Author: psteitz
Date: Mon Aug 23 02:55:01 2010
New Revision: 987983
URL: http://svn.apache.org/viewvc?rev=987983&view=rev
Log:
Added R-squared and adjusted R-squared statistics to
OLSMultipleLinearRegression
JIRA: MATH-386
Modified:
commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/regression/OLSMultipleLinearRegression.java
commons/proper/math/trunk/src/site/xdoc/changes.xml
commons/proper/math/trunk/src/test/R/multipleOLSRegressionTestCases
commons/proper/math/trunk/src/test/java/org/apache/commons/math/stat/regression/OLSMultipleLinearRegressionTest.java
Modified:
commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/regression/OLSMultipleLinearRegression.java
URL:
http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/regression/OLSMultipleLinearRegression.java?rev=987983&r1=987982&r2=987983&view=diff
==============================================================================
---
commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/regression/OLSMultipleLinearRegression.java
(original)
+++
commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/regression/OLSMultipleLinearRegression.java
Mon Aug 23 02:55:01 2010
@@ -22,6 +22,7 @@ import org.apache.commons.math.linear.QR
import org.apache.commons.math.linear.QRDecompositionImpl;
import org.apache.commons.math.linear.RealMatrix;
import org.apache.commons.math.linear.RealVector;
+import org.apache.commons.math.stat.descriptive.moment.SecondMoment;
/**
* <p>Implements ordinary least squares (OLS) to estimate the parameters of a
@@ -122,6 +123,55 @@ public class OLSMultipleLinearRegression
}
/**
+ * Returns the sum of squared deviations of Y from its mean.
+ *
+ * @return total sum of squares
+ */
+ public double calculateTotalSumOfSquares() {
+ return new SecondMoment().evaluate(Y.getData());
+ }
+
+ /**
+ * Returns the sum of square residuals.
+ *
+ * @return residual sum of squares
+ */
+ public double calculateResidualSumOfSquares() {
+ final RealVector residuals = calculateResiduals();
+ return residuals.dotProduct(residuals);
+ }
+
+ /**
+ * Returns the R-Squared statistic, defined by the formula <pre>
+ * R<sup>2</sup> = 1 - SSR / SSTO
+ * </pre>
+ * where SSR is the {...@link #calculateResidualSumOfSquares() sum of
squared residuals}
+ * and SSTO is the {...@link #calculateTotalSumOfSquares() total sum of
squares}
+ *
+ * @return R-square statistic
+ */
+ public double calculateRSquared() {
+ return 1 - calculateResidualSumOfSquares() /
calculateTotalSumOfSquares();
+ }
+
+ /**
+ * Returns the adjusted R-squared statistic, defined by the formula <pre>
+ * R<sup>2</sup><sub>adj</sub> = 1 - [SSR (n - 1)] / [SSTO (n - p)]
+ * </pre>
+ * where SSR is the {...@link #calculateResidualSumOfSquares() sum of
squared residuals},
+ * SSTO is the {...@link #calculateTotalSumOfSquares() total sum of
squares}, n is the number
+ * of observations and p is the number of parameters estimated (including
the intercept).
+ *
+ * @return adjusted R-Squared statistic
+ */
+ public double calculateAdjustedRSquared() {
+ final double n = X.getRowDimension();
+ return 1 - (calculateResidualSumOfSquares() * (n - 1)) /
+ (calculateTotalSumOfSquares() * (n - X.getColumnDimension()));
+ // return 1 - ((1 - calculateRSquare()) * (n - 1) / (n -
X.getColumnDimension() - 1));
+ }
+
+ /**
* Loads new x sample data, overriding any previous sample
*
* @param x the [n,k] array representing the x sample
Modified: commons/proper/math/trunk/src/site/xdoc/changes.xml
URL:
http://svn.apache.org/viewvc/commons/proper/math/trunk/src/site/xdoc/changes.xml?rev=987983&r1=987982&r2=987983&view=diff
==============================================================================
--- commons/proper/math/trunk/src/site/xdoc/changes.xml (original)
+++ commons/proper/math/trunk/src/site/xdoc/changes.xml Mon Aug 23 02:55:01 2010
@@ -52,6 +52,9 @@ The <action> type attribute can be add,u
If the output is not quite correct, check for invisible trailing spaces!
-->
<release version="2.2" date="TBD" description="TBD">
+ <action dev="psteitz" type="fix" issue="MATH-386">
+ Added R-squared and adjusted R-squared statistics to
OLSMultipleLinearRegression.
