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* Fixed all checkstyle errors and eliminated redundant NaN checks. Now have 

100% test path coverage.

* Used distribution framework TDistribution to implement
getSlopeConfidenceInterval and getSignificance methods.

PR: Issue #20657
Obtained from: Bugzilla
Submitted by: Phil Steitz
Reviewed by: Tim O'Brien


git-svn-id: https://svn.apache.org/repos/asf/jakarta/commons/proper/math/trunk@140900 13f79535-47bb-0310-9956-ffa450edef68
This commit is contained in:
Tim O'Brien 2003-06-11 03:33:05 +00:00
parent b58585fb8d
commit 431f303889
2 changed files with 258 additions and 123 deletions
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339
src/java/org/apache/commons/math/stat/BivariateRegression.java
View File

@ -50,30 +50,33 @@
* individuals on behalf of the Apache Software Foundation. For more
* information on the Apache Software Foundation, please see
* <http://www.apache.org/>.
*
*/
package org.apache.commons.math.stat;
import org.apache.commons.math.stat.distribution.DistributionFactory;
import org.apache.commons.math.stat.distribution.TDistribution;
/**
* Estimates an ordinary least squares regression model
* with one independent variable: <p>
*
* y = intercept + slope * x </code><p>
*
* with one independent variable.
* <p>
* <code> y = intercept + slope * x </code>
* <p>
* Standard errors for <code>intercept</code> and <code>slope</code> are
* available as well as ANOVA, r-square and Pearson's r statistics.<p>
*
* available as well as ANOVA, r-square and Pearson's r statistics.
* <p>
* 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. <p>
*
* added to the model.
* <p>
* <strong>Usage Notes</strong>: <ul>
* <li> 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 <code>NaN</code>. At least two observations with
* different x coordinates are requred to estimate a bivariate regression model.</li>
* different x coordinates are requred to estimate a bivariate regression
* model.
* </li>
* <li> 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
@ -82,7 +85,7 @@ package org.apache.commons.math.stat;
* </ul>
*
* @author Phil Steitz
* @version $Revision: 1.1 $ $Date: 2003/05/29 20:35:45 $
* @version $Revision: 1.2 $ $Date: 2003/06/11 03:33:05 $
*/
public class BivariateRegression {
@ -114,31 +117,34 @@ public class BivariateRegression {
*/
public void addData(double x, double y) {
sumX += x;
sumSqX += x*x;
sumSqX += x * x;
sumY += y;
sumSqY += y*y;
sumXY += x*y;
sumSqY += y * y;
sumXY += x * y;
n++;
}
/**
* Adds the observations represented by the elements in <code>data.</code><p>
* Adds the observations represented by the elements in
* <code>data</code>.
* <p>
* <code>(data[0][0],data[0][1])</code> will be the first observation, then
* <code>(data[1][0],data[1][1])</code>, etc. <p>
*
* This method does not replace data that has already been added.
* To replace all data, use <code>clear()</code> before adding the new data.
* To replace all data, use <code>clear()</code> before adding the new
* data.
*
* @param data array of observations to be added
*/
public void addData(double[][] data) {
for (int i = 0; i < data.length; i++) {
addData(data[i][0],data[i][1]);
addData(data[i][0], data[i][1]);
}
}
/*
* Clears all data from the model
/**
* Clears all data from the model.
*/
public void clear() {
sumX = 0d;
@ -150,9 +156,9 @@ public class BivariateRegression {
}
/**
* Returns the number of observations that have been added to the model
* Returns the number of observations that have been added to the model.
*
* @return n
* @return n number of observations that have been added.
*/
public long getN() {
return n;
@ -160,37 +166,38 @@ public class BivariateRegression {
/**
* Returns the "predicted" <code>y</code> value associated with the
* supplied <code>x</code> value. Specifically, <p>
*
* <code> predict(x) = intercept + slope * x </code> <p>
*
* At least two observations (with at least two different x values)
* supplied <code>x</code> value.
* <p>
* <code> predict(x) = intercept + slope * x </code>
* <p>
* <strong>Preconditions</strong>: <ul>
* <li>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, <code>Double,NaN</code> is
* returned.
