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<?php |
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namespace PhpOffice\PhpSpreadsheet\Shared\Trend; |
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abstract class BestFit |
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{ |
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/** |
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* Indicator flag for a calculation error. |
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* |
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* @var bool |
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*/ |
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protected $error = false; |
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/** |
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* Algorithm type to use for best-fit. |
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* |
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* @var string |
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*/ |
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protected $bestFitType = 'undetermined'; |
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/** |
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* Number of entries in the sets of x- and y-value arrays. |
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* |
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* @var int |
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*/ |
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protected $valueCount = 0; |
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/** |
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* X-value dataseries of values. |
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* |
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* @var float[] |
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*/ |
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protected $xValues = []; |
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/** |
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* Y-value dataseries of values. |
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* |
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* @var float[] |
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*/ |
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protected $yValues = []; |
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/** |
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* Flag indicating whether values should be adjusted to Y=0. |
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* |
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* @var bool |
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*/ |
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protected $adjustToZero = false; |
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/** |
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* Y-value series of best-fit values. |
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* |
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* @var float[] |
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*/ |
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protected $yBestFitValues = []; |
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/** @var float */ |
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protected $goodnessOfFit = 1; |
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/** @var float */ |
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protected $stdevOfResiduals = 0; |
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/** @var float */ |
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protected $covariance = 0; |
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/** @var float */ |
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protected $correlation = 0; |
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/** @var float */ |
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protected $SSRegression = 0; |
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/** @var float */ |
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protected $SSResiduals = 0; |
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/** @var float */ |
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protected $DFResiduals = 0; |
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/** @var float */ |
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protected $f = 0; |
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/** @var float */ |
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protected $slope = 0; |
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/** @var float */ |
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protected $slopeSE = 0; |
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/** @var float */ |
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protected $intersect = 0; |
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/** @var float */ |
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protected $intersectSE = 0; |
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/** @var float */ |
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protected $xOffset = 0; |
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/** @var float */ |
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protected $yOffset = 0; |
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/** @return bool */ |
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public function getError() |
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{ |
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return $this->error; |
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} |
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/** @return string */ |
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public function getBestFitType() |
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{ |
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return $this->bestFitType; |
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} |
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/** |
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* Return the Y-Value for a specified value of X. |
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* |
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* @param float $xValue X-Value |
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* |
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* @return float Y-Value |
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*/ |
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abstract public function getValueOfYForX($xValue); |
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/** |
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* Return the X-Value for a specified value of Y. |
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* |
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* @param float $yValue Y-Value |
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* |
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* @return float X-Value |
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*/ |
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abstract public function getValueOfXForY($yValue); |
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/** |
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* Return the original set of X-Values. |
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* |
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* @return float[] X-Values |
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*/ |
