BioPHP - Linear Correlation and Regresion Curve

Original code submitted by joseba
Code bellow is covered by GNU GPL v2 license.

Description

Last change: 2010/10/18 17:09 | Recent Changes | Original description

Will calculate a lineal relation ship between x and y values by solving a
and b values at y=ax+b. Correlation coeficient will be computed (r)

Code

Last change: 2010/10/18 17:09 | Recent Changes | Download | Original code and

<html>
<head>
<title>Linear Correlation and Regression</title>
</head>
<body bgcolor=FFFFFF>
<center>
<h1>Linear Correlation and Regression</h1>

<?

// author    Joseba Bikandi
// license   GNU GPL v2
// biophp.org

error_reporting(0);


if (!$_POST){
   if ($_GET["show"]=="example"){
        // when nothing is posted, and an example is requested
        // example is included within the form
        print_form("10\n20\n30\n40\n50\n60\n70\n80\n90\n100","31\n58\n93\n125\n144\n177\n209\n249\n270\n303");
        // tipical output for results
        print_results(3.03,-0.67,0.999);
        // example is explained
        print_example(3.03,-0.67,0.999);
    }else{
        // print out form
        print_form();

    }
}else{
        // when data is posted, discriminatory power is computed
        // get the data
        $vals_x=$_POST["vals_x"];
        $vals_x=preg_replace("/ |\r/","",$vals_x);   // removed spaces and returns

        $vals_y=$_POST["vals_y"];
        $vals_y=preg_replace("/ |\r/","",$vals_y);   // removed spaces and returns

        // parse data to an array
        $vals_x_array=preg_split("/\n/",$vals_x,-1,PREG_SPLIT_NO_EMPTY);
        $vals_y_array=preg_split("/\n/",$vals_y,-1,PREG_SPLIT_NO_EMPTY);
        
        // compute discriminatory power
        $curve=correlation_regression ($vals_x_array,$vals_y_array);

        // print results
        print_form($vals_x,$vals_y);
        if ($curve){
                print_results($curve["a"],$curve["b"],$curve["r"]);
        }else{
                print "error: input data is not correct";
        }

}

function correlation_regression ($vals_x,$vals_y){
        if (sizeof($vals_x)!= sizeof($vals_y)){return;}
        $sum_x=0;
        $sum_x2=0;
        $sum_y=0;
        $sum_y2=0;
        $sum_xy=0;
        $n=sizeof($vals_x);
        foreach($vals_x as $key => $val){
                $val_x=$val;
                $val_y=$vals_y[$key];
                $sum_x+=$val_x;
                $sum_x2+=$val_x*$val_x;
                $sum_y+=$val_y;
                $sum_y2+=$val_y*$val_y;
                $sum_xy+=$val_x*$val_y;
                //print "$val_x\t$val_y\n";
        }
        //print "<hr>sum_x\t$sum_x\nsum_y\t$sum_y\nsum_x2\t$sum_x2\nsum_y2\t$sum_y2\nsum_xy\t$sum_xy\n";

        // y=ax+b
        // calculate a
        $curve["a"]=($n*$sum_xy-$sum_x*$sum_y)/($n*$sum_x2-$sum_x*$sum_x);
         // calculate b
        $curve["b"]=($sum_y/$n)-($curve["a"]*$sum_x/$n);
        // calculate regression
        $curve["r"]=($sum_xy-(1/$n)*$sum_x*$sum_y)/((sqrt($sum_x2-(1/$n)*$sum_x*$sum_x)*(sqrt($sum_y2-(1/$n)*$sum_y*$sum_y))));
        return $curve;
}

//########print form
function print_form($vals_x,$vals_y,$a,$b,$r){
?>
        <form method=post action="<? print $_SERVER["PHP_SELF"]; ?>">
        <table width=600>
        <tr><td align=center>
                Values for x:<br><textarea cols="5" rows="12" name="vals_x"><? print $vals_x; ?></textarea>
        </td><td align=center>
                Values for y:<br><textarea cols="5" rows="12" name="vals_y"><? print $vals_y; ?></textarea>
        </td><td align=center valign=bottom>
                <input type=submit value=compute>
                <br><a href=?show=example>example</a>
        </td></tr>
        </table>
        </form>
<?

}

//########print results
function print_results($a,$b,$r){
        print " <table bgcolor=CCCCFF>
                <tr><td>
                Values for curve <b>y=ax+b</b>
                <br> a = $a
                <br> b = $b
                <br> Regresion (r) = $r
                </tr>
                </table>";

}

//########print example
function print_example($a,$b,$r){
$apples=round($a*35+$b);
print "
        <table width=550>
        <tr><td>
                <b>Example</b>: the number of apples per kilograms are counted in
                plastic boxes in order to get a formula to calculate this parameter
                when a new box arrives to the restaurant, so that we may decide
                the number of menus with apples we may offer to our clients.
                <p>When a box with 35 kilos arrives, by applying the formula
                y=ax+b, number of apples in the box may easily calculated:
                <center><p>y= $a *35 + $b =  $apples apples</center>
                <p>As regresion is good (r = $r), the number of apples we have calculated
                will be a good stimation.

        </td></tr>
        </table>
     ";
}

?>
<p><hr>
Source code available at <a href=http://www.biophp.org/stats/linear_correlation_regression/>biophp.org</a>
</center>
</body>
</html>