* </li></ul>
*
* @param x input <code>x</code> value
* @return predicted <code>y</code> value
*/
public double predict(double x) {
double b1 = getSlope();
if (b1 == Double.NaN) {
return b1;
}
return getIntercept(b1) + b1*x;
return getIntercept(b1) + b1 * x;
}
/**
* Returns the intercept of the estimated regression line.
* The least squares estimate of the intercept is computed using the normal
* equations, as described
* <a href=http://www.xycoon.com/estimation4.htm>here</a>.
* The intercept is sometimes denoted b0. <p>
*
* At least two distinct data pairs (with at least two different x values)
* <p>
* The least squares estimate of the intercept is computed using the
* <a href="http://www.xycoon.com/estimation4.htm">normal equations</a>.
* The intercept is sometimes denoted b0.
* <p>
* <strong>Preconditions</strong>: <ul>
* <li>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, <code>Double,NaN</code> is
* returned.
* </li></ul>
*
* @return the intercept of the regression line
*/
@ -200,15 +207,17 @@ public class BivariateRegression {
/**
* Returns the slope of the estimated regression line.
* The least squares estimate of the slope is computed using the normal
* equations, as described
* <a href=http://www.xycoon.com/estimation4.htm>here</a>.
* The slope is sometimes denoted b1. <p>
*
* At least two observations (with at least two different x values)
* <p>
* The least squares estimate of the slope is computed using the
* <a href="http://www.xycoon.com/estimation4.htm">normal equations</a>.
* The slope is sometimes denoted b1.
* <p>
* <strong>Preconditions</strong>: <ul>
* <li>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, <code>Double,NaN</code> is
* returned.
* </li></ul>
*
* @return the slope of the regression line
*/
@ -217,22 +226,24 @@ public class BivariateRegression {
return Double.NaN; //not enough data
}
double dn = (double) n;
double denom = sumSqX - (sumX*sumX/dn);
if (Math.abs(denom)< 10*Double.MIN_VALUE) {
double denom = sumSqX - (sumX * sumX / dn);
if (Math.abs(denom) < 10 * Double.MIN_VALUE) {
return Double.NaN; //not enough variation in x
}
return (sumXY - (sumX*sumY/dn))/denom;
return (sumXY - (sumX * sumY / dn)) / denom;
}
/**
* Returns the sum of squared errors</a> associated with the regression
* model. This is defined as SSE
* <a href=http://www.xycoon.com/SumOfSquares.htm>here</a>. <p>
*
* At least two distinct data pairs (with at least two different x values)
* Returns the <a href="http://www.xycoon.com/SumOfSquares.htm">
* sum of squared errors</a> (SSE) associated with the regression
* model.
* <p>
* <strong>Preconditions</strong>: <ul>
* <li>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, <code>Double,NaN</code> is
* returned.
* </li></ul>
*
* @return sum of squared errors associated with the regression model
*/
@ -242,10 +253,11 @@ public class BivariateRegression {
/**
* Returns the sum of squared deviations of the y values about their mean.
* This is defined as SSTO
* <a href=http://www.xycoon.com/SumOfSquares.htm>here</a>.
* <p>
* If n < 2, this returns NaN.
* This is defined as SSTO
* <a href="http://www.xycoon.com/SumOfSquares.htm">here</a>.
* <p>
* If <code>n < 2</code>, this returns <code>Double.NaN</code>.
*
* @return sum of squared deviations of y values
*/
@ -253,36 +265,37 @@ public class BivariateRegression {
if (n < 2) {
return Double.NaN;
}
return sumSqY - sumY*sumY/(double) n;
return sumSqY - sumY * sumY / (double) n;
}
/**
* Returns the sum of squared deviations of the predicted y values about
* their mean (which equals the mean of y).
* <p>
* This is usually abbreviated SSR or SSM. It is defined as SSM
* <a href=http://www.xycoon.com/SumOfSquares.htm>here</a><p>
*
* At least two distinct data pairs (with at least two different x values)
* <a href="http://www.xycoon.com/SumOfSquares.htm">here</a>
* <p>
* <strong>Preconditions</strong>: <ul>
* <li>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, <code>Double,NaN</code> is
* returned.
