SimpleRegression ("The Adobe AEM Quickstart and Web Application.")

java.lang.Object
- org.apache.commons.math.stat.regression.SimpleRegression

All Implemented Interfaces:

java.io.Serializable
```
public class SimpleRegression
extends java.lang.Object
implements java.io.Serializable
```
Estimates an ordinary least squares regression model with one independent variable.
y = intercept + slope * x

Standard errors for intercept and slope are available as well as ANOVA, r-square and Pearson's r statistics.

Observations (x,y pairs) can be added to the model one at a time or they can be provided in a 2-dimensional array. The observations are not stored in memory, so there is no limit to the number of observations that can be added to the model.

Usage Notes:
- When there are fewer than two observations in the model, or when there is no variation in the x values (i.e. all x values are the same) all statistics return NaN. At least two observations with different x coordinates are requred to estimate a bivariate regression model.
- getters for the statistics always compute values based on the current set of observations -- i.e., you can get statistics, then add more data and get updated statistics without using a new instance. There is no "compute" method that updates all statistics. Each of the getters performs the necessary computations to return the requested statistic.
See Also:

Serialized Form

Constructor Summary

Constructors
Constructor and Description
`SimpleRegression()` Create an empty SimpleRegression instance
`SimpleRegression(int degrees)` Create an empty SimpleRegression.
`SimpleRegression(TDistribution t)` Deprecated. in 2.2 (to be removed in 3.0). Please use the `other constructor` instead.

Method Summary

All Methods Instance Methods Concrete Methods Deprecated Methods
Modifier and Type	Method and Description
`void`	`addData(double[][] data)` Adds the observations represented by the elements in `data`.
`void`	`addData(double x, double y)` Adds the observation (x,y) to the regression data set.
`void`	`clear()` Clears all data from the model.
`double`	`getIntercept()` Returns the intercept of the estimated regression line.
`double`	`getInterceptStdErr()` Returns the standard error of the intercept estimate, usually denoted s(b0).
`double`	`getMeanSquareError()` Returns the sum of squared errors divided by the degrees of freedom, usually abbreviated MSE.
`long`	`getN()` Returns the number of observations that have been added to the model.
`double`	`getR()` Returns Pearson's product moment correlation coefficient, usually denoted r.
`double`	`getRegressionSumSquares()` Returns the sum of squared deviations of the predicted y values about their mean (which equals the mean of y).
`double`	`getRSquare()` Returns the coefficient of determination, usually denoted r-square.
`double`	`getSignificance()` Returns the significance level of the slope (equiv) correlation.
`double`	`getSlope()` Returns the slope of the estimated regression line.
`double`	`getSlopeConfidenceInterval()` Returns the half-width of a 95% confidence interval for the slope estimate.
`double`	`getSlopeConfidenceInterval(double alpha)` Returns the half-width of a (100-100*alpha)% confidence interval for the slope estimate.
`double`	`getSlopeStdErr()` Returns the standard error of the slope estimate, usually denoted s(b1).
`double`	`getSumOfCrossProducts()` Returns the sum of crossproducts, x_i*y_i.
`double`	`getSumSquaredErrors()` Returns the sum of squared errors (SSE) associated with the regression model.
`double`	`getTotalSumSquares()` Returns the sum of squared deviations of the y values about their mean.
`double`	`getXSumSquares()` Returns the sum of squared deviations of the x values about their mean.
`double`	`predict(double x)` Returns the "predicted" `y` value associated with the supplied `x` value, based on the data that has been added to the model when this method is activated.
`void`	`removeData(double[][] data)` Removes observations represented by the elements in `data`.
`void`	`removeData(double x, double y)` Removes the observation (x,y) from the regression data set.
`void`	`setDistribution(TDistribution value)` Deprecated. in 2.2 (to be removed in 3.0).

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

- Constructor Detail
  - SimpleRegression
```
public SimpleRegression()
```
    Create an empty SimpleRegression instance
  - SimpleRegression
```
@Deprecated
public SimpleRegression(TDistribution t)
```
    Deprecated. in 2.2 (to be removed in 3.0). Please use the other constructor instead.
    
    Create an empty SimpleRegression using the given distribution object to compute inference statistics.
    
    Parameters:
    
    t - the distribution used to compute inference statistics.
    
    Since:
    
    1.2
  - SimpleRegression
```
public SimpleRegression(int degrees)
```
    Create an empty SimpleRegression.
    
    Parameters:
    
    degrees - Number of degrees of freedom of the distribution used to compute inference statistics.
    
    Since:
    
    2.2
- Method Detail
  - addData
```
public void addData(double x,
                    double y)
```
    Adds the observation (x,y) to the regression data set.
    Uses updating formulas for means and sums of squares defined in "Algorithms for Computing the Sample Variance: Analysis and Recommendations", Chan, T.F., Golub, G.H., and LeVeque, R.J. 1983, American Statistician, vol. 37, pp. 242-247, referenced in Weisberg, S. "Applied Linear Regression". 2nd Ed. 1985.
    
