papaya
Class Linear.StdErr

java.lang.Object
  papaya.Linear.StdErr

Enclosing class:

Linear

public static class Linear.StdErr
extends Object

Contains methods related to computing the standard errors of the residuals, slope and intercept associated with the best-fit linear line.

Method Summary

static float	intercept(float[] x, float residualStdErr) Returns the standard error of the computed slope given x and the standard error in the residuals.
static float	residual(float[] residuals, int df) Returns the standard error of the residuals given the degrees of freedom.
static float	slope(float[] x, float residualStdErr) Returns the standard error of the computed slope given x and the standard error in the residuals.

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Detail

residual

public static float residual(float[] residuals,
                             int df)

Returns the standard error of the residuals given the degrees of freedom. That is,

 residualStdErr = Sqrt ( Sum( (delta[i] - mean(delta))^2 ) / df )
 

where df is the degrees of freedom ( (n-1) if the y-intercept was pre-specified in the best-fit line, (n-2) if neither slope nor intercept were specified.)

Parameters:

residuals -

df -

Returns:

standard error of the residual

slope

public static float slope(float[] x,
                          float residualStdErr)

Returns the standard error of the computed slope given x and the standard error in the residuals. That is,

 slopeStdErr = residualStdErr / Sum ( (x[i] - mean(x))^2 ).
 

Parameters:

x - the independent variable

residualStdErr - the standard error of the residual

Returns:

the error in the slope.

intercept

public static float intercept(float[] x,
                              float residualStdErr)

Returns the standard error of the computed slope given x and the standard error in the residuals. That is,

 interceptStdErr = slopeStdErr / Sqrt( Sum(x[i]*x[i])/size ).
 

where the slopeStdErr is computed using the methods specified in slope(float[], float).

Parameters:

x - the independent variable

residualStdErr - the standard error of the residual

Returns:

error in the slope.