Question

We have a dataset with n = 10 pairs of observations (Li, Yi), and Xi = 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 10 = 60?

Answer 1

Formula for 95% Confidence interval for the individual mean x0=60 is = ŵp t* Se 1 + (v0- 2)2 n Sxx x=683, Ły=813, x2 =47405, y2 =66731, Sxy=56089 Sxx = x2. £x)? -=756.1 n Syy = y2 =634.1 n Ex) Ey) = 561.1 Sxy=xy- n Slope bi 561.1 Sxy -0.7421 Sxx 756.1 Intercept bo =ỹ –b x = 81.3-0.7421*68.3 = 30.6147 The regression equation is û =bo+bıx= 30.6147 +0.7421x Predicted value for x = 60 is ŵp = 30.6147 +0.7421(60) = 75.1407

Standard error of the estimate Se= Syy-b Sxy n-2 634.1-0.7421*561.1 -=5.21667 10-2 Estimate of the standard deviation 1 Shp Se + (x0 - 2)2 Sxx - 2.2805 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 t* Sỹ, = P = = 75.1407=2.306*2.2805 = 0.7421 +5.2589 =( 69.8817,80.3995)