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Regression latex documentation

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This commit is contained in:
Dennis Eichhorn 2016-08-25 09:52:19 +02:00
parent 51a016d228
commit fed381ba8a
6 changed files with 16 additions and 35 deletions
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4
Math/Statistic/Forecast/Error.php
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@ -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

12
Math/Statistic/Forecast/Regression/LevelLogRegression.php
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@ -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 <d.eichhorn@oms.com>
* {@inheritdoc}
*/
public static function getRegression(array $x, array $y) : array
{

12
Math/Statistic/Forecast/Regression/LogLevelRegression.php
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@ -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 <d.eichhorn@oms.com>
* {@inheritdoc}
*/
public static function getRegression(array $x, array $y) : array
{

12
Math/Statistic/Forecast/Regression/LogLogRegression.php
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@ -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 <d.eichhorn@oms.com>
* {@inheritdoc}
*/
public static function getRegression(array $x, array $y) : array
{

3
Math/Statistic/Forecast/Regression/MultipleLinearRegression.php
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@ -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]));

8
Math/Statistic/Forecast/Regression/RegressionAbstract.php
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@ -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