    Parameters:
    
    x - independent variable value
    
    y - dependent variable value
  - removeData
```
public void removeData(double x,
                       double y)
```
    Removes the observation (x,y) from the regression data set.
    Mirrors the addData method. This method permits the use of SimpleRegression instances in streaming mode where the regression is applied to a sliding "window" of observations, however the caller is responsible for maintaining the set of observations in the window.
    The method has no effect if there are no points of data (i.e. n=0)
    
    Parameters:
    
    x - independent variable value
    
    y - dependent variable value
  - addData
```
public void addData(double[][] data)
```
    Adds the observations represented by the elements in data.
    (data[0][0],data[0][1]) will be the first observation, then (data[1][0],data[1][1]), etc.
    
    This method does not replace data that has already been added. The observations represented by data are added to the existing dataset.
    
    To replace all data, use clear() before adding the new data.
    
    Parameters:
    
    data - array of observations to be added
  - removeData
```
public void removeData(double[][] data)
```
    Removes observations represented by the elements in data.
    If the array is larger than the current n, only the first n elements are processed. This method permits the use of SimpleRegression instances in streaming mode where the regression is applied to a sliding "window" of observations, however the caller is responsible for maintaining the set of observations in the window.
    
    To remove all data, use clear().
    
    Parameters:
    
    data - array of observations to be removed
  - clear
```
public void clear()
```
    Clears all data from the model.
  - getN
```
public long getN()
```
    Returns the number of observations that have been added to the model.
    
    Returns:
    
    n number of observations that have been added.
  - predict
```
public double predict(double x)
```
    Returns the "predicted" y value associated with the supplied x value, based on the data that has been added to the model when this method is activated.
    predict(x) = intercept + slope * x
    
    Preconditions:
    - At least two observations (with at least two different x values) must have been added before invoking this method. If this method is invoked before a model can be estimated, Double,NaN is returned.
    Parameters:
    
    x - input x value
    
    Returns:
    
    predicted y value
  - getIntercept
```
public double getIntercept()
```
    Returns the intercept of the estimated regression line.
    The least squares estimate of the intercept is computed using the normal equations. The intercept is sometimes denoted b0.
    
    Preconditions:
    - At least two observations (with at least two different x values) must have been added before invoking this method. If this method is invoked before a model can be estimated, Double,NaN is returned.
    Returns:
    
    the intercept of the regression line
  - getSlope
```
public double getSlope()
```
    Returns the slope of the estimated regression line.
    The least squares estimate of the slope is computed using the normal equations. The slope is sometimes denoted b1.
    
    Preconditions:
    - At least two observations (with at least two different x values) must have been added before invoking this method. If this method is invoked before a model can be estimated, Double.NaN is returned.
    Returns:
    
    the slope of the regression line
  - getSumSquaredErrors
```
public double getSumSquaredErrors()
```
    Returns the sum of squared errors (SSE) associated with the regression model.
    The sum is computed using the computational formula
    
    SSE = SYY - (SXY * SXY / SXX)
    
    where SYY is the sum of the squared deviations of the y values about their mean, SXX is similarly defined and SXY is the sum of the products of x and y mean deviations.
    The sums are accumulated using the updating algorithm referenced in addData(double, double).
    
    The return value is constrained to be non-negative - i.e., if due to rounding errors the computational formula returns a negative result, 0 is returned.
    
    Preconditions:
    - At least two observations (with at least two different x values) must have been added before invoking this method. If this method is invoked before a model can be estimated, Double,NaN is returned.
    Returns:
    
    sum of squared errors associated with the regression model
  - getTotalSumSquares
```
public double getTotalSumSquares()
```
    Returns the sum of squared deviations of the y values about their mean.
    This is defined as SSTO here.
    
    If n < 2, this returns Double.NaN.
    
    Returns:
    
    sum of squared deviations of y values
  - getXSumSquares
```
public double getXSumSquares()
```
    Returns the sum of squared deviations of the x values about their mean. If n < 2, this returns Double.NaN.
    
    Returns:
    
    sum of squared deviations of x values
  - getSumOfCrossProducts
```
public double getSumOfCrossProducts()
```
    Returns the sum of crossproducts, x_i*y_i.
    
