Question

Short Answer Question We have a dataset with n = 10 pairs of observations (), and = 68,813 Wii -47,405, 3.91 = 56,089 66.731. 3-06,781. What is an approximate 95% prediction interval for the response at To = 907

Answer 1

Formula for 95% Confidence interval for the individual mean x0=90 is = ÝP* Se + (x0 - 2)2 Sxx n Xx=683, Xy=813, 2x2 =47405, Zy2 =66731, Sxy=56089 (Ex)2 Sxx = x2 - =756.1 n (Ey)2 Syy = y2 =634.1 n (2x)Ey) Say = xy - 561.1 n Slope bi Sxy - 561.1 = 0.7421 Sxx 756.1 Intercept bo =) -61 x = 81.3-0.7421*68.3 = 30.6147 The regression equation is û =bo+bıx = 30.6147 +0.7421x Predicted value for x = 90 is ŵp = 30.6147 +0.7421(90) = 97.4035

Standard error of the estimate Se= Syy-b1Sxy n-2 634.1-0.7421*561.1 -=5.2167 10-2 Estimate of the standard deviation Sợp = Se + (x0-x) Sxx = 4.43505 n Df=n-2 = 10-2=8 Level of significance a = 1-0.95=0.05 Critical value to =T.INV.2T(0.05,8)=2.306 (Using excel) 95% Confidence interval for the individual mean x0=60 is İp #t* Smp = 97.4035=2.306*4.43505 =97.4035= 10.2272 (87.1763, 107.6307)