Principal Component Analysis

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Presentation transcript:

Principal Component Analysis LPGA Golf Performance Variables – 2008 Season

Principal Components - Description Data: p Variables observed on n Experimental/Sampling units Goal: Describe the Variance-Covariance structure of the variables through uncorrelated linear combinations of the variables Data Reduction: Fewer linear combinations (k) that “explain” large portion of total variation than the number of variables (p) Interpretation: New variables (principal components) can simplify the summary of the original variables. Used as input to other procedures such as Factor Analysis and Linear Regression when Predictors are Correlated

Population Principal Components - I

Population Principal Components - II

Principal Components - Bivariate Case (Sample)

LPGA 2008 Data

Population Principal Components - III

LPGA 2008 Data

Population Principal Components - IV

LPGA 2008 Data

Population Principal Components - V

LPGA 2008 Data

95% Density Ellipsoid and Principal Components

Principal Components for Standardized Variables

LPGA 2008 Data

LPGA 2008 Data

95% Density Ellipsoid and Principal Components