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<html><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><title>Chapter 18. Miscellaneous formatting and tools</title><link rel="stylesheet" type="text/css" href="manual.css"><meta name="generator" content="DocBook XSL Stylesheets V1.76.0"><link rel="home" href="index.html" title="JpGraph Manual"><link rel="up" href="pt04.html" title="Part IV. Creating linear and non-linear graphs"></head><body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Chapter 18. Miscellaneous formatting and tools</th></tr><tr><td width="20%" align="left"> </td><th width="60%" align="center">Part IV. Creating linear and non-linear graphs</th><td width="20%" align="right"> </td></tr></table><hr></div><div class="chapter" title="Chapter 18. Miscellaneous formatting and tools"><div class="titlepage"><div><div><h2 class="title"><a name="id2578622"></a>Chapter 18. Miscellaneous formatting and tools</h2></div></div></div><div class="toc"><p><b>Table of Contents</b></p><dl><dt><span class="sect1"><a href="ch18.html#sec.linear-regression-analysis">18.1. Linear regression analysis</a></span></dt></dl></div>
<p>This chapter tries to collect all other formatting options (and tricks) available in
the library that doesn't really fit anywhere else</p>
<div class="sect1" title="Linear regression analysis"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a name="sec.linear-regression-analysis"></a>Linear regression analysis</h2></div></div></div>
<p>The library offers support to do basic linear regression analysis with the help of
the utility : <code class="code">class LinearRegression</code> defined in the utility module
"<code class="filename">jpgraph_utils.inc.php</code>". With this class it is possible to
make a linear estimation of data and calculate some of the basic statistics of the
data, i.e. correlation coefficient and standard error.</p>
<p>The <code class="code">LinearRegression</code> class is instantiated with the data to be
analyzed and it is then possible to both get hold of the statistics that corresponds
to the data and also to automatically calculate a range of estimated y-values for a
given set of x-coordinates.</p>
<p>The following code snippet shows how to instantiate a regression analysis with
some data</p>
<p>
</p><div class="hl-main"><table class="hl-table" width="100%"><tr><td class="hl-gutter" align="right" valign="top"><pre>1
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</pre></td><td class="hl-main" valign="top"><pre><span class="hl-inlinetags">&lt;?php</span><span class="hl-code">
</span><span class="hl-reserved">require_once</span><span class="hl-brackets">(</span><span class="hl-code"> </span><span class="hl-quotes">'</span><span class="hl-string">jpgraph_utils.inc.php</span><span class="hl-quotes">'</span><span class="hl-brackets">)</span><span class="hl-code">
</span><span class="hl-comment">//</span><span class="hl-comment"> Some data to be analyzed (both x, and y-data must be specified)</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-var">$datay</span><span class="hl-code"> = </span><span class="hl-reserved">array</span><span class="hl-brackets">(</span><span class="hl-code"> ... </span><span class="hl-brackets">)</span><span class="hl-code"> ;
</span><span class="hl-var">$datax</span><span class="hl-code"> = </span><span class="hl-reserved">array</span><span class="hl-brackets">(</span><span class="hl-code"> ... </span><span class="hl-brackets">)</span><span class="hl-code"> ;
</span><span class="hl-comment">//</span><span class="hl-comment"> Instantiate the linear regression class</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-var">$linreg</span><span class="hl-code"> = </span><span class="hl-reserved">new</span><span class="hl-code"> </span><span class="hl-identifier">LinearRegression</span><span class="hl-brackets">(</span><span class="hl-var">$datax</span><span class="hl-code">, </span><span class="hl-var">$datay</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-comment">//</span><span class="hl-comment"> Get the basic statistics</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-reserved">list</span><span class="hl-brackets">(</span><span class="hl-code"> </span><span class="hl-var">$stderr</span><span class="hl-code">, </span><span class="hl-var">$corr</span><span class="hl-code"> </span><span class="hl-brackets">)</span><span class="hl-code"> = </span><span class="hl-var">$linreg</span><span class="hl-code">-&gt;</span><span class="hl-identifier">GetStat</span><span class="hl-brackets">(</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-comment">//</span><span class="hl-comment"> Get a set of estimated y-value for x-values in range [0,20]</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-reserved">list</span><span class="hl-brackets">(</span><span class="hl-var">$x</span><span class="hl-code">, </span><span class="hl-var">$esty</span><span class="hl-brackets">)</span><span class="hl-code"> = </span><span class="hl-var">$linreg</span><span class="hl-code">-&gt;</span><span class="hl-identifier">GetY</span><span class="hl-brackets">(</span><span class="hl-number">0</span><span class="hl-code">,</span><span class="hl-number">20</span><span class="hl-brackets">)</span><span class="hl-code">
...
