/**
* Standard error of the regression parameters (coefficients)
*
* _________
* / ∑eᵢ²
* / -----
* se(m) = / ν
* / ---------
* √ ∑⟮xᵢ - μ⟯²
*
* where
* eᵢ = residual (difference between observed value and value predicted by the model)
* ν = n - 2 degrees of freedom
*
* ______
* / ∑xᵢ²
* se(b) = / ----
* √ n
*
* @return array [m => se(m), b => se(b)]
*/
public function standardErrors()
{
$X = new VandermondeMatrix($this->xs, 2);
$⟮XᵀX⟯⁻¹ = $this->⟮XᵀX⟯⁻¹;
$σ² = $this->meanSquareResidual();
$standard_error_matrix = $⟮XᵀX⟯⁻¹->scalarMultiply($σ²);
$standard_error_array = Single::sqrt($standard_error_matrix->getDiagonalElements());
return ['m' => $standard_error_array[1], 'b' => $standard_error_array[0]];
}