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public function getXValues() |
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{ |
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return $this->xValues; |
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} |
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/** |
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* Return the Equation of the best-fit line. |
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* |
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* @param int $dp Number of places of decimal precision to display |
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* |
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* @return string |
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*/ |
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abstract public function getEquation($dp = 0); |
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/** |
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* Return the Slope of the line. |
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* |
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* @param int $dp Number of places of decimal precision to display |
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* |
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* @return float |
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*/ |
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public function getSlope($dp = 0) |
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{ |
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if ($dp != 0) { |
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return round($this->slope, $dp); |
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} |
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return $this->slope; |
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} |
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/** |
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* Return the standard error of the Slope. |
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* |
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* @param int $dp Number of places of decimal precision to display |
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* |
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* @return float |
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*/ |
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public function getSlopeSE($dp = 0) |
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{ |
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if ($dp != 0) { |
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return round($this->slopeSE, $dp); |
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} |
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return $this->slopeSE; |
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} |
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/** |
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* Return the Value of X where it intersects Y = 0. |
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* |
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* @param int $dp Number of places of decimal precision to display |
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* |
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* @return float |
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*/ |
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public function getIntersect($dp = 0) |
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{ |
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if ($dp != 0) { |
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return round($this->intersect, $dp); |
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} |
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return $this->intersect; |
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} |
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/** |
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* Return the standard error of the Intersect. |
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* |
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* @param int $dp Number of places of decimal precision to display |
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* |
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* @return float |
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*/ |
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public function getIntersectSE($dp = 0) |
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{ |
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if ($dp != 0) { |
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return round($this->intersectSE, $dp); |
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} |
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return $this->intersectSE; |
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} |
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/** |
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* Return the goodness of fit for this regression. |
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* |
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* @param int $dp Number of places of decimal precision to return |
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* |
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* @return float |
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*/ |
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public function getGoodnessOfFit($dp = 0) |
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{ |
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if ($dp != 0) { |
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return round($this->goodnessOfFit, $dp); |
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} |
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return $this->goodnessOfFit; |
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} |
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/** |
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* Return the goodness of fit for this regression. |
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* |
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* @param int $dp Number of places of decimal precision to return |
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* |
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* @return float |
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*/ |
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public function getGoodnessOfFitPercent($dp = 0) |
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{ |
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if ($dp != 0) { |
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return round($this->goodnessOfFit * 100, $dp); |
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} |
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return $this->goodnessOfFit * 100; |
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} |
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/** |
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* Return the standard deviation of the residuals for this regression. |
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* |
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* @param int $dp Number of places of decimal precision to return |
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* |
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* @return float |
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*/ |
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public function getStdevOfResiduals($dp = 0) |
