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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 11 12 13 14 1 = 1 4 4 j =1 1 j 2 21 22 23 24 2 = 1 4 4 j =1 2 j 3 31 32 33 34 3 = 1 4 4 j =1 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 11 12 13 14 1 = 1 4 4 j =1 1 j 2 21 22 23 24 2 = 1 4 4 j =1 2 j 3 31 32 33 34 3 = 1 4 4 j =1 3 j Average 1 2 3 4 = 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 11 12 13 14 1 = 1 4 4 j =1 1 j 2 21 22 23 24 2 = 1 4 4 j =1 2 j 3 31 32 33 34 3 = 1 4 4 j =1 3 j Average 1 2 3 4 = Figure: Cell means with their row and column averages in a 3 4 design j = 1 r r X i =1 ij , = 1 r r X i =1 i = 1 c c X j =1 j = 1 rc r X i =1 c X j =1...
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 Akritas

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