</span><span class="hl-inlinetags">?&gt;</span></pre></td></tr></table></div><p>
</p>
<p>The methods available in the <code class="code">LinearRegression</code> class that can be used
are</p>
<p>
</p><div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
<p><code class="code">LinearRegression::GetStat()</code></p>
<p>Returns an array with (standard error, correlation coefficient,
determination coefficient)</p>
<p>The closer the correlation coefficient is to 1 the more of the data
variation can be explained by a linear estimate.</p>
</li><li class="listitem">
<p><code class="code">LinearRegression::GetAB()</code></p>
<p>Return an array of the linear coefficients (a,b) where the linear
estimation is <span class="italic">y = a + b*x</span></p>
</li><li class="listitem">
<p><code class="code">LinearRegression::GetY($aMinX, $aMaxX, $aStep=1)</code></p>
<p>Return an array with (xdata, ydata) corresponding to an x-range
between x values in range [<code class="code">$aMinX</code>, <code class="code">$aMaxX</code>]
with steps of <code class="code">$aStep</code></p>
</li></ul></div><p>
</p>
<p>The following example shows how to use this utility class to plot both the
original data as well as the estimated linear line.</p>
<p>
</p><div class="example"><a name="example.example16.6"></a><p class="title"><b>Example 18.1. Linear regression using utility class (<code class="filename">example16.6.php</code>) </b></p><div class="example-contents"> <div class="hl-main"><table class="hl-table" width="100%"><tr><td class="hl-gutter" align="right" valign="top"><pre>1
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</pre></td><td class="hl-main" valign="top"><pre><span class="hl-inlinetags">&lt;?php</span><span class="hl-code"> </span><span class="hl-comment">//</span><span class="hl-comment"> content=&quot;text/plain; charset=utf-8&quot;</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-reserved">require_once</span><span class="hl-code"> </span><span class="hl-brackets">(</span><span class="hl-quotes">'</span><span class="hl-string">jpgraph/jpgraph.php</span><span class="hl-quotes">'</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-reserved">require_once</span><span class="hl-code"> </span><span class="hl-brackets">(</span><span class="hl-quotes">'</span><span class="hl-string">jpgraph/jpgraph_scatter.php</span><span class="hl-quotes">'</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-reserved">require_once</span><span class="hl-code"> </span><span class="hl-brackets">(</span><span class="hl-quotes">'</span><span class="hl-string">jpgraph/jpgraph_line.php</span><span class="hl-quotes">'</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-reserved">require_once</span><span class="hl-code"> </span><span class="hl-brackets">(</span><span class="hl-quotes">'</span><span class="hl-string">jpgraph/jpgraph_utils.inc.php</span><span class="hl-quotes">'</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-comment">//</span><span class="hl-comment"> Create some &quot;fake&quot; regression data</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-var">$datay</span><span class="hl-code"> = </span><span class="hl-reserved">array</span><span class="hl-brackets">(</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-var">$datax</span><span class="hl-code"> = </span><span class="hl-reserved">array</span><span class="hl-brackets">(</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-var">$a</span><span class="hl-code">= </span><span class="hl-number">3</span><span class="hl-number">.2</span><span class="hl-code">;
</span><span class="hl-var">$b</span><span class="hl-code">= </span><span class="hl-number">2</span><span class="hl-number">.5</span><span class="hl-code">;
</span><span class="hl-reserved">for</span><span class="hl-brackets">(</span><span class="hl-var">$x</span><span class="hl-code">=</span><span class="hl-number">0</span><span class="hl-code">; </span><span class="hl-var">$x</span><span class="hl-code"> &lt; </span><span class="hl-number">20</span><span class="hl-code">; ++</span><span class="hl-var">$x</span><span class="hl-brackets">)</span><span class="hl-code"> </span><span class="hl-brackets">{</span><span class="hl-code">
</span><span class="hl-var">$datax</span><span class="hl-brackets">[</span><span class="hl-var">$x</span><span class="hl-brackets">]</span><span class="hl-code"> = </span><span class="hl-var">$x</span><span class="hl-code">;
</span><span class="hl-var">$datay</span><span class="hl-brackets">[</span><span class="hl-var">$x</span><span class="hl-brackets">]</span><span class="hl-code"> = </span><span class="hl-var">$a</span><span class="hl-code"> + </span><span class="hl-var">$b</span><span class="hl-code">*</span><span class="hl-var">$x</span><span class="hl-code"> + </span><span class="hl-identifier">rand</span><span class="hl-brackets">(</span><span class="hl-code">-</span><span class="hl-number">20</span><span class="hl-code">,</span><span class="hl-number">20</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-brackets">}</span><span class="hl-code">
