/**
* Calculate the regression parameters using the Theil-Sen method
*
* Procedure:
* Calculate the slopes of all pairs of points and select the median value
* Calculate the intercept using the slope, and the medians of the X and Y values.
* b = Ymedian - (m * Xmedian)
*/
public function calculate()
{
// The slopes array will be a list of slopes between all pairs of points
$slopes = [];
$n = count($this->points);
for ($i = 0; $i < $n; $i++) {
for ($j = $i + 1; $j < $n; $j++) {
$pointi = $this->points[$i];
$pointj = $this->points[$j];
$slopes[] = ($pointj[1] - $pointi[1]) / ($pointj[0] - $pointi[0]);
}
}
$this->m = Average::median($slopes);
$this->b = Average::median($this->ys) - $this->m * Average::median($this->xs);
$this->parameters = [$this->b, $this->m];
}
/**
* Five number summary
* A descriptive statistic that provides information about a set of observations.
* It consists of the five most important sample percentiles:
* 1) the sample minimum (smallest observation)
* 2) the lower quartile or first quartile
* 3) the median (middle value)
* 4) the upper quartile or third quartile
* 5) the sample maximum (largest observation)
*
* https://en.wikipedia.org/wiki/Five-number_summary
*
* @param array $numbers
*
* @return array [min, Q1, median, Q3, max]
*/
public static function fiveNumberSummary(array $numbers)
{
$quartiles = self::quartiles($numbers);
return ['min' => min($numbers), 'Q1' => $quartiles['Q1'], 'median' => Average::median($numbers), 'Q3' => $quartiles['Q3'], 'max' => max($numbers)];
}