查找“最适合"方程

本文介绍了查找“最适合"方程的处理方法，对大家解决问题具有一定的参考价值，需要的朋友们下面随着小编来一起学习吧！ 问题描述

自从我上大学以来已经有一段时间了，知道如何计算最佳拟合线，但是我发现自己需要这样做.假设我有一组要点，我想找到最适合这些要点的线.

It's been a while since I was in college and knew how to calculate a best fit line, but I find myself needing to. Suppose I have a set of points, and I want to find the line that is the best of those points.

确定最佳拟合线的方程是什么? 我将如何使用PHP做到这一点?

What is the equation to determine a best fit line? How would I do that with PHP?

推荐答案

这条线的拟合度可能是另外一个有趣的问题. 为此，请在PHP函数中使用Pearson相关性:

Of additional interest is probably how good of a fit the line is. For that, use the Pearson correlation, here in a PHP function:

/** * returns the pearson correlation coefficient (least squares best fit line) * * @param array $x array of all x vals * @param array $y array of all y vals */ function pearson(array $x, array $y) { // number of values $n = count($x); $keys = array_keys(array_intersect_key($x, $y)); // get all needed values as we step through the common keys $x_sum = 0; $y_sum = 0; $x_sum_sq = 0; $y_sum_sq = 0; $prod_sum = 0; foreach($keys as $k) { $x_sum += $x[$k]; $y_sum += $y[$k]; $x_sum_sq += pow($x[$k], 2); $y_sum_sq += pow($y[$k], 2); $prod_sum += $x[$k] * $y[$k]; } $numerator = $prod_sum - ($x_sum * $y_sum / $n); $denominator = sqrt( ($x_sum_sq - pow($x_sum, 2) / $n) * ($y_sum_sq - pow($y_sum, 2) / $n) ); return $denominator == 0 ? 0 : $numerator / $denominator; }