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b.lect17

b.lect17 - Outline Parameters of a Multivariate...

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Unformatted text preview: Outline Parameters of a Multivariate Distribution (Continued) Models for Joint Distributions Lecture 17 Chapter 4: Multivariate Variables and Their Distribution Michael Akritas Michael Akritas Lecture 17 Chapter 4: Multivariate Variables and Their Distribu Outline Parameters of a Multivariate Distribution (Continued) Models for Joint Distributions Parameters of a Multivariate Distribution (Continued) Quantifying Effects: The decomposition of means Models for Joint Distributions Regression Models The Bivariate Normal Distribution Multinomial Distribution Michael Akritas Lecture 17 Chapter 4: Multivariate Variables and Their Distribu Outline Parameters of a Multivariate Distribution (Continued) Models for Joint Distributions Quantifying Effects: The decomposition of means Michael Akritas Lecture 17 Chapter 4: Multivariate Variables and Their Distribu Outline Parameters of a Multivariate Distribution (Continued) Models for Joint Distributions Quantifying Effects: The decomposition of means Consider the rc means and their averages in an array as shown (for r = 3, c = 4): Michael Akritas Lecture 17 Chapter 4: Multivariate Variables and Their Distribu Outline Parameters of a Multivariate Distribution (Continued) Models for Joint Distributions Quantifying Effects: The decomposition of means Consider the rc means and their averages in an array as shown (for r = 3, c = 4): Column Factor Row Factor 1 2 3 4 Average 1 μ 11 μ 12 μ 13 μ 14 μ 1 · = 1 4 ∑ 4 j =1 μ 1 j 2 μ 21 μ 22 μ 23 μ 24 μ 2 · = 1 4 ∑ 4 j =1 μ 2 j 3 μ 31 μ 32 μ 33 μ 34 μ 3 · = 1 4 ∑ 4 j =1 μ 3 j Michael Akritas Lecture 17 Chapter 4: Multivariate Variables and Their Distribu Outline Parameters of a Multivariate Distribution (Continued) Models for Joint Distributions Quantifying Effects: The decomposition of means Consider the rc means and their averages in an array as shown (for r = 3, c = 4): Column Factor Row Factor 1 2 3 4 Average 1 μ 11 μ 12 μ 13 μ 14 μ 1 · = 1 4 ∑ 4 j =1 μ 1 j 2 μ 21 μ 22 μ 23 μ 24 μ 2 · = 1 4 ∑ 4 j =1 μ 2 j 3 μ 31 μ 32 μ 33 μ 34 μ 3 · = 1 4 ∑ 4 j =1 μ 3 j Average μ · 1 μ · 2 μ · 3 μ · 4 μ = μ ·· Figure: Cell means with their row and column averages in a 3 × 4 design Michael Akritas Lecture 17 Chapter 4: Multivariate Variables and Their Distribu Outline Parameters of a Multivariate Distribution (Continued) Models for Joint Distributions Quantifying Effects: The decomposition of means Consider the rc means and their averages in an array as shown (for r = 3, c = 4): Column Factor Row Factor 1 2 3 4 Average 1 μ 11 μ 12 μ 13 μ 14 μ 1 · = 1 4 ∑ 4 j =1 μ 1 j 2 μ 21 μ 22 μ 23 μ 24 μ 2 · = 1 4 ∑ 4 j =1 μ 2 j 3 μ 31 μ 32 μ 33 μ 34 μ 3 · = 1 4 ∑ 4 j =1 μ 3 j Average μ · 1 μ · 2 μ · 3 μ · 4 μ = μ ·· Figure: Cell means with their row and column averages in a 3 × 4 design μ · j = 1 r r X i =1 μ ij , μ ·· = 1 r r X i =1 μ i · = 1 c c X j =1 μ · j = 1 rc r X i =1 c X j =1 μ...
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