    Returns:
    
    sum of cross products
  - getRegressionSumSquares
```
public double getRegressionSumSquares()
```
    Returns the sum of squared deviations of the predicted y values about their mean (which equals the mean of y).
    This is usually abbreviated SSR or SSM. It is defined as SSM here
    
    Preconditions:
    - At least two observations (with at least two different x values) must have been added before invoking this method. If this method is invoked before a model can be estimated, Double.NaN is returned.
    Returns:
    
    sum of squared deviations of predicted y values
  - getMeanSquareError
```
public double getMeanSquareError()
```
    Returns the sum of squared errors divided by the degrees of freedom, usually abbreviated MSE.
    If there are fewer than three data pairs in the model, or if there is no variation in x, this returns Double.NaN.
    
    Returns:
    
    sum of squared deviations of y values
  - getR
```
public double getR()
```
    Returns Pearson's product moment correlation coefficient, usually denoted r.
    Preconditions:
    - At least two observations (with at least two different x values) must have been added before invoking this method. If this method is invoked before a model can be estimated, Double,NaN is returned.
    Returns:
    
    Pearson's r
  - getRSquare
```
public double getRSquare()
```
    Returns the coefficient of determination, usually denoted r-square.
    Preconditions:
    - At least two observations (with at least two different x values) must have been added before invoking this method. If this method is invoked before a model can be estimated, Double,NaN is returned.
    Returns:
    
    r-square
  - getInterceptStdErr
```
public double getInterceptStdErr()
```
    Returns the standard error of the intercept estimate, usually denoted s(b0).
    If there are fewer that three observations in the model, or if there is no variation in x, this returns Double.NaN.
    
    Returns:
    
    standard error associated with intercept estimate
  - getSlopeStdErr
```
public double getSlopeStdErr()
```
    Returns the standard error of the slope estimate, usually denoted s(b1).
    If there are fewer that three data pairs in the model, or if there is no variation in x, this returns Double.NaN.
    
    Returns:
    
    standard error associated with slope estimate
  - getSlopeConfidenceInterval
```
public double getSlopeConfidenceInterval()
                                  throws MathException
```
    Returns the half-width of a 95% confidence interval for the slope estimate.
    The 95% confidence interval is
    
    (getSlope() - getSlopeConfidenceInterval(), getSlope() + getSlopeConfidenceInterval())
    
    If there are fewer that three observations in the model, or if there is no variation in x, this returns Double.NaN.
    
    Usage Note:
    The validity of this statistic depends on the assumption that the observations included in the model are drawn from a Bivariate Normal Distribution.
    
    Returns:
    
    half-width of 95% confidence interval for the slope estimate
    
    Throws:
    
    MathException - if the confidence interval can not be computed.
  - getSlopeConfidenceInterval
```
public double getSlopeConfidenceInterval(double alpha)
                                  throws MathException
```
    Returns the half-width of a (100-100*alpha)% confidence interval for the slope estimate.
    The (100-100*alpha)% confidence interval is
    
    (getSlope() - getSlopeConfidenceInterval(), getSlope() + getSlopeConfidenceInterval())
    
    To request, for example, a 99% confidence interval, use alpha = .01
    
    Usage Note:
    The validity of this statistic depends on the assumption that the observations included in the model are drawn from a Bivariate Normal Distribution.
    
    Preconditions:
    - If there are fewer that three observations in the model, or if there is no variation in x, this returns Double.NaN.
    - (0 < alpha < 1); otherwise an IllegalArgumentException is thrown.
    Parameters:
    
    alpha - the desired significance level
    
    Returns:
    
    half-width of 95% confidence interval for the slope estimate
    
    Throws:
    
    MathException - if the confidence interval can not be computed.
  - getSignificance
```
public double getSignificance()
                       throws MathException
```
    Returns the significance level of the slope (equiv) correlation.
    Specifically, the returned value is the smallest alpha such that the slope confidence interval with significance level equal to alpha does not include 0. On regression output, this is often denoted Prob(|t| > 0)
    Usage Note:
    The validity of this statistic depends on the assumption that the observations included in the model are drawn from a Bivariate Normal Distribution.
    
    If there are fewer that three observations in the model, or if there is no variation in x, this returns Double.NaN.
    
    Returns:
    
    significance level for slope/correlation
    
    Throws:
    
    MathException - if the significance level can not be computed.
  - setDistribution
```
@Deprecated
public void setDistribution(TDistribution value)
```
    Deprecated. in 2.2 (to be removed in 3.0).
    
    Modify the distribution used to compute inference statistics.
    
    Parameters:
    
    value - the new distribution
    
    Since:
    
    1.2

Class SimpleRegression

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

SimpleRegression

SimpleRegression

SimpleRegression

Method Detail

addData

removeData

addData

removeData

clear

getN

predict

getIntercept

getSlope

getSumSquaredErrors

getTotalSumSquares

getXSumSquares

getSumOfCrossProducts

getRegressionSumSquares

getMeanSquareError

getR

getRSquare

getInterceptStdErr

getSlopeStdErr

getSlopeConfidenceInterval

getSlopeConfidenceInterval

getSignificance

setDistribution