diff --git a/Math/Statistic/Forecast/Error.php b/Math/Statistic/Forecast/Error.php index f806b55cd..2e4fab592 100644 --- a/Math/Statistic/Forecast/Error.php +++ b/Math/Statistic/Forecast/Error.php @@ -142,7 +142,9 @@ class Error /** * Goodness of fit. * - * Evaluating how well the observed data fit the linear regression model + * Evaluating how well the observed data fit the linear regression model. + * + * @latex R^{2} = \frac{\sum \left(\hat{y}_{i} - \bar{y}\right)^2}{\sum \left(y_{i} - \bar{y}\right)^2} * * @param array $observed Obersved y values * @param array $forecasted Forecasted y values diff --git a/Math/Statistic/Forecast/Regression/LevelLogRegression.php b/Math/Statistic/Forecast/Regression/LevelLogRegression.php index 15b9d3457..d6661ded9 100644 --- a/Math/Statistic/Forecast/Regression/LevelLogRegression.php +++ b/Math/Statistic/Forecast/Regression/LevelLogRegression.php @@ -30,17 +30,7 @@ namespace phpOMS\Math\Statistic\Forecast\Regression; class LevelLogRegression extends RegressionAbstract { /** - * Get linear regression based on scatter plot. - * - * y = b0 + b1 * x - * - * @param array $x Obersved x values - * @param array $y Observed y values - * - * @return array [b0 => ?, b1 => ?] - * - * @since 1.0.0 - * @author Dennis Eichhorn + * {@inheritdoc} */ public static function getRegression(array $x, array $y) : array { diff --git a/Math/Statistic/Forecast/Regression/LogLevelRegression.php b/Math/Statistic/Forecast/Regression/LogLevelRegression.php index 52322db47..1428283af 100644 --- a/Math/Statistic/Forecast/Regression/LogLevelRegression.php +++ b/Math/Statistic/Forecast/Regression/LogLevelRegression.php @@ -30,17 +30,7 @@ namespace phpOMS\Math\Statistic\Forecast\Regression; class LogLevelRegression extends RegressionAbstract { /** - * Get linear regression based on scatter plot. - * - * y = b0 + b1 * x - * - * @param array $x Obersved x values - * @param array $y Observed y values - * - * @return array [b0 => ?, b1 => ?] - * - * @since 1.0.0 - * @author Dennis Eichhorn + * {@inheritdoc} */ public static function getRegression(array $x, array $y) : array { diff --git a/Math/Statistic/Forecast/Regression/LogLogRegression.php b/Math/Statistic/Forecast/Regression/LogLogRegression.php index acdcf7822..2c89caab8 100644 --- a/Math/Statistic/Forecast/Regression/LogLogRegression.php +++ b/Math/Statistic/Forecast/Regression/LogLogRegression.php @@ -30,17 +30,7 @@ namespace phpOMS\Math\Statistic\Forecast\Regression; class LogLogRegression extends RegressionAbstract { /** - * Get linear regression based on scatter plot. - * - * y = b0 + b1 * x - * - * @param array $x Obersved x values - * @param array $y Observed y values - * - * @return array [b0 => ?, b1 => ?] - * - * @since 1.0.0 - * @author Dennis Eichhorn + * {@inheritdoc} */ public static function getRegression(array $x, array $y) : array { diff --git a/Math/Statistic/Forecast/Regression/MultipleLinearRegression.php b/Math/Statistic/Forecast/Regression/MultipleLinearRegression.php index 2ba3ee6a0..ef8084dc4 100644 --- a/Math/Statistic/Forecast/Regression/MultipleLinearRegression.php +++ b/Math/Statistic/Forecast/Regression/MultipleLinearRegression.php @@ -4,6 +4,9 @@ namespace phpOMS\Math\Statistic\Forecast\Regression; class MultipleLinearRegression { + /** + * {@inheritdoc} + */ public static function getRegression(array $x, array $y) : array { $X = new Matrix(count($x), count($x[0])); diff --git a/Math/Statistic/Forecast/Regression/RegressionAbstract.php b/Math/Statistic/Forecast/Regression/RegressionAbstract.php index 2b4498956..fcd353482 100644 --- a/Math/Statistic/Forecast/Regression/RegressionAbstract.php +++ b/Math/Statistic/Forecast/Regression/RegressionAbstract.php @@ -11,7 +11,7 @@ abstract class RegressionAbstract /** * Get linear regression based on scatter plot. * - * y = b0 + b1 * x + * @latex y = b_{0} + b_{1} \cdot x * * @param array $x Obersved x values * @param array $y Observed y values @@ -37,6 +37,8 @@ abstract class RegressionAbstract * * Used in order to evaluate the performance of the linear regression * + * @latex s_{e} = \sqrt{\frac{1}{N - 2}\sum_{i = 1}^{N} e_{i}^{2}} + * * @param array $errors Errors (e = y - y_forecasted) * * @return float @@ -88,6 +90,8 @@ abstract class RegressionAbstract /** * Get linear regression parameter beta 1. * + * @latex \beta_{1} = \frac{\sum_{i=1}^{N} \left(y_{i} - \bar{y}\right)\left(x_{i} - \bar{x}\right)}{\sum_{i=1}^{N} \left(x_{i} - \bar{x}\right)^{2}} + * * @param array $x Obersved x values * @param array $y Observed y values * @@ -116,6 +120,8 @@ abstract class RegressionAbstract /** * Get linear regression parameter beta 0. * + * @latex \beta_{0} = \bar{x} - b_{1} \cdot \bar{x} + * * @param array $x Obersved x values * @param array $y Observed y values * @param float $b1 Beta 1