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Questions: 1. Let In be the n x n identity matrix and 1 the n-vector whose all entries are 1's. Let Y = (y1 y2 Yn) and y = 1 i. Show the followings: ... (a) [2] y = 11 y n (b) [2]=y'y n (c) [4] A · A = A, where A = In − 1½1n1n. . (d) [3] tr(A): = n − 1 (e) [4] Σ¦±1(Yi — ÿ)² = y¹Ay. where ẞ(Bo ẞ1 Bp) and ... Yi = = ß³xi + €i, i = 1, . . ., n, Ꮖ ; = (1 xil ... xip) for i 1,. assumptions about & are satisfied, i.e., ε¿ IID = (1) ..., n. We assume that all the DD N(0, 0²). Suppose that n > p+1. We denote the design matrix for the MLR as X and the response vector as y. We assume that XTX is invertible and denote the hat matrix as H, i.e. H = X(X'X)¯¹X'.

Questions: 1. Let In be the n x n identity matrix and 1 the n-vector whose all entries are 1's. Let Y = (y1 y2 Yn) and y = 1 i. Show the followings: ... (a) [2] y = 11 y n (b) [2]=y'y n (c) [4] A · A = A, where A = In − 1½1n1n. . (d) [3] tr(A): = n − 1 (e) [4] Σ¦±1(Yi — ÿ)² = y¹Ay. where ẞ(Bo ẞ1 Bp) and ... Yi = = ß³xi + €i, i = 1, . . ., n, Ꮖ ; = (1 xil ... xip) for i 1,. assumptions about & are satisfied, i.e., ε¿ IID = (1) ..., n. We assume that all the DD N(0, 0²). Suppose that n > p+1. We denote the design matrix for the MLR as X and the response vector as y. We assume that XTX is invertible and denote the hat matrix as H, i.e. H = X(X'X)¯¹X'.

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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Questions: 1. Let In be the n x n identity matrix and 1 the n-vector whose all entries are 1's. Let Y = (y1 y2 Yn) and y = 1 i. Show the followings: ... (a) [2] y = 11 y n (b) [2]=y'y n (c) [4] A · A = A, where A = In − 1½1n1n. . (d) [3] tr(A): = n − 1 (e) [4] Σ¦±1(Yi — ÿ)² = y¹Ay.
Transcribed Image Text:Questions: 1. Let In be the n x n identity matrix and 1 the n-vector whose all entries are 1's. Let Y = (y1 y2 Yn) and y = 1 i. Show the followings: ... (a) [2] y = 11 y n (b) [2]=y'y n (c) [4] A · A = A, where A = In − 1½1n1n. . (d) [3] tr(A): = n − 1 (e) [4] Σ¦±1(Yi — ÿ)² = y¹Ay.
where ẞ(Bo ẞ1 Bp) and ... Yi = = ß³xi + €i, i = 1, . . ., n, Ꮖ ; = (1 xil ... xip) for i 1,. assumptions about & are satisfied, i.e., ε¿ IID = (1) ..., n. We assume that all the DD N(0, 0²). Suppose that n > p+1. We denote the design matrix for the MLR as X and the response vector as y. We assume that XTX is invertible and denote the hat matrix as H, i.e. H = X(X'X)¯¹X'.
Transcribed Image Text:where ẞ(Bo ẞ1 Bp) and ... Yi = = ß³xi + €i, i = 1, . . ., n, Ꮖ ; = (1 xil ... xip) for i 1,. assumptions about & are satisfied, i.e., ε¿ IID = (1) ..., n. We assume that all the DD N(0, 0²). Suppose that n > p+1. We denote the design matrix for the MLR as X and the response vector as y. We assume that XTX is invertible and denote the hat matrix as H, i.e. H = X(X'X)¯¹X'.
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