* </li></ul>
*
* @return sum of squared deviations of y values
*/
public double getRegressionSumSquares() {
double b1 = getSlope();
if (b1 == Double.NaN) {
return b1;
}
return b1*(sumXY - sumX*sumY/(double) n);
return b1 * (sumXY - sumX * sumY / (double) n);
}
/**
* Returns the sum of squared errors divided by the degrees of freedom.
* This is usually abbreviated MSE. <p>
*
* Returns the sum of squared errors divided by the degrees of freedom,
* usually abbreviated MSE.
* <p>
* If there are fewer than <strong>three</strong> data pairs in the model,
* or if there is no variation in x, this returns <code>NaN</code>.
* or if there is no variation in <code>x</code>, this returns
* <code>Double.NaN</code>.
*
* @return sum of squared deviations of y values
*/
@ -291,29 +304,25 @@ public class BivariateRegression {
return Double.NaN;
}
double sse = getSumSquaredErrors();
if (sse == Double.NaN) {
return sse;
}
return sse/(double) (n - 2);
return sse / (double) (n - 2);
}
/**
* Returns <a href=http://www.stt.msu.edu/~xiaoyimi/STT200/Lecture5.pdf>
* Pearson's product moment correlation coefficient</a>.
* This is usually denoted r. <p>
*
* At least two observations (with at least two different x values)
* Returns <a href="http://www.stt.msu.edu/~xiaoyimi/STT200/Lecture5.pdf">
* Pearson's product moment correlation coefficient</a>,
* usually denoted r.
* <p>
* <strong>Preconditions</strong>: <ul>
* <li>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, <code>Double,NaN</code> is
* returned.
* </li></ul>
*
* @return Pearson's r
*/
public double getR() {
double b1 = getSlope();
if (b1 == Double.NaN) {
return b1;
}
double result = Math.sqrt(getRSquare(b1));
if (b1 < 0) {
result = -result;
@ -322,14 +331,16 @@ public class BivariateRegression {
}
/**
* Returns the <a href=http://www.xycoon.com/coefficient1.htm> coefficient
* of determination</a>.
* This is usually denoted r-square. <p>
*
* At least two observaions (with at least two different x values)
* Returns the <a href="http://www.xycoon.com/coefficient1.htm">
* coefficient of determination</a>,
* usually denoted r-square.
* <p>
* <strong>Preconditions</strong>: <ul>
* <li>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, <code>Double,NaN</code> is
* returned.
* </li></ul>
*
* @return r-square
*/
@ -339,70 +350,150 @@ public class BivariateRegression {
/**
* Returns the <a href=http://www.xycoon.com/standarderrorb0.htm>standard
* error of the intercept estimate</a>.
* This is usually denoted s(b0). <p>
*
* If there are fewer that <strong>three</strong> observations in the model,
* or if there is no variation in x, this returns <code>NaN</code>.
* Returns the <a href="http://www.xycoon.com/standarderrorb0.htm">
* standard error of the intercept estimate</a>,
* usually denoted s(b0).
* <p>
* If there are fewer that <strong>three</strong> observations in the
* model, or if there is no variation in x, this returns
* <code>Double.NaN</code>.
*
* @return standard error associated with intercept estimate
*/
public double getInterceptStdErr() {
double ssx = getSumSquaresX();
if (ssx == Double.NaN) {
return ssx;
}
return Math.sqrt(getMeanSquareError()*sumSqX/(((double) n)*ssx));
return Math.sqrt(getMeanSquareError() * sumSqX / (((double) n) * ssx));
}
/**
* Returns the <a http://www.xycoon.com/standerrorb(1).htm>standard
* error of the slope estimate</a>.
* This is usually denoted s(b1). <p>
*
* Returns the <a href="http://www.xycoon.com/standerrorb(1).htm">standard
* error of the slope estimate</a>,
* usually denoted s(b1).
* <p>
* If there are fewer that <strong>three</strong> data pairs in the model,
* or if there is no variation in x, this returns <code>NaN</code>.
