# Documentation

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# `plot`::`Scatterplot`

Statistical scatter plots

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## Syntax

```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`)
```

## Description

`plot::Scatterplot` creates a scatter plot of two discrete data samples ```[x1, x2, …]``` and ```[y1, y2, …]```. A scatter plot displays the collection of points with coordinates ```[x1, y1]```, ```[x2, y2]``` etc.

In addition, a regression line y = a + bx through the given data pairs `[x1, y1]` etc. is computed and added to the plot. The estimators a, b of the regression are computed by `stats::linReg`.

The regression line can be suppressed by specifying the attribute `LinesVisible` = `FALSE`.

The samples [x1, x2, ] and [y1, y2, ] 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:

### Note

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 ```(x1, y1) = (a, b)``` and ```(x2, y2) = (c, d)```, not of the points ```(x1, y1) = (a, c)``` and ```(x2, y2) = (b, d)```!

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 x (the “predictor”) and y (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 (x, y) where x is a predictor value and y is the corresponding value of the criterion.

If there is a linear relation y = a + bx between x and y, 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 x and y.

## Attributes

AttributePurposeDefault Value
`AffectViewingBox`influence of objects on the `ViewingBox` of a scene`TRUE`
`AntiAliased`antialiased lines and points?`TRUE`
`Data`the (statistical) data to plot
`Frames`the number of frames in an animation`50`
`Legend`makes a legend entry
`LegendText`short explanatory text for legend
`LegendEntry`add this object to the legend?`FALSE`
`LineColor`color of lines`RGB::Red`
`LineWidth`width of lines`0.35`
`LineStyle`solid, dashed or dotted lines?`Solid`
`LinesVisible`visibility of lines`TRUE`
`Name`the name of a plot object (for browser and legend)
`ParameterEnd`end value of the animation parameter
`ParameterName`name of the animation parameter
`ParameterBegin`initial value of the animation parameter
`ParameterRange`range of the animation parameter
`PointSize`the size of points`1.5`
`PointColor`the color of points`RGB::Black`
`PointStyle`the presentation style of points`FilledCircles`
`PointsVisible`visibility of mesh points`TRUE`
`TimeEnd`end time of the animation`10.0`
`TimeBegin`start time of the animation`0.0`
`TimeRange`the real time span of an animation`0.0` .. `10.0`
`Title`object title
`TitleFont`font of object titles[`" sans-serif "`, `11`]
`TitlePosition`position of object titles
`TitleAlignment`horizontal alignment of titles w.r.t. their coordinates`Center`
`TitlePositionX`position of object titles, x component
`TitlePositionY`position of object titles, y component
`Visible`visibility`TRUE`
`VisibleAfter`object visible after this time value
`VisibleBefore`object visible until this time value
`VisibleFromTo`object visible during this time range
`VisibleAfterEnd`object visible after its animation time ended?`TRUE`
`VisibleBeforeBegin`object visible before its animation time starts?`TRUE`

## Examples

### 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)```

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)`

`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))`

There seems to be a relationship, indeed.

`delete TimesAndScores:`

## 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 i-th row is regarded as the data point (xi, yi). 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 x- and y-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 x and y-values, respectively. `a` Animation parameter, specified as `a```` = amin..amax```, where `amin` is the initial parameter value, and `amax` is the final parameter value.
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