Question

We have a dataset with n = 10 pairs of observations (i, yi), and n 2x = 683, y = 813, i=1 n 72 x = 47,405, rxyz = 56,089, vi = 66,731. il =1 What is an approximate 95% confidence interval for the mean response at 20 = = 60?

Answer 1

given n=10. Txi = 683 Zy; = 813 X: 68:3, Typ = 47405, I seiyi - 56089 1 7 7-81.3 I 92=6673) To find, confidence 95.). Predients mterval for mean the response at Ro -608 Here, Find segoessios em =bot bi x Exy, - (2x) (64) bi = Ex² - 6x2? 56089 - 55527.9 47405 - 46648.9 561.1 756.1 bi= og 0.74 01 bo = 9 - bi = 81.3 · (0.74 21) (683) -8.3 50.68543 = 30. 61457 bo = 30. 6146 the oegoession ean is, = bo +bito 30.6146 + 0.742) X put Xo = 66 30.6146 +0.7421760) teo 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). C.I is , 2 756:1 う ( it toys (ma) se h + (20-8>> S Sala 75.1406. (2-3060) (5.2767) + (60-68.3) ( 75:1406 + (2.3060) (5.2167) (0.437163)) 75.1406 £ 5.258955) 75.1406 + 5.25896) 5 ( 751406- 6.25895 75.1406 + 5.25896) 69.88165 9 80.39 956) 다 69.8817) 80. 3996) 957. GI For mean response is, ( [69.8817, 80.8996]) The