</span><span class="hl-var">$lr</span><span class="hl-code"> = </span><span class="hl-reserved">new</span><span class="hl-code"> </span><span class="hl-identifier">LinearRegression</span><span class="hl-brackets">(</span><span class="hl-var">$datax</span><span class="hl-code">, </span><span class="hl-var">$datay</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-reserved">list</span><span class="hl-brackets">(</span><span class="hl-code"> </span><span class="hl-var">$stderr</span><span class="hl-code">, </span><span class="hl-var">$corr</span><span class="hl-code"> </span><span class="hl-brackets">)</span><span class="hl-code"> = </span><span class="hl-var">$lr</span><span class="hl-code">-&gt;</span><span class="hl-identifier">GetStat</span><span class="hl-brackets">(</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-reserved">list</span><span class="hl-brackets">(</span><span class="hl-code"> </span><span class="hl-var">$xd</span><span class="hl-code">, </span><span class="hl-var">$yd</span><span class="hl-code"> </span><span class="hl-brackets">)</span><span class="hl-code"> = </span><span class="hl-var">$lr</span><span class="hl-code">-&gt;</span><span class="hl-identifier">GetY</span><span class="hl-brackets">(</span><span class="hl-number">0</span><span class="hl-code">,</span><span class="hl-number">19</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-comment">//</span><span class="hl-comment"> Create the graph</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-var">$graph</span><span class="hl-code"> = </span><span class="hl-reserved">new</span><span class="hl-code"> </span><span class="hl-identifier">Graph</span><span class="hl-brackets">(</span><span class="hl-number">300</span><span class="hl-code">,</span><span class="hl-number">250</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-var">$graph</span><span class="hl-code">-&gt;</span><span class="hl-identifier">SetScale</span><span class="hl-brackets">(</span><span class="hl-quotes">'</span><span class="hl-string">linlin</span><span class="hl-quotes">'</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-comment">//</span><span class="hl-comment"> Setup title</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-var">$graph</span><span class="hl-code">-&gt;</span><span class="hl-identifier">title</span><span class="hl-code">-&gt;</span><span class="hl-identifier">Set</span><span class="hl-brackets">(</span><span class="hl-quotes">&quot;</span><span class="hl-string">Linear regression</span><span class="hl-quotes">&quot;</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-var">$graph</span><span class="hl-code">-&gt;</span><span class="hl-identifier">title</span><span class="hl-code">-&gt;</span><span class="hl-identifier">SetFont</span><span class="hl-brackets">(</span><span class="hl-identifier">FF_ARIAL</span><span class="hl-code">,</span><span class="hl-identifier">FS_BOLD</span><span class="hl-code">,</span><span class="hl-number">14</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-var">$graph</span><span class="hl-code">-&gt;</span><span class="hl-identifier">subtitle</span><span class="hl-code">-&gt;</span><span class="hl-identifier">Set</span><span class="hl-brackets">(</span><span class="hl-quotes">'</span><span class="hl-string">(stderr=</span><span class="hl-quotes">'</span><span class="hl-code">.</span><span class="hl-identifier">sprintf</span><span class="hl-brackets">(</span><span class="hl-quotes">'</span><span class="hl-string">%.2f</span><span class="hl-quotes">'</span><span class="hl-code">,</span><span class="hl-var">$stderr</span><span class="hl-brackets">)</span><span class="hl-code">.</span><span class="hl-quotes">'</span><span class="hl-string">, corr=</span><span class="hl-quotes">'</span><span class="hl-code">.</span><span class="hl-identifier">sprintf</span><span class="hl-brackets">(</span><span class="hl-quotes">'</span><span class="hl-string">%.2f</span><span class="hl-quotes">'</span><span class="hl-code">,</span><span class="hl-var">$corr</span><span class="hl-brackets">)</span><span class="hl-code">.