LMResiduals (NMDEV 1.2.9 API)

java.lang.Object
- dev.nm.stat.regression.linear.residualanalysis.LMResiduals

Direct Known Subclasses:

GLMResiduals, LogisticResiduals, OLSResiduals
```
public class LMResiduals
extends Object
```
This is the residual analysis of the results of a 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:

Constructor Summary

Constructors
Constructor and Description

LMResiduals(LMProblem problem, Vector fitted)
Performs residual analysis for a linear regression problem.

Constructors
Constructor and Description
`LMResiduals(LMProblem problem, Vector fitted)` Performs residual analysis for a linear regression problem.

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`double`	`AR2()` Gets the diagnostic measure: adjusted R-squared
`int`	`df()` Gets the degree of freedom.
`ImmutableVector`	`fitted()` Gets the fitted values, \(\hat{y}\).
`double`	`Fstat()` Gets the 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.
`LMProblem`	`getProblem()` Gets the linear regression problem.
`ImmutableMatrix`	`hHat()` Gets the projection matrix, H-hat.
`ImmutableVector`	`leverage()` Gets the leverage.
`double`	`R2()` Gets the diagnostic measure: R-squared.
`ImmutableVector`	`residuals()` Gets the residuals, ε, the differences between sample and fitted values.
`double`	`RSS()` Gets the diagnostic measure: sum of squared residuals, \(\sum \epsilon^2\).
`ImmutableVector`	`standardized()` standard residual = residual / v1 / sqrt(RSS / (n-m))
`double`	`stderr()` Gets the standard error of the residuals.
`ImmutableVector`	`studentized()` studentized residual = standardized sqrt((n-m-1) / (n-m-standardized^2))*
`double`	`TSS()` Gets the diagnostic measure: total sum of squares, \(\sum (y-y_mean)^2 \).
`ImmutableVector`	`weightedFittedValues()` Gets the weighted, fitted values.
`ImmutableVector`	`weightedResiduals()` Gets the weighted residuals.

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

- Constructor Detail
  - LMResiduals
```
public LMResiduals(LMProblem problem,
                   Vector fitted)
```
    Performs residual analysis for a linear regression problem.
    
    Parameters:
    
    problem - the linear regression problem to be solved
    
    fitted - the fitted values, \(\hat{y}\)
- Method Detail
  - getProblem
```
public LMProblem getProblem()
```
    Gets the linear regression problem.
    
    Returns:
    
    the linear regression problem
  - fitted
```
public ImmutableVector fitted()
```
    Gets the fitted values, \(\hat{y}\).
    
    Returns:
    
    the fitted values, \(\hat{y}\)
  - residuals
```
public ImmutableVector residuals()
```
    Gets the residuals, ε, the differences between sample and fitted values.
    
    Returns:
    
    the residuals, ε
  - weightedFittedValues
```
public ImmutableVector weightedFittedValues()
```
    Gets the weighted, fitted values.
    
    Returns:
    
    the weighted, fitted values
  - weightedResiduals
```
public ImmutableVector weightedResiduals()
```
    Gets the weighted residuals.
    
    Returns:
    
    the weighted residuals
  - RSS
```
public double RSS()
```
    Gets the diagnostic measure: sum of squared residuals, \(\sum \epsilon^2\).
    
    Returns:
    
    sum of squared residuals, \(\sum \epsilon^2\)
  - TSS
```
public double TSS()
```
    Gets the diagnostic measure: total sum of squares, \(\sum (y-y_mean)^2 \).
    
    Returns:
    
    total sum of squares, \(\sum (y-y_mean)^2 \)
  - R2
```
public double R2()
```
    Gets the diagnostic measure: R-squared.
    
    Returns:
    
    R-squared
  - AR2
```
public double AR2()
```
    Gets the diagnostic measure: adjusted R-squared
    
    Returns:
    
    adjusted R-squared
  - stderr
```
public double stderr()
```
    Gets the standard error of the residuals.
    
    Returns:
    
    the standard error of the residuals
  - Fstat
```
public double Fstat()
```
    Gets the 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.
    Returns:
    
    F statistics
    
    See Also:
    
    "Kutner, Nachtsheim and Neter, "p.69, equation (2.60)," Applied linear regression models. 4th edition."
  - hHat
```
public ImmutableMatrix hHat()
```
    Gets the projection matrix, H-hat.
    
    Returns:
    
    the projection matrix
    
    See Also:
    
    "Sanford Weisberg, "p.168, Section 8.1, Chapter 8," Applied Linear Regression, 3rd edition, 2005. Wiley-Interscience."
  - leverage
```
public ImmutableVector leverage()
```
    Gets the leverage. The bigger the leverage for an observation, the bigger influence on the prediction.
    
    Returns:
    
    the leverage
  - standardized
```
public ImmutableVector standardized()
```
    standard residual = residual / v1 / sqrt(RSS / (n-m))
    
    Returns:
    
    standardized residuals
  - studentized
```
public ImmutableVector studentized()
```
    studentized residual = standardized * sqrt((n-m-1) / (n-m-standardized^2))
    Returns:
    
    studentized residuals
    
    See Also:
    "Chatterjee, Hadi and Price, "p.90 (4.15), Section 4.3," Regression Analysis by Example, 3rd edition, 2000. Wiley Series in Probability and Statistics."
    
    @see Wikipedia: Studentized residual
  - df
```
public int df()
```
    Gets the degree of freedom.
    TODO: User should be able to modify this method for a different regression.
    
    Returns:
    
    the degree of freedom

Class LMResiduals

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

LMResiduals

Method Detail

getProblem

fitted

residuals

weightedFittedValues

weightedResiduals

RSS

TSS

R2

AR2

stderr

Fstat

hHat

leverage

standardized

studentized

df