Bivariate and Multivariate Relationships

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Chapter 13

• Bivariate and Multivariate Relationships

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Univariate Density Estimation

• Smooth summary of the data

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Bivariate Density Estimation
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Three Species
virginica
versicolor
setosa

• Notice the contours are sort of eliptical
• Bivariate normal has eliptical contours

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Bivariate Normal Model per species
Large ve correlation
Small ve correlation
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Scatterplot Matrix
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Bivariate Outliers
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Mahalanobis Distance

• Multivariate distance measure that takes account
  of correlations (its like a multivariate z-score)

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Principal Components

• First principal component
• Direction that explains the most variability

• Second principal component
• Orthogonal to the first p.c., explains the rest
  of the variability

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Spining plot shows p.c.s
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Principal Components in Higher Dimensions

• There are many p.c.s as there are dimensions
• If the first 2 or 3 p.c.s explain most of the
  variability, this can facilitate a dimensionality
  reduction

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Outliers in 6-D