* or if there is no variation in x, this returns <code>Double.NaN</code>.
*
* @return standard error associated with slope estimate
*/
public double getSlopeStdErr() {
double ssx = getSumSquaresX();
if (ssx == Double.NaN) {
return ssx;
return Math.sqrt(getMeanSquareError() / ssx);
}
/**
* Returns the half-width of a 95% confidence interval for the slope
* estimate.
* <p>
* The 95% confidence interval is
* <p>
* <code>(getSlope() - getSlopeConfidenceInterval(),
* getSlope() + getSlopeConfidenceInterval())</code>
* <p>
* If there are fewer that <strong>three</strong> observations in the
* model, or if there is no variation in x, this returns
* <code>Double.NaN</code>.
* <p>
* <strong>Usage Note</strong>:<br>
* The validity of this statistic depends on the assumption that the
* observations included in the model are drawn from a
* <a href="http://mathworld.wolfram.com/
* BivariateNormalDistribution.html">Bivariate Normal Distribution</a>.
*
* @return half-width of 95% confidence interval for the slope estimate
*/
public double getSlopeConfidenceInterval() {
return getSlopeConfidenceInterval(0.05d);
}
/**
* Returns the half-width of a (100-100*alpha)% confidence interval for
* the slope estimate.
* <p>
* The (100-100*alpha)% confidence interval is
* <p>
* <code>(getSlope() - getSlopeConfidenceInterval(),
* getSlope() + getSlopeConfidenceInterval())</code>
* <p>
* To request, for example, a 99% confidence interval, use
* <code>alpha = .01</code>
* <p>
* <strong>Usage Note</strong>:<br>
* The validity of this statistic depends on the assumption that the
* observations included in the model are drawn from a
* <a href="http://mathworld.wolfram.com/
* BivariateNormalDistribution.html">Bivariate Normal Distribution</a>.
* <p>
* <strong> Preconditions:</strong><ul>
* <li>If there are fewer that <strong>three</strong> observations in the
* model, or if there is no variation in x, this returns
* <code>Double.NaN</code>.
* </li>
* <li><code>(0 < alpha < 1)</code>; otherwise an
* <code>IllegalArgumentException</code> is thrown.
* </li></ul>
*
* @param alpha the desired significance level
* @return half-width of 95% confidence interval for the slope estimate
*/
public double getSlopeConfidenceInterval(double alpha) {
if (alpha >= 1 || alpha <= 0) {
throw new IllegalArgumentException();
}
return Math.sqrt(getMeanSquareError()/ssx);
return getSlopeStdErr() *
getTDistribution().inverseCummulativeProbability(1d - alpha / 2d);
}
/**
* Returns the significance level of the slope (equiv) correlation.
* <p>
* Specifically, the returned value is the smallest <code>alpha</code>
* such that the slope confidence interval with significance level
* equal to <code>alpha</code> does not include <code>0</code>.
* On regression output, this is often denoted <code>Prob(|t| > 0)</code>
* <p>
* <strong>Usage Note</strong>:<br>
* The validity of this statistic depends on the assumption that the
* observations included in the model are drawn from a
* <a href="http://mathworld.wolfram.com/
* BivariateNormalDistribution.html">Bivariate Normal Distribution</a>.
* <p>
* If there are fewer that <strong>three</strong> observations in the
* model, or if there is no variation in x, this returns
* <code>Double.NaN</code>.
*
* @return significance level for slope/correlation
*/
public double getSignificance() {
return (1d - getTDistribution().cummulativeProbability(
Math.abs(getSlope()) / getSlopeStdErr()));
}
// ---------------------Private methods-----------------------------------
/**
* Returns the intercept of the estimated regression line, given the slope.
* <p>
* Will return <code>NaN</code> if slope is <code>NaN</code>.
*
* @param slope current slope
* @return the intercept of the regression line
*/
private double getIntercept(double slope) {
if (slope == Double.NaN) {
return slope;
}
return (sumY - slope*sumX)/((double) n);
return (sumY - slope * sumX) / ((double) n);
}
/**
* Returns the sum of squared errors</a> associated with the regression
* model, using the slope of the regression line. Returns NaN if the slope
* is NaN.
