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<title>线性回归 Linear Regression</title>
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<h2>计算线性回归方程式 Y = a + bX</h2>
<p>
如果两组数据相关系数很高, 可以用一条近似直线Y=a + bX 来预估, 谓之线性回归<br />
根据统计学理论, Y = a + bX 中 <br />
斜率 b = X,Y 离均差交乘积和 / X离均差平方和 <br />
常数项 a = Y平均值 - b * X平均值<br />
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<form method="post" action="http://kangyihong.com/ttttttt.php">
参考值：
X : <input type="text" name="X" size="30" value="12.5,25,50"><br>
可变值
Y : <input type="text" name="Y" size="30" value="35452,58505,63097"><br>
<input type="submit" value="ok">
</form>
<?php
header("Content-Type: text/html; charset=utf-8");
if (empty($_REQUEST["X"])) {
?>
<?php
} else {
$X = explode(",",$_REQUEST["X"]);
$Y = explode(",",$_REQUEST["Y"]);
$xavg = array_sum($X)/count($X); // X 平均值
$yavg = array_sum($Y)/count($Y); // Y 平均值
$XMD = Array(); // X 离均差
$YMD = Array(); // Y 离均差
$mdcross_sum = 0; // X,Y 离均差交乘积和
$xdif_square_sum = 0; // X 离均差平方和
$count = count($X);
for ($i=0; $i<$count; $i++) {
$xdif = (float)$X[$i]-$xavg; // X 离均差
$ydif = (float)$Y[$i]-$yavg; // Y 离均差
$XMD[$i] = $xdif;
$YMD[$i] = $ydif;
$mdcross_sum += $xdif*$ydif; // X,Y 离均差交乘积和
$xdif_square_sum += pow($xdif, 2); // X 离均差平方和
} //end of for
$b = round($mdcross_sum/$xdif_square_sum, 2); // 计算斜率 b
$a = round($yavg-$b*$xavg, 2); // 计算常数项 a
echo "X = ".join(", ",$X)."<br>";
echo "Y = ".join(", ",$Y)."<br>";
echo "常数项 a = ".$a."<br>";
echo "斜率 b = ".$b."<br>";
echo "线性回归方程式 Y = ".$a." + (".$b.")X<br>";
echo "X 平均值 = ".$xavg."<br>";
echo "Y 平均值 = ".$yavg."<br>";
echo "X 离均差 = ".join(", ",$XMD)."<br>";
echo "Y 离均差 = ".join(", ",$YMD)."<br>";
echo "X,Y 离均差交乘积和 = ".$mdcross_sum."<br>";
echo "X 离均差平方和 = ".$xdif_square_sum."<br>";}
echo '<hr />';
echo '计算两点之间的角度。';
$a = array('x' => 10, 'y' => 0);
$c = array('x' => 80, 'y' => 80);
$pi_v = atan2($c['y'] - $a['y'], $c['x'] - $a['x']);
$n_v = rad2deg($pi_v);echo '弧度：',$pi_v,' 角度：',$n_v; ?>
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