</span><span class="hl-quotes">'</span><span class="hl-string">)</span><span class="hl-quotes">'</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-var">$graph</span><span class="hl-code">-&gt;</span><span class="hl-identifier">subtitle</span><span class="hl-code">-&gt;</span><span class="hl-identifier">SetFont</span><span class="hl-brackets">(</span><span class="hl-identifier">FF_ARIAL</span><span class="hl-code">,</span><span class="hl-identifier">FS_NORMAL</span><span class="hl-code">,</span><span class="hl-number">12</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-comment">//</span><span class="hl-comment"> make sure that the X-axis is always at the</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-comment">//</span><span class="hl-comment"> bottom at the plot and not just at Y=0 which is</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-comment">//</span><span class="hl-comment"> the default position</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-var">$graph</span><span class="hl-code">-&gt;</span><span class="hl-identifier">xaxis</span><span class="hl-code">-&gt;</span><span class="hl-identifier">SetPos</span><span class="hl-brackets">(</span><span class="hl-quotes">'</span><span class="hl-string">min</span><span class="hl-quotes">'</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-comment">//</span><span class="hl-comment"> Create the scatter plot with some nice colors</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-var">$sp1</span><span class="hl-code"> = </span><span class="hl-reserved">new</span><span class="hl-code"> </span><span class="hl-identifier">ScatterPlot</span><span class="hl-brackets">(</span><span class="hl-var">$datay</span><span class="hl-code">,</span><span class="hl-var">$datax</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-var">$sp1</span><span class="hl-code">-&gt;</span><span class="hl-identifier">mark</span><span class="hl-code">-&gt;</span><span class="hl-identifier">SetType</span><span class="hl-brackets">(</span><span class="hl-identifier">MARK_FILLEDCIRCLE</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-var">$sp1</span><span class="hl-code">-&gt;</span><span class="hl-identifier">mark</span><span class="hl-code">-&gt;</span><span class="hl-identifier">SetFillColor</span><span class="hl-brackets">(</span><span class="hl-quotes">&quot;</span><span class="hl-string">red</span><span class="hl-quotes">&quot;</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-var">$sp1</span><span class="hl-code">-&gt;</span><span class="hl-identifier">SetColor</span><span class="hl-brackets">(</span><span class="hl-quotes">&quot;</span><span class="hl-string">blue</span><span class="hl-quotes">&quot;</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-var">$sp1</span><span class="hl-code">-&gt;</span><span class="hl-identifier">SetWeight</span><span class="hl-brackets">(</span><span class="hl-number">3</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-var">$sp1</span><span class="hl-code">-&gt;</span><span class="hl-identifier">mark</span><span class="hl-code">-&gt;</span><span class="hl-identifier">SetWidth</span><span class="hl-brackets">(</span><span class="hl-number">4</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-comment">//</span><span class="hl-comment"> Create the regression line</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-var">$lplot</span><span class="hl-code"> = </span><span class="hl-reserved">new</span><span class="hl-code"> </span><span class="hl-identifier">LinePlot</span><span class="hl-brackets">(</span><span class="hl-var">$yd</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-var">$lplot</span><span class="hl-code">-&gt;</span><span class="hl-identifier">SetWeight</span><span class="hl-brackets">(</span><span class="hl-number">2</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-var">$lplot</span><span class="hl-code">-&gt;</span><span class="hl-identifier">SetColor</span><span class="hl-brackets">(</span><span class="hl-quotes">'</span><span class="hl-string">navy</span><span class="hl-quotes">'</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-comment">//</span><span class="hl-comment"> Add the pltos to the line</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-var">$graph</span><span class="hl-code">-&gt;</span><span class="hl-identifier">Add</span><span class="hl-brackets">(</span><span class="hl-var">$sp1</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-var">$graph</span><span class="hl-code">-&gt;</span><span class="hl-identifier">Add</span><span class="hl-brackets">(</span><span class="hl-var">$lplot</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-comment">//</span><span class="hl-comment"> ... and stroke</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-var">$graph</span><span class="hl-code">-&gt;</span><span class="hl-identifier">Stroke</span><span class="hl-brackets">(</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-inlinetags">?&gt;</span></pre></td></tr></table></div></div></div><p><br class="example-break"> </p><div class="figure"><a name="fig.example16.6"></a><p class="title"><b>Figure 18.1. Linear regression using utility class <code class="uri"><a class="uri" href="example_src/example16.6.html" target="_top">(<code class="filename">example16.6.php</code>)</a></code> </b></p><div class="figure-contents"> <span class="inlinemediaobject"><img src="images/example16.6.png" alt="Linear regression using utility class (example16.6.php)"></span> </div></div><p><br class="figure-break">
</p>
</div>
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