Scatter Plot (Statistical Plots)

Scatter Plot with best-fit line using StatPlots

Complete Code

POD for Macro Files

PG problem file

Explanation

DOCUMENT();

loadMacros(
    'PGstandard.pl',       'PGML.pl',
    'StatisticalPlots.pl', 'PGstatisticsmacros.pl',
    'PGcourse.pl'
);

Preamble

Make sure that StatisticalPlots.pl is loaded. This is a version of the problem in Scatter Plot that uses the scatter plot feature in StatisticalPlots.pl.

@data = ([ 5, 40 ], [ 7, 120 ], [ 12, 180 ], [ 16, 210 ], [ 20, 240 ]);

$x = [ map { $_->[0] } @data ];
$y = [ map { $_->[1] } @data ];
($m, $b) = linear_regression($x, $y);

$plot = StatPlot(
    xmin        => 0,
    xmax        => 24,
    xtick_delta => 4,
    ymin        => 0,
    ymax        => 300,
    ytick_delta => 50,
    aria_label  => 'Linear Regression'
);

$plot->add_scatterplot(
    ~~@data,
    marks => 'circle',
    color => 'blue'
);
$plot->add_function(
    "$m x + $b",
    'x',
    1,
    23,
    color => 'black',
    width => 1,
);

Setup

For this problem, we have a data set stored as an array of array references. First we find the best-fit line using the linear_regression function of PGstatisticsmacros.pl. Note that the x and y data values need to be in array references, and the 2nd and 3rd lines extract the components.

Set up the StatPlot with a plotting window that will contain the data. The add_dataset method adds the data to the plot with circle marks that are colored blue.

The line is added to the dataset with the add_function method. The 3rd and 4th arguments are the xmin and xmax of the domain.

BEGIN_PGML
A scatter plot of the data:

[``` [@ join(', ', map { "($_->[0], $_->[1])" }  @data)  @] ```]

together with the best-fit line is given by the following plot.

>> [! Scatter Plot with best fit line !]{$plot}{500} <<

END_PGML

Statement

To format the points in the @data array in a human-readable manner, these are first put in “(x, y)” form using the map function. The resulting array is then concatenated with the join command. Since both map and join are perl commands, this compound command is placed within a [@ @].

The [! !]{}{} is a PGML format for inserting an image.

BEGIN_PGML_SOLUTION
Solution explanation goes here.
END_PGML_SOLUTION

ENDDOCUMENT();

Solution

A solution should be provided here.