*
* Returns the sum of squared errors associated with the regression
* model, using the slope of the regression line.
* <p>
* Returns NaN if the slope is NaN.
*
* @param b1 current slope
* @return sum of squared errors associated with the regression model
*/
private double getSumSquaredErrors(double b1) {
if (b1 == Double.NaN) {
return b1;
}
double b0 = getIntercept(b1);
return sumSqY - b0*sumY - b1*sumXY;
return sumSqY - b0 * sumY - b1 * sumXY;
}
/**
@ -416,24 +507,30 @@ public class BivariateRegression {
if (n < 2) {
return Double.NaN;
}
return sumSqX - sumX*sumX/(double) n;
return sumSqX - sumX * sumX / (double) n;
}
/**
* Computes r-square from the slope.
* will return NaN if slope is Nan
* <p>
* will return NaN if slope is Nan.
*
* @param b1 current slope
* @return r-square
*/
private double getRSquare(double b1) {
if (b1 == Double.NaN) {
return b1;
}
double ssto = getTotalSumSquares();
if (ssto == Double.NaN) {
return ssto;
}
return (ssto - getSumSquaredErrors(b1))/ssto;
return (ssto - getSumSquaredErrors(b1)) / ssto;
}
/**
* Uses distribution framework to get a t distribution instance
* with df = n - 2
*
* @return t distribution with df = n - 2
*/
private TDistribution getTDistribution() {
return DistributionFactory.newInstance().createTDistribution(n - 2);
}
}

42
src/test/org/apache/commons/math/stat/BivariateRegressionTest.java
View File

@ -60,7 +60,7 @@ import junit.framework.TestSuite;
* Test cases for the TestStatistic class.
*
* @author Phil Steitz
* @version $Revision: 1.1 $ $Date: 2003/05/29 20:35:46 $
* @version $Revision: 1.2 $ $Date: 2003/06/11 03:33:05 $
*/
public final class BivariateRegressionTest extends TestCase {
@ -87,6 +87,18 @@ public final class BivariateRegressionTest extends TestCase {
{90.6,111.6},{86.5,122.2},{89.7,117.6},{90.6,121.1},{82.8,136.0},
{70.1,154.2},{65.4,153.6},{61.3,158.5},{62.5,140.6},{63.6,136.2},
{52.6,168.0},{59.7,154.3},{59.5,149.0},{61.3,165.5}};
/*
* From Moore and Mcabe, "Introduction to the Practice of Statistics"
* Example 10.3
*/
private double[][] infData = {{15.6,5.2},{26.8,6.1},{37.8,8.7},{36.4,8.5},
{35.5,8.8},{18.6,4.9},{15.3,4.5},{7.9,2.5},{0.0,1.1}};
/*
* From http://www.xycoon.com/simple_linear_regression.htm
*/
private double[][] infData2 = {{1,3},{2,5},{3,7},{4,14},{5,11}};
public BivariateRegressionTest(String name) {
super(name);
@ -221,6 +233,32 @@ public final class BivariateRegressionTest extends TestCase {
regression.addData(data);
assertEquals("number of observations",53,regression.getN());
}
public void testInference() {
BivariateRegression regression = new BivariateRegression();
regression.addData(infData);
assertEquals("slope confidence interval", 0.0271,
regression.getSlopeConfidenceInterval(),0.0001);
assertEquals("slope std err",0.01146,
regression.getSlopeStdErr(),0.0001);
regression = new BivariateRegression();
regression.addData(infData2);
assertEquals("significance", 0.023331,
regression.getSignificance(),0.0001);
//FIXME: get a real example to test against with alpha = .01
assertTrue("tighter means wider",
regression.getSlopeConfidenceInterval() <
regression.getSlopeConfidenceInterval(0.01));
try {
double x = regression.getSlopeConfidenceInterval(1);
fail("expecting IllegalArgumentException for alpha = 1");
} catch (IllegalArgumentException ex) {
;
}
}
}