Question

25. Short Answer Question We have a dataset with n = 10 pairs of observations (Li, Yi), and n n di = 683, Yi = 813, n n2 -* = 47,405, Xiyi = 56,089, ył = 66, 731. i=1 What is an approximate 95% prediction interval for the response yo at Xo = 60?

Answer 1

Formula for 95% Prediction interval for the individual value x0=60 is (x0x) = ġett* Se 1 +++ Sxx n x=683, Ły=813, x2 =47405, y2 =66731, Sxy=56089 (Ex) Sxx = x2 - =756.1 n Sy = y2 =634.1 n Sx)(y) Sxy=xy- 561.1 n Slope b, =Sxy _561.1 0.7421 Sxx 756.1 Intercept bo =ỹ –b x = 81.3-0.7421*68.3 = 30.6147 The regression equation is ĝ=bo+bıx= 30.6147 +0.7421x Predicted value for x = 60 is Ýp = 30.6147 +0.7421(90) = 75.1406

Standard error of the estimate Se= Syy-b1Sxy n-2 634.1-0.7421*561.1 =5.2167 10-2 Standard deviation of the independent value ofy for x is Sindp= Se 1+-+ (x0-2)2 Sxx = 5.69337 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% Prediction interval for the individual value x0=60 is = Ýptt* Sindp = = 75.1406–2.306*5.69337 = 75.1406+ 13.1289 =(62.0117,88.2695)