/**
* Calculates the sum-squared total of the regression. This is the sum
* of the squared distances of observations from their average, a useful
* measure to put the sum-squared error (SSE) and sum-squared model (SSM)
* into context.
*
* @return float
*/
private function getSumSquaredTotal() : float
{
if (is_null($this->sumSquaredTotal)) {
$average = array_sum($this->observations->getOutcomes()) / count($this->observations->getOutcomes());
$this->sumSquaredTotal = static::sumSquaredDifference($this->observations->getOutcomes(), $average);
}
return $this->sumSquaredTotal;
}
/**
* @param Observations $observations
* @return array
* @throws InvalidArgumentException
*/
public function regress(Observations $observations) : array
{
$design = new Matrix($observations->getFeatures());
$observed = (new Matrix([$observations->getOutcomes()]))->transpose();
if ($design->getRowCount() < $design->getColumnCount()) {
throw new InvalidArgumentException('Not enough observations to perform regression. You need to have more observations than explanatory variables.');
}
$designTranspose = $design->transpose();
$prediction = $designTranspose->multiplyMatrix($design)->inverse()->multiplyMatrix($designTranspose->multiplyMatrix($observed));
return $prediction->transpose()->toArray()[0];
}
