Residuals (SuanShuExtension API)

java.lang.Object
- com.numericalmethod.suanshu.stats.regression.linear.Residuals
- - com.numericalmethod.suanshu.stats.regression.linear.ols.Residuals

All Implemented Interfaces:

java.io.Serializable
```
public class Residuals
extends Residuals
```
Residual analysis of the results of an Ordinary Least Square linear regression model.
Once a regression model has been constructed, it may be important to confirm the goodness of fit of the model and the statistical significance of the estimated parameters. Commonly used checks of goodness of fit include the R-squared, analysis of the pattern of residuals and hypothesis testing. Statistical significance can be checked by an F-test of the overall fit, followed by t-tests of individual parameters.
See Also:
, Serialized Form

Field Summary

Fields
Modifier and Type	Field and Description
`double`	`AR2` diagnostic measure: the adjusted R-squared
`double`	`f` diagnostic measure: F statistics mean of regression / mean squared error = sum((y_i_hat-y_mean)^2) / mean squared error [(TSS-RSS)/n] / [RSS/(m-n)] y_i_hat are the fitted values of the regression.
`ImmutableMatrix`	`hHat` projection matrix H-hat
`ImmutableVector`	`leverage` leverage; the bigger the leverage for an observation, the bigger influence on the prediction
`double`	`R2` diagnostic measure: the R-squared
`double`	`RSS` diagnostic measure: the sum of squared residuals, Σ(ε^2)
`double`	`stderr` the standard error of the residuals
`double`	`TSS` diagnostic measure: the total sum of squares, Σ((y-y_mean)^2)
`ImmutableVector`	`wFitted` the weighted, fitted values
`ImmutableVector`	`wResiduals` the weighted residuals

Fields inherited from class com.numericalmethod.suanshu.stats.regression.linear.Residuals
fitted, problem, residuals

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`ImmutableVector`	`standardized()` standard residual = residual / v1 / sqrt(RSS / (n-m))
`Vector`	`studentized()` studentized residual = standardized * sqrt((n-m-1) / (n-m-standardized^2))

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Field Detail
  - wFitted
```
public final ImmutableVector wFitted
```
    the weighted, fitted values
  - wResiduals
```
public final ImmutableVector wResiduals
```
    the weighted residuals
  - stderr
```
public final double stderr
```
    the standard error of the residuals
  - RSS
```
public final double RSS
```
    diagnostic measure: the sum of squared residuals, Σ(ε^2)
  - TSS
```
public final double TSS
```
    diagnostic measure: the total sum of squares, Σ((y-y_mean)^2)
  - R2
```
public final double R2
```
    diagnostic measure: the R-squared
  - AR2
```
public final double AR2
```
    diagnostic measure: the adjusted R-squared
  - f
```
public final double f
```
    diagnostic measure: F statistics
    mean of regression / mean squared error = sum((y_i_hat-y_mean)^2) / mean squared error [(TSS-RSS)/n] / [RSS/(m-n)]
    y_i_hat are the fitted values of the regression.
    
    See Also:
    
    "p.69, equation (2.60). Applied linear regression models. Kutner, Nachtsheim and Neter. 4th edition."
  - hHat
```
public final ImmutableMatrix hHat
```
    projection matrix H-hat
    
    See Also:
    
    "p.168 Section 8.1, Chapter 8. Applied Linear Regression, 3rd edition, 2005. Sanford Weisberg. Wiley-Interscience."
  - leverage
```
public final ImmutableVector leverage
```
    leverage; the bigger the leverage for an observation, the bigger influence on the prediction
- Method Detail
  - standardized
```
public ImmutableVector standardized()
```
    standard residual = residual / v1 / sqrt(RSS / (n-m))
    
    Returns:
    
    standardized residuals
  - studentized
```
public Vector studentized()
```
    studentized residual = standardized * sqrt((n-m-1) / (n-m-standardized^2))
    Returns:
    
    studentized residuals
    
    See Also:
    "p.90 (4.15). Section 4.3. Regression Analysis by Example, 3rd edition, 2000. Chatterjee, Hadi and Price. Wiley Series in Probability and Statistics."
    @see Wikipedia: Studentized residual

Class Residuals

Field Summary

Fields inherited from class com.numericalmethod.suanshu.stats.regression.linear.Residuals

Method Summary

Methods inherited from class java.lang.Object

Field Detail

wFitted

wResiduals

stderr

RSS

TSS

R2

AR2

f

hHat

leverage

Method Detail

standardized

studentized