+ </action>
<action dev="psteitz" type="fix" issue="MATH-392" due-to="Mark Devaney">
Corrected the formula used for Y variance returned by
calculateYVariance and associated
methods in multiple regression classes
(AbstractMultipleLinearRegression,
Modified: commons/proper/math/trunk/src/test/R/multipleOLSRegressionTestCases
URL:
http://svn.apache.org/viewvc/commons/proper/math/trunk/src/test/R/multipleOLSRegressionTestCases?rev=987983&r1=987982&r2=987983&view=diff
==============================================================================
--- commons/proper/math/trunk/src/test/R/multipleOLSRegressionTestCases
(original)
+++ commons/proper/math/trunk/src/test/R/multipleOLSRegressionTestCases Mon Aug
23 02:55:01 2010
@@ -32,11 +32,13 @@ options(digits=16) # override
# function to verify OLS computations
verifyRegression <- function(model, expectedBeta, expectedResiduals,
- expectedErrors, expectedStdError, modelName) {
+ expectedErrors, expectedStdError, expectedRSquare, expecteAdjRSquare,
modelName) {
betaHat <- as.vector(coefficients(model))
residuals <- as.vector(residuals(model))
errors <- as.vector(as.matrix(coefficients(summary(model)))[,2])
stdError <- summary(model)$sigma
+ rSquare <- summary(model)$r.squared
+ adjRSquare <- summary(model)$adj.r.squared
output <- c("Parameter test dataset = ", modelName)
if (assertEquals(expectedBeta,betaHat,tol,"Parameters")) {
displayPadded(output, SUCCEEDED, WIDTH)
@@ -61,6 +63,18 @@ verifyRegression <- function(model, expe
} else {
displayPadded(output, FAILED, WIDTH)
}
+ output <- c("RSquared test dataset = ", modelName)
+ if (assertEquals(expectedRSquare,rSquare,tol,"RSquared")) {
+ displayPadded(output, SUCCEEDED, WIDTH)
+ } else {
+ displayPadded(output, FAILED, WIDTH)
+ }
+ output <- c("Adjusted RSquared test dataset = ", modelName)
+ if (assertEquals(expecteAdjRSquare,adjRSquare,tol,"Adjusted RSquared")) {
+ displayPadded(output, SUCCEEDED, WIDTH)
+ } else {
+ displayPadded(output, FAILED, WIDTH)
+ }
}
#--------------------------------------------------------------------------
@@ -78,8 +92,10 @@ expectedBeta <- c(11.0,0.5,0.66666666666
expectedResiduals <- c(0,0,0,0,0,0)
expectedErrors <- c(NaN,NaN,NaN,NaN,NaN,NaN)
expectedStdError <- NaN
-verifyRegression(model, expectedBeta, expectedResiduals, expectedErrors,
expectedStdError,
- "perfect fit")
+expectedRSquare <- 1
+expectedAdjRSquare <- NaN
+verifyRegression(model, expectedBeta, expectedResiduals, expectedErrors,
+ expectedStdError, expectedRSquare, expectedAdjRSquare, "perfect fit")
# Longly
#
@@ -134,9 +150,11 @@ expectedResiduals <- c( 267.340029759711
-39.0550425226967,-155.5499735953195,-85.6713080421283,341.9315139607727,
-206.7578251937366)
expectedStdError <- 304.8540735619638
+expectedRSquare <- 0.995479004577296
+expectedAdjRSquare <- 0.992465007628826
-verifyRegression(model, expectedBeta, expectedResiduals, expectedErrors,
expectedStdError,
- "Longly")
+verifyRegression(model, expectedBeta, expectedResiduals, expectedErrors,
+expectedStdError, expectedRSquare, expectedAdjRSquare, "Longly")
# Swiss Fertility (R dataset named "swiss")
@@ -225,9 +243,11 @@ expectedResiduals <- c(7.104426785973051
-0.4515205619767598,-10.2916870903837587,-15.7812984571900063)
expectedStdError <- 7.73642194433223
+expectedRSquare <- 0.649789742860228
+expectedAdjRSquare <- 0.6164363850373927
-verifyRegression(model, expectedBeta, expectedResiduals, expectedErrors,
expectedStdError,
- "Swiss Fertility")
+verifyRegression(model, expectedBeta, expectedResiduals, expectedErrors,
+expectedStdError, expectedRSquare, expectedAdjRSquare, "Swiss Fertility")
displayDashes(WIDTH)
Modified:
commons/proper/math/trunk/src/test/java/org/apache/commons/math/stat/regression/OLSMultipleLinearRegressionTest.java
URL:
http://svn.