Scatter Plot

Scatter Plot with best-fit line

Complete Code

POD for Macro Files

PG problem file

Explanation

DOCUMENT();

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

Preamble

Make sure that plots.pl is loaded.

@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 = Plot(
    xmin        => 0,
    xmax        => 24,
    xtick_delta => 4,
    ymin        => 0,
    ymax        => 300,
    aria_label  => 'Linear Regression'
);
$plot->add_dataset(
    @data,
    linestyle => 'none',
    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: the x and y data needs to be array references and the 2nd and 3rd lines extract the components.

For the plot, first set up the Plot with a plotting window that will caputure the data. The add_dataset method adds the data to the plot with circles and color 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

The data is formatted by putting the array data in a nice format using both join (which joins an array separated by ‘,’) and map (which creates a new array that formats as (x1, y1)). The [@ @] is used to run perl.

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.