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{ |
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if ($dp != 0) { |
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return round($this->stdevOfResiduals, $dp); |
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} |
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return $this->stdevOfResiduals; |
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} |
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/** |
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* @param int $dp Number of places of decimal precision to return |
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* |
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* @return float |
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*/ |
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public function getSSRegression($dp = 0) |
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{ |
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if ($dp != 0) { |
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return round($this->SSRegression, $dp); |
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} |
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return $this->SSRegression; |
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} |
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/** |
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* @param int $dp Number of places of decimal precision to return |
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* |
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* @return float |
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*/ |
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public function getSSResiduals($dp = 0) |
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{ |
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if ($dp != 0) { |
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return round($this->SSResiduals, $dp); |
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} |
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return $this->SSResiduals; |
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} |
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/** |
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* @param int $dp Number of places of decimal precision to return |
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* |
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* @return float |
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*/ |
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public function getDFResiduals($dp = 0) |
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{ |
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if ($dp != 0) { |
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return round($this->DFResiduals, $dp); |
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} |
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return $this->DFResiduals; |
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} |
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/** |
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* @param int $dp Number of places of decimal precision to return |
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* |
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* @return float |
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*/ |
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public function getF($dp = 0) |
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{ |
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if ($dp != 0) { |
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return round($this->f, $dp); |
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} |
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return $this->f; |
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} |
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/** |
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* @param int $dp Number of places of decimal precision to return |
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* |
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* @return float |
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*/ |
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public function getCovariance($dp = 0) |
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{ |
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if ($dp != 0) { |
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return round($this->covariance, $dp); |
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} |
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return $this->covariance; |
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} |
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/** |
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* @param int $dp Number of places of decimal precision to return |
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* |
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* @return float |
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*/ |
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public function getCorrelation($dp = 0) |
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{ |
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if ($dp != 0) { |
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return round($this->correlation, $dp); |
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} |
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return $this->correlation; |
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} |
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/** |
344
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* @return float[] |
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*/ |
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public function getYBestFitValues() |
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{ |
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return $this->yBestFitValues; |
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} |
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/** @var mixed */ |
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private static $scrutinizerZeroPointZero = 0.0; |
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/** |
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* @param mixed $x |
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* @param mixed $y |
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*/ |
358
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private static function scrutinizerLooseCompare($x, $y): bool |
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{ |
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return $x == $y; |
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} |
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363
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/** |
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* @param float $sumX |
365
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* @param float $sumY |
366
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* @param float $sumX2 |
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* @param float $sumY2 |
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* @param float $sumXY |
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* @param float $meanX |
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* @param float $meanY |
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* @param bool|int $const |
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*/ |
