Homework 3 - HOMEWORK III JAN DE LEEUW 1 PROBLEM Consider a...

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Unformatted text preview: HOMEWORK III JAN DE LEEUW 1. PROBLEM Consider a table with n rows and m columns and an unequal number of observations in each cell. We can index the observations as x i jk with i = 1 , ··· , n and j = 1 , ··· , m and k = 1 , ··· ,‘ i j . An example of such a table will look like the following-1.3690510 0.8803977-0.3459382-0.1190956 0.4348185 0.2042370 0.4662728 1.1817889-0.3297959-0.6008543-0.6795710-0.9254206 This gets coded as the data structure 1 1-1.3690510 1 1 0.8803977 1 1-0.3459382 1 2-0.1190956 1 2 0.4348185 2 1 0.2042370 2 2 0.4662728 2 2 1.1817889 2 3-0.3297959 2 3-0.6008543 2 3-0.6795710 2 3-0.9254206 The first two columns only indicate which cell in the design the observation comes from. They are not for computing, only for indexing. Date : November 10, 2010 — 21h 8min — Typeset in TIMES ROMAN. 1 2 JAN DE LEEUW We want to fit a main effect approximation of the form x i jk ≈ μ + α i + β j using least squares. Thus we want to minimize the loss function σ ( μ , α , β ) = n ∑ i = 1 m ∑ j = 1 ‘ ij ∑ k = 1 ( x i jk- μ- α i- β j ) 2 ....
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This note was uploaded on 01/14/2011 for the course STATS 102A 102A taught by Professor Jandeleeuw during the Fall '10 term at UCLA.

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Homework 3 - HOMEWORK III JAN DE LEEUW 1 PROBLEM Consider a...

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