Class Notes:  Tuesday 10/29/02
 

    -    Check new material on student pages (from Class Home Page)
 

Scatterplots:    Useful view of 2-dimensional data
 

Idea:  for ordered pairs of data values,  (X, Y),
 

E.g.  (height, weight),    (age, income),    (size, price),    (fuel economy, horsepower)
 

Study relationship between X & Y
 

Visual Device:   "scatterplot"
 

Plot points as:   X (on x-axis)  and Y (on y-axis)
 

Example 1:

Data from Prof. Tim Bralower, Dept. of Geological Sciences
 

Each data point represents one fossil shell,

    -    Dated by surrounding material  (x-axis)

    -    Ratio of isotopes of strontium  (y-axis)

    -    surrogate for "sea level"

    -    allows study of global climate (e.g. ice ages)

    -    obvious big changes

    -    what about smaller changes???
 

Example 2:

Data from Prof. Aman Ullah, Economics, Univ. Calif. Riverside

Shows how earning power (y-axis) depends on age (x-axis)

For 205 males in survey in Canada

    -    Youngest have little earning power

    -    But increases rapidly

    -    Eventually falls off

    -    Variation increases over time
 

Example 3:

Trappings of Canadian Lynx

    -    A few very big years?

    -    More very small years?

    -    Some type of cyclic structure?
 

Nicer scale???   (addresses "data compressed at bottom")

Still not easy to see "real structure"
 

Another useful graphical device:   connected lines

Note:   this makes cyclical structure "pop out" in clear visual way

Explanation:   related to food supply

    -    many lynx eat up most of food

    -    so lynx die off

    -    leads to more food

    -    leads to more lynx

    -    cycle repeats
 

General issue:   Should scatterplots be "just dots", or "connected by lines"?
 

Depends on context:

    -    When there is "structure", connecting can highlight

    -    But is distracting when no structure

    -    Should try both, and then choose
 

Scatterplots in Excel:

Toy Data Set:    Old Faithful Geyser Data

        1st Column:    Duration of Eruption

        2nd Column:    Time before Eruptions

        Expect Relationship?
 

Excel Scatterplot:

    -    Chart Wizard

    -    Chart Type XY (scatter)

    -    "Series Plot" is not interesting

    -    Instead Plot:    X-values = time before    Y-values = Duration

    -    Clearly shows "2 different types of eruptions"

    -    With "big ones" coming after "big lead up time"
 

Caution:    Don't use "line plot":

    -    Chart Wizard

    -    Chart Type Line

    -    Because this does some strange "reordering":

    -    Note numbers on x axis not in "correct order"

    -    instead appear to be in "list order"

    -    so cannot see interesting "2 cluster" structure in data

    -    so stay away from this version of Chart Wizard for scatterplots
 
 

Instead use different subtype under "XY (scatter)"

Note:  in this case, connecting with lines clearly detracts from seeing "2 clusters"

Here is a case where "just dots" is more useful
 

Scatterplots in Matlab:

    -    Use command   >>   plot(vx,vy,'+')

    -    Then fiddle other things as above

    -    See "Matlab Graphics" in Computing Tips
 

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