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b.lect15

b.lect15 - Outline Parameters of a Multivariate...

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Outline Parameters of a Multivariate Distribution Lecture 15 Chapter 4: Multivariate Variables and Their Distribution Michael Akritas Michael Akritas Lecture 15 Chapter 4: Multivariate Variables and Their Distribu

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Outline Parameters of a Multivariate Distribution Parameters of a Multivariate Distribution The Regression Function Covariance Pearson’s (or Linear) Correlation Coefficient Spearman’s (or Monotone) Correlation Michael Akritas Lecture 15 Chapter 4: Multivariate Variables and Their Distribu
Outline Parameters of a Multivariate Distribution The Regression Function Covariance Pearson’s (or Linear) Correlation Coefficient Spearman’s (or Monotone) Correlation Michael Akritas Lecture 15 Chapter 4: Multivariate Variables and Their Distribu

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Outline Parameters of a Multivariate Distribution The Regression Function Covariance Pearson’s (or Linear) Correlation Coefficient Spearman’s (or Monotone) Correlation For a bivariate r.v. ( X , Y ), the regression function of Y on X shows how the conditional mean of Y changes with the observed value of X . More precisely, Definition The conditional expected value of Y given that X = x , i.e. μ Y | X ( x ) = E ( Y | X = x ) , when considered as a function of x , is called the regression function of Y on X . Michael Akritas Lecture 15 Chapter 4: Multivariate Variables and Their Distribu
Outline Parameters of a Multivariate Distribution The Regression Function Covariance Pearson’s (or Linear) Correlation Coefficient Spearman’s (or Monotone) Correlation For a bivariate r.v. ( X , Y ), the regression function of Y on X shows how the conditional mean of Y changes with the observed value of X . More precisely, Definition The conditional expected value of Y given that X = x , i.e. μ Y | X ( x ) = E ( Y | X = x ) , when considered as a function of x , is called the regression function of Y on X . The regression function of Y on X is the fundamental ingredient for predicting Y from and observed value of X . Michael Akritas Lecture 15 Chapter 4: Multivariate Variables and Their Distribu

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Outline Parameters of a Multivariate Distribution The Regression Function Covariance Pearson’s (or Linear) Correlation Coefficient Spearman’s (or Monotone) Correlation Example In Lecture 14 we discussed the example where X = amount of drug administered, Y = number of tumors developed. In this example, y 0 1 2 p Y | X =0 ( y ) .97 .0225 .0075 p Y | X =1 ( y ) .97 .02 .01 p Y | X =2 ( y ) .9 .08 .02 Find the regression function of Y on X . Michael Akritas Lecture 15 Chapter 4: Multivariate Variables and Their Distribu
Outline Parameters of a Multivariate Distribution The Regression Function Covariance Pearson’s (or Linear) Correlation Coefficient Spearman’s (or Monotone) Correlation Example In Lecture 14 we discussed the example where X = amount of drug administered, Y = number of tumors developed. In this example, y 0 1 2 p Y | X =0 ( y ) .97 .0225 .0075 p Y | X =1 ( y ) .97 .02 .01 p Y | X =2 ( y ) .9 .08 .02 Find the regression function of Y on X .

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• Spring '00
• Akritas
• Correlation and dependence, Pearson product-moment correlation coefficient, Covariance and correlation, Spearman's rank correlation coefficient, Multivariate Distribution, Function Covariance Pearson

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b.lect15 - Outline Parameters of a Multivariate...

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