7077 8 2 Se MSE = 27. 2135 Se = 5.21665 Se = 5.2167 > talon-2) critical value to.o5, (10-2) 3) t0.0598 2:30 60

The 95.1 C.I isi 1+1 + (28, 2e)? SS2Qol 756. 1 ý & tala (n=2) se itt 75.1406 + (2.8066) (5.2167) + + (60–63.3)2 = ( 75-1406 + (2-3060) (5.2167) (1.09138)) = ( 75-1406 £ 13. 128999 75.1406 – 13.128996, 75.1406 + 13.128.996 62.011604, 88.269596) 62.01162 88.2696 T 니 Ans The 95.8. poediction con interval is G2-0116 88.2696