function stat_covp($data1, $data2)
{
//calculate covariance between 2 arrays
// covariance = sum((data1-mean1) * (data2-mean2)) / samplesize -1
$data1_sum = 0;
$data2_sum = 0;
$len1 = count($data1);
$len2 = count($data2);
$mean1 = stat_mean($data1);
$mean2 = stat_mean($data2);
$count = 0;
for ($x = 0; $x < $len1; $x++) {
$sum_array[$x] = ($data1[$x] - $mean1) * ($data2[$x] - $mean2);
}
return array_sum($sum_array) / $len1;
}
function stat_simple_regression($x, $y)
{
// runs a simple linear regression on $x and $y
// returns an associative array containing the following fields:
// a - intercept
// b - slope
// s - standard error of estimate
// r - correlation coefficient
// r2 - coefficient of determination (r-squared)
// cov - covariation
// t - t-statistic
$output = array();
$output['a'] = 0;
$n = min(count($x), count($y));
$mean_x = stat_mean($x);
$mean_y = stat_mean($y);
$SS_x = 0;
foreach ($x as $element) {
$SS_x += pow($element - $mean_x, 2);
}
$SS_y = 0;
foreach ($y as $element) {
$SS_y += pow($element - $mean_y, 2);
}
$SS_xy = 0;
for ($i = 0; $i < $n; $i++) {
$SS_xy += ($x[$i] - $mean_x) * ($y[$i] - $mean_y);
}
$output['b'] = $SS_xy / $SS_x;
$output['a'] = $mean_y - $output['b'] * $mean_x;
$output['s'] = sqrt(($SS_y - $output['b'] * $SS_xy) / ($n - 2));
$output['r'] = $SS_xy / sqrt($SS_x * $SS_y);
$output['r2'] = pow($output['r'], 2);
$output['cov'] = $SS_xy / ($n - 1);
$output['t'] = $output['r'] / sqrt((1 - $output['r2']) / ($n - 2));
return $output;
}
