plot::Scatterplot – statistical scatter plots

plot::Scatterplot(data) creates a scatter plot of the given data.

→ Examples

Calls:

plot::Scatterplot([x1, x2, ...], [y1, y2, ...], <a = amin .. amax>, Options)

plot::Scatterplot([[x1, x2, ...], [y1, y2, ...]], <a = amin .. amax>, Options)

plot::Scatterplot([x1, y1], [x2, y2], ..., <a = amin .. amax>, Options)

plot::Scatterplot([[x1, y1], [x2, y2], ...], <a = amin .. amax>, Options)

plot::Scatterplot(A, <a = amin .. amax>, Options)

plot::Scatterplot(s, <c1, c2>, <a = amin .. amax>, Options)

Parameters:

x1, y1, x2, y2, ...:	the statistical data: numerical real values or arithmetical expressions of the animation parameter a. x1, y1, x2, y2, ... is equivalent to the attribute Data.
A:	an array of domain type DOM_ARRAY or a matrix of category Cat::Matrix (e.g., of type matrix or densematrix) providing numerical real values or arithmetical expressions of the animation parameter a. The -th row is regarded as the data point . The array/matrix must have 2 columns. If more columns are provided, the superfluous columns are ignored. A is equivalent to the attribute Data.
s:	a data collection of domain type stats::sample. The columns in s are regarded as - and -values, respectively. s is equivalent to the attribute Data.
c1, c2:	column indices into s: positive integers. These indices, if given, indicate that only the specified columns in s should be used. If no column indices are specified, the first two columns in s are used as and -values, respectively.

Details:

plot::Scatterplot creates a scatter plot of two discrete data samples and . A scatter plot displays the collection of points with coordinates , etc.

In addition, a regression line through the given data pairs etc. is computed and added to the plot. The estimators , of the regression are computed by stats::linReg.

The regression line can be suppressed by specifying the attribute LinesVisible = FALSE.
The samples and should have the same number of elements. Otherwise, superflous elements in the longer list are ignored.
There is an ambiguity between the various input formats if only 2 data points are provided:

For two data points the calls plot::Scatterplot([a, b], [c, d]) and plot::Scatterplot([[a, b], [c, d]]) both yield plots of the two points and , not of the points and !

The routines plot::Listplot and plot::PointList2d have a similar functionality. The main additional feature of plot::Scatterplot is the regression line.
Scatter plots are useful to visualize the relationship between two variables (the “predictor”) and (the “criterion”).

The variable regarded as a predictor corresponds to the horizontal axis while the variable regarded as the criterion corresponds to the vertical axis. The criterion variable represents the behavior to be predicted. The predictor variable represents the activity which is believed to be associated with the criterion.

The scatter plot consists of points where is a predictor value and is the corresponding value of the criterion.

If there is a linear relation between and , the data points should form a line, potentially marred by statistical deviations. The regression line provided by the scatter plot allows a visual test of such a relation between and .

Example 1

We plot some data samples:

xdata := [6, 9, 17, 0, 13, 9, 9, 12, 12, 12]:
ydata := [7, 8, 20, 2, 11, 8, 9, 12, 13, 15]:
b := plot::Scatterplot(xdata, ydata):
plot(b)

MuPAD graphics

We can modify the appearance of the scatter plot in various ways:

b::PointColor := RGB::Red:
b::PointSize := 3*unit::mm:
b::LineColor := RGB::Black:
b::LineWidth := 1*unit::mm:

plot(b)

MuPAD graphics

delete xdata, ydata, b:

Example 2

We analyze the relationship between the time students spent on preparing for a test and the result of the test. We collect the data in a matrix. Each row corresponds to a student. The first column describes the numbers of hours spent for the preparation, the second column contains the corresponding test score (points out of 100):

TimesAndScores := matrix([[ 1, 61],
                          [10, 75],
                          [4,   55],
                          [3,   18],
                          [4,   77],
                          [6,   72],
                          [3,   18],
                          [1,   25],
                          [0,   50],
                          [4,   68],
                          [4,   68],
                          [8,   87],
                          [9,   74],
                          [11, 79],
                          [6,   28],
                          [4,   65],
                          [7,   52],
                          [8,   78],
                          [2,   36],
                          [3,   48],
                          [4,   39]
                         ]):

We draw a scatter plot to identify a possible relationship between the two variables:

plot(plot::Scatterplot(TimesAndScores))

MuPAD graphics

There seems to be a relationship, indeed.

delete TimesAndScores:

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