Visual exploration of dependency shapes for two or more variables using SPLUS

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LECTURE 17

• Visual exploration of dependency shapes for
  two (or more) variables using S-PLUS
• Scatter Plot Visualization of 2D Distributions
• Trellis Conditional Distribution Plots for 2D
  Data
• Visualizing Higher Dimensional Data
• Scatterplot Matrices (static visualization)
• Trellis Conditioning Plots (static visualization)
• Brush and Spin (interactive, dynamic
  visualization)

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2D SCATTER PLOTS

• Two independent N(0,1) variables
• Scatterplots with marginal histograms
• 2D shapes of independent vs. dependent normally
  distributed random variables
• 2D shapes of some real data sets
• All kinds of shapes!

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Two independent N(0,1) R.V.s
Done with GUI 2D Plots pallet Can also be
done at the command line with plot(x,y), with x,
y vectors, or using plot(dmat) with dmat a
data matrix with two columns
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Scatterplot with Marginal Histograms

• Choose Graph gt Brush and Spin from the S-PLUS
  toolbar, and in the dialog that appears, uncheck
  the Spin Window box and check the Draw Histograms
  box

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Y1 N(4,9), Y2 N(2,1)Y1 and Y2 independent
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Y1 N(4,9), Y2 N(2,1)Y1 and Y2 with
positive dependence
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Y1 N(4,9), Y2 N(2,1)Y1 and Y2 with
negative dependence
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View the previous three scatterplots with
marginal histogramsDo just as in slide
5Marginal histograms are all much the same
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The organic data set
A positive fairly linear relation for most of the
data, plus a few outliers
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Responses of two sensors to gas in the air
Distinctly nonlinear relationship
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Stock returns versus firm size
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prim4 data see S-PLUS Help(prim4)
Elementary particle physics experiment data. Two
highly dependent variables with
interesting special structure
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TRELLIS CONDITIONAL DENSITY PLOTS

• A way of looking at the conditional distribution
  of Y given Xx, using histogram or smoothed
  histogram views
• Demo of drag and drop GUI use
• Can also be done at the command line (see Chapter
  9 of S-PLUS 6 Programmers Guide)
• Also useful for higher dimensional data
• Scatter plots of y versus x conditioned on z
• More on this kind of thing later

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Two independent N(0,1) R.V.s
What should the conditional density f(y2y1) look
like for various values of y1?
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Marginal Histogram of y2, and Trellis conditional
histograms of y2 conditioned on y1
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Y1 N(4,9), Y2 N(2,1)Y1 and Y2 with
positive dependence
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Marginal Histogram of y2, and Trellis conditional
histograms of y2 conditioned on y1
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Visualizing Multi-Dimensional Data

• Scatterplot matrices (Static Views)
• Many 2D scatterplots in a single display
• Trellis Graphics (Static Views)
• Brush and Spin (Dynamic Views)
• Linked views highlighting
• Dynamic slicing

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Scatterplot Matrices
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Trellis conditional scatter plots of returns
versus size, conditioned on book/market
Marginal scatter plot of returns (over all
values of ln.bm)
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Brush and Spin prim4 (see S-PLUS Help)