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protected function calculateGoodnessOfFit($sumX, $sumY, $sumX2, $sumY2, $sumXY, $meanX, $meanY, $const): void |
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{ |
375
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36 |
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$SSres = $SScov = $SStot = $SSsex = 0.0; |
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36 |
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foreach ($this->xValues as $xKey => $xValue) { |
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36 |
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$bestFitY = $this->yBestFitValues[$xKey] = $this->getValueOfYForX($xValue); |
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379
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36 |
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$SSres += ($this->yValues[$xKey] - $bestFitY) * ($this->yValues[$xKey] - $bestFitY); |
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36 |
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if ($const === true) { |
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31 |
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$SStot += ($this->yValues[$xKey] - $meanY) * ($this->yValues[$xKey] - $meanY); |
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} else { |
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5 |
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$SStot += $this->yValues[$xKey] * $this->yValues[$xKey]; |
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} |
385
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36 |
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$SScov += ($this->xValues[$xKey] - $meanX) * ($this->yValues[$xKey] - $meanY); |
386
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36 |
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if ($const === true) { |
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31 |
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$SSsex += ($this->xValues[$xKey] - $meanX) * ($this->xValues[$xKey] - $meanX); |
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} else { |
389
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5 |
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$SSsex += $this->xValues[$xKey] * $this->xValues[$xKey]; |
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} |
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} |
392
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393
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36 |
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$this->SSResiduals = $SSres; |
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36 |
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$this->DFResiduals = $this->valueCount - 1 - ($const === true ? 1 : 0); |
395
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396
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36 |
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if ($this->DFResiduals == 0.0) { |
397
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1 |
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$this->stdevOfResiduals = 0.0; |
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} else { |
399
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35 |
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$this->stdevOfResiduals = sqrt($SSres / $this->DFResiduals); |
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} |
401
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// Scrutinizer thinks $SSres == $SStot is always true. It is wrong. |
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36 |
|
if ($SStot == self::$scrutinizerZeroPointZero || self::scrutinizerLooseCompare($SSres, $SStot)) { |
403
|
|
|
$this->goodnessOfFit = 1; |
404
|
|
|
} else { |
405
|
36 |
|
$this->goodnessOfFit = 1 - ($SSres / $SStot); |
406
|
|
|
} |
407
|
|
|
|
408
|
36 |
|
$this->SSRegression = $this->goodnessOfFit * $SStot; |
409
|
36 |
|
$this->covariance = $SScov / $this->valueCount; |
410
|
36 |
|
$this->correlation = ($this->valueCount * $sumXY - $sumX * $sumY) / sqrt(($this->valueCount * $sumX2 - $sumX ** 2) * ($this->valueCount * $sumY2 - $sumY ** 2)); |
411
|
36 |
|
$this->slopeSE = $this->stdevOfResiduals / sqrt($SSsex); |
412
|
36 |
|
$this->intersectSE = $this->stdevOfResiduals * sqrt(1 / ($this->valueCount - ($sumX * $sumX) / $sumX2)); |
413
|
36 |
|
if ($this->SSResiduals != 0.0) { |
414
|
25 |
|
if ($this->DFResiduals == 0.0) { |
415
|
|
|
$this->f = 0.0; |
416
|
|
|
} else { |
417
|
25 |
|
$this->f = $this->SSRegression / ($this->SSResiduals / $this->DFResiduals); |
418
|
|
|
} |
419
|
|
|
} else { |
420
|
12 |
|
if ($this->DFResiduals == 0.0) { |
421
|
1 |
|
$this->f = 0.0; |
422
|
|
|
} else { |
423
|
11 |
|
$this->f = $this->SSRegression / $this->DFResiduals; |
424
|
|
|
} |
425
|
|
|
} |
426
|
|
|
} |
427
|
|
|
|
428
|
|
|
/** @return float|int */ |
429
|
36 |
|
private function sumSquares(array $values) |
430
|
|
|
{ |
431
|
36 |
|
return array_sum( |
432
|
36 |
|
array_map( |
433
|
36 |
|
function ($value) { |
434
|
36 |
|
return $value ** 2; |
435
|
36 |
|
}, |
436
|
36 |
|
$values |
437
|
36 |
|
) |
438
|
36 |
|
); |
439
|
|
|
} |
440
|
|
|
|
441
|
|
|
/** |
442
|
|
|
* @param float[] $yValues |
443
|
|
|
* @param float[] $xValues |
444
|
|
|
*/ |
445
|
36 |
|
protected function leastSquareFit(array $yValues, array $xValues, bool $const): void |
446
|
|
|
{ |
447
|
|
|
// calculate sums |
448
|
36 |
|
$sumValuesX = array_sum($xValues); |
449
|
36 |
|
$sumValuesY = array_sum($yValues); |
450
|
36 |
|
$meanValueX = $sumValuesX / $this->valueCount; |
451
|
36 |
|
$meanValueY = $sumValuesY / $this->valueCount; |
452
|
36 |
|
$sumSquaresX = $this->sumSquares($xValues); |
453
|
36 |
|
$sumSquaresY = $this->sumSquares($yValues); |
454
|
36 |
|
$mBase = $mDivisor = 0.0; |
455
|
36 |
|
$xy_sum = 0.0; |
456
|
36 |
|
for ($i = 0; $i < $this->valueCount; ++$i) { |
457
|
36 |
|
$xy_sum += $xValues[$i] * $yValues[$i]; |
458
|
|
|
|
459
|
36 |
|
if ($const === true) { |
460
|
31 |
|
$mBase += ($xValues[$i] - $meanValueX) * ($yValues[$i] - $meanValueY); |
461
|
31 |
|
$mDivisor += ($xValues[$i] - $meanValueX) * ($xValues[$i] - $meanValueX); |
462
|
|
|
} else { |
463
|
5 |
|
$mBase += $xValues[$i] * $yValues[$i]; |
464
|
5 |
|
$mDivisor += $xValues[$i] * $xValues[$i]; |
465
|
|
|
} |
466
|
|
|
} |
467
|
|
|
|
468
|
|
|
// calculate slope |
469
|
36 |
|
$this->slope = $mBase / $mDivisor; |
470
|
|
|
|
471
|
|
|
// calculate intersect |
472
|
36 |
|
$this->intersect = ($const === true) ? $meanValueY - ($this->slope * $meanValueX) : 0.0; |
473
|
|
|
|
474
|
36 |
|
$this->calculateGoodnessOfFit($sumValuesX, $sumValuesY, $sumSquaresX, $sumSquaresY, $xy_sum, $meanValueX, $meanValueY, $const); |
475
|
|
|
} |
476
|
|
|
|
477
|
|
|
/** |
478
|
|
|
* Define the regression. |
479
|
|
|
* |
480
|
|
|
* @param float[] $yValues The set of Y-values for this regression |
481
|
|
|
* @param float[] $xValues The set of X-values for this regression |
482
|
|
|
*/ |
483
|
36 |
|
public function __construct($yValues, $xValues = []) |
484
|
|
|
{ |
485
|
|
|
// Calculate number of points |
486
|
36 |
|
$yValueCount = count($yValues); |
487
|
36 |
|
$xValueCount = count($xValues); |
488
|
|
|
|
489
|
|
|
// Define X Values if necessary |
490
|
36 |
|
if ($xValueCount === 0) { |
491
|
|
|
$xValues = range(1, $yValueCount); |
492
|
36 |
|
} elseif ($yValueCount !== $xValueCount) { |
493
|
|
|
// Ensure both arrays of points are the same size |
494
|
|
|
$this->error = true; |
495
|
|
|
} |
496
|
|
|
|
497
|
36 |
|
$this->valueCount = $yValueCount; |
498
|
36 |
|
$this->xValues = $xValues; |
499
|
36 |
|
$this->yValues = $yValues; |
500
|
|
|
} |
501
|
|
|
} |
502
|
|
|
|