Regression latex documentation

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

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.
+     * {@inheritdoc}
-     *
-     * 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 <d.eichhorn@oms.com>
      */
     public static function getRegression(array $x, array $y) : array
     {

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.
+     * {@inheritdoc}
-     *
-     * 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 <d.eichhorn@oms.com>
      */
     public static function getRegression(array $x, array $y) : array
     {

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.
+     * {@inheritdoc}
-     *
-     * 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 <d.eichhorn@oms.com>
      */
     public static function getRegression(array $x, array $y) : array
     {

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]));

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