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Material Type: Assignment; Class: Regression Analysis; Subject: Industrial & Systems Engr; University: Georgia Institute of Technology-Main Campus; Term: Unknown 1989;

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Download Solutions to Homework 6 for Regression Analysis | ISYE 6414 and more Assignments Systems Engineering in PDF only on Docsity! Solution to homework 6 11.7 (a) Yi = −5.7 + 0.188Xi The absolute value of residual increases as X increases. It suggests that unequal variance may exist. (b) H0 : γ1 = 0 vs. H1 : γ 6= 0 Reject H0 if χ2BP > χ 2 0.9,1 = 2.71 χ2BP = SSR∗/2 (SSE/n)2 = 123753/2 (2316.5/12)2 = 1.66 < 2.71 Thus, fail to reject H0. The error variance is constant at α = 0.1. (c) The squared residual increases as X increases. (d) ν̂ = −180.1 + 1.2437X The estimated weights are: 0.0146, 0.0032, 0.0052, 0.0032, 0.0146, 0.0052, 0.0052, 0.0032, 0.0146, 0.0032, 0.0146, 0.0052 (e) Yi = −6.23 + 0.1891Xi Two models are similar. (f) OLS: S{β0} = 16.73, S{β1} = 0.054 WLS: S{β0} = 13.17, S{β1} = 0.051 The estimated standard deviations in WLS is smaller than those in OLS. (g) The variance function is: ν̂ = −180.3 + 1.2446X The estimated weights are: 0.0146, 0.0032, 0.0052, 0.0032, 0.0146, 0.0052, 0.0052, 0.0032, 0.0146, 0.0032, 0.0146, 0.0052 The regression equation of Y on X with new weights is: Yi = −6.23+ 0.1891Xi Since the models are similar, there is no need to re-estimate variance function and weights. 11.9 (a) Yes, bR1 and b R 2 exhibit substantial changes near c equals 0. (b) It is judgemental. (c = 0.06 to 0.1) (c) When c=0.1, b1 = 3.4641.758 × 0.394 = 0.776 b2 = 3.4641.628 × 0.356 = 0.757 b3 = 3.4640.864 × 0.164 = 0.658 b0 = 9.301− 0.776× 3.702− 0.757× 3.609− 0.658× 3.598 = 1.329 So, Ŷ = 1.329 + 0.776X1 + 0.757X2 + 0.658X3 The fitted values are similar to those from OLS. 1