MathPHP\Statistics\Regression\Methods\LeastSquares::DFFITS PHP Метод

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DFFITS() публичный Метод

https://en.wikipedia.org/wiki/DFFITS ŷᵢ - ŷᵢ₍ᵢ₎ DFFITS = ---------- s₍ᵢ₎ √hᵢᵢ where ŷᵢ is the prediction for point i with i included in the regression ŷᵢ₍ᵢ₎ is the prediction for point i without i included in the regression s₍ᵢ₎ is the standard error estimated without the point in question hᵢᵢ is the leverage for the point Putting it another way: sᵢ is the studentized residual eᵢ sᵢ = -------------- √(MSₑ(1 - hᵢ)) where eᵢ is the residual MSₑ is the mean squares residual Then, s₍ᵢ₎ is the studentized residual with the i-th observation removed: eᵢ s₍ᵢ₎ = ----------------- √(MSₑ₍ᵢ₎(1 - hᵢ)) where _ _ | eᵢ² | ν MSₑ₍ᵢ₎ =| MSₑ - -------- | ----- |_ (1 - h)ν _| ν - 1 Then, ______ hᵢ DFFITS = s₍ᵢ₎ / ------ √ 1 - hᵢ

public DFFITS ( ) : array
Результат	array

    public function DFFITS() : array
    {
        $ys = $this->reg_ys;
        $xs = $this->reg_xs;
        $ν = $this->ν;
        $h = $this->leverages();
        $e = $this->residuals();
        $MSₑ = $this->meanSquareResidual();
        // Mean square residuals with the the i-th observation removed
        $MSₑ₍ᵢ₎ = array_map(function ($eᵢ, $hᵢ) use($MSₑ, $ν) {
            return ($MSₑ - $eᵢ ** 2 / ((1 - $hᵢ) * $ν)) * ($ν / ($ν - 1));
        }, $e, $h);
        // Studentized residual with the i-th observation removed
        $s = array_map(function ($eᵢ, $mseᵢ, $hᵢ) {
            return $eᵢ / sqrt($mseᵢ * (1 - $hᵢ));
        }, $e, $MSₑ₍ᵢ₎, $h);
        $DFFITS = array_map(function ($s₍ᵢ₎, $hᵢ) {
            return $s₍ᵢ₎ * sqrt($hᵢ / (1 - $hᵢ));
        }, $s, $h);
        return $DFFITS;
    }

LeastSquares

DFFITS

FProbability

FStatistic

coefficientOfDetermination

cooksD

correlationCoefficient

createDesignMatrix

degreesOfFreedom

errorSD

getProjectionMatrix

leastSquares