Class SimpleRegression
y = intercept + slope * x
Standard errors for intercept
and slope
are
available as well as ANOVA, rsquare 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 2dimensional 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 required 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.
 The intercept term may be suppressed by passing
false
to theSimpleRegression(boolean)
constructor. When thehasIntercept
property is false, the model is estimated without a constant term andgetIntercept()
returns0
.

Constructor Summary
ConstructorDescriptionCreate an empty SimpleRegression instanceSimpleRegression
(boolean includeIntercept) Create a SimpleRegression instance, specifying whether or not to estimate an intercept. 
Method Summary
Modifier and TypeMethodDescriptionvoid
addData
(double x, double y) Adds the observation (x,y) to the regression data set.void
append
(SimpleRegression reg) Appends data from another regression calculation to this one.void
clear()
Clears all data from the model.double
Returns the intercept of the estimated regression line, ifhasIntercept()
is true; otherwise 0.double
Returns the standard error of the intercept estimate, usually denoted s(b0).double
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
Returns the sum of squared deviations of the predicted y values about their mean (which equals the mean of y).double
Returns the coefficient of determination, usually denoted rsquare.double
getSlope()
Returns the slope of the estimated regression line.double
Returns the standard error of the slope estimate, usually denoted s(b1).double
Returns the sum of crossproducts, x_{i}*y_{i}.double
Returns the sum of squared errors (SSE) associated with the regression model.double
Returns the sum of squared deviations of the y values about their mean.double
Returns the sum of squared deviations of the x values about their mean.boolean
Returns true if the model includes an intercept term.double
predict
(double x) Returns the "predicted"y
value associated with the suppliedx
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 indata
.void
removeData
(double x, double y) Removes the observation (x,y) from the regression data set.

Constructor Details

SimpleRegression
public SimpleRegression()Create an empty SimpleRegression instance 
SimpleRegression
public SimpleRegression(boolean includeIntercept) Create a SimpleRegression instance, specifying whether or not to estimate an intercept.Use
false
to estimate a model with no intercept. When thehasIntercept
property is false, the model is estimated without a constant term andgetIntercept()
returns0
. Parameters:
includeIntercept
 whether or not to include an intercept term in the regression model


Method Details

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. 242247, referenced in Weisberg, S. "Applied Linear Regression". 2nd Ed. 1985.
 Parameters:
x
 independent variable valuey
 dependent variable value

append
Appends data from another regression calculation to this one.The mean update formulae are based on a paper written by Philippe Pébay: Formulas for Robust, OnePass Parallel Computation of Covariances and ArbitraryOrder Statistical Moments, 2008, Technical Report SAND20086212, Sandia National Laboratories.
 Parameters:
reg
 model to append data from Since:
 3.3

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 valuey
 dependent variable value

removeData
public void removeData(double[][] data) Removes observations represented by the elements indata
.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 suppliedx
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
 inputx
value Returns:
 predicted
y
value
 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,

getIntercept
public double getIntercept()Returns the intercept of the estimated regression line, ifhasIntercept()
is true; otherwise 0.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 if the model includes an intercept; 0 otherwise
 See Also:
 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,

hasIntercept
public boolean hasIntercept()Returns true if the model includes an intercept term. Returns:
 true if the regression includes an intercept; false otherwise
 See Also:

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
 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,

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 andSXY
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 nonnegative  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
 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,

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 returnsDouble.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. Ifn < 2
, this returnsDouble.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
 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,

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 returnsDouble.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
 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,

getRSquare
public double getRSquare()Returns the coefficient of determination, usually denoted rsquare.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:
 rsquare
 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,

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
Additionally, aDouble.NaN
.Double.NaN
is returned when the intercept is constrained to be zero 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
