Question

We have a dataset with n = 10 pairs of observations (li, yi), and n X; = 683, Yi = 813, n _ x* = 47, 405, Xiyi = 56,089, y = 66, 731. i=1 What is an approximate 95% confidence interval for the mean response at Xo = 60?

Answer 1

given that, 1:10 8/5 E xi = 683 ST 11 E se i ² = 47405, [xiyi = 56089 [y; ² = = 66731 is is know that the fitted linear regression equation wherer Ý = 8 + Bi x so is the estimate of y-interept of regression line Bi is the estimate of stope of regsession line and coyl X,Y) ssay sati) ssa. Where, ssay ssa Exiyi nă 2 7 = Exi 683 68.3 813 81-3 jo ssay ::ssay 56089 - 10 (68.34 81.3) 5 6)-1 Ssa= 47405- 10(68.32 7561 :ssa = .:ßi= ssay Ssx 561-1 7561 0.7421

and Bå: Ý - Bi 333 - (0.9421 X 68.5) 3006147 Y: 30.0147 + 0.9421 X and. SST = {(Yi - 7 3 = {y; ²- n72 iSST= 66731 - 10181:3)² 634.1 .:SST = we have, SSpes = SST- F SSI 634•|- (0.7421_X 56111 217.7090 - iisspes and mopes a Spes 217. 7020 8 n-2 Pipes = 2702136 response Here we have to construct a 95% G. I for the mean at do= 60. .: Ely lau) = erypto Båt Bixo. 75.1400 .: cy1oa 30-6147 + 0.9421600) we know that, 100 11-d] % confidence inteenal on response at the point the mean А xado is freemały? Lünlyo mSpes Malyo 7 1212, n.2 ㅗ + sar

Here given that significance level (2) (2) = 0.05 (5) t2/2,0-2= n-2= tooos 9 8 = 2.3060 .: The required as is (75.1405 7 2-3060 27. 2136 (60-68.321 + 7561 C. 69.8817 80.3995