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4. Show that (1) SST = Cu – 9)* = vy - ng = v (1. -) (2) sSR= Em – )* = ³ X'y – ng° = v ( H - )v (3) SSE = ( - )² = y'y – ³ X'y = y' (I. – H) y

4. Show that (1) SST = Cu – 9)* = vy - ng = v (1. -) (2) sSR= Em – )* = ³ X'y – ng° = v ( H - )v (3) SSE = ( - )² = y'y – ³ X'y = y' (I. – H) y

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Regression analysis
4. Show that (1) SST = (u. – 0)² = y/'y – nj² = y | (2) SSR = (m - n)° = ³ X'y – ný* = y' ( H – (3) SSE =E( - i)² = y'y – B'X'y = y' (1, – H) y 1 5. Show that the residual vector, e, can be written as e = (In – H)y, where H is a hat matrix. Furthermore, show both H and (I, – H) are idempotent matrices. 6. Find E(e) and Cov(e). What is the Variance of e,? What is the Variance of Cov(ei, es)?
Transcribed Image Text:4. Show that (1) SST = (u. – 0)² = y/'y – nj² = y | (2) SSR = (m - n)° = ³ X'y – ný* = y' ( H – (3) SSE =E( - i)² = y'y – B'X'y = y' (1, – H) y 1 5. Show that the residual vector, e, can be written as e = (In – H)y, where H is a hat matrix. Furthermore, show both H and (I, – H) are idempotent matrices. 6. Find E(e) and Cov(e). What is the Variance of e,? What is the Variance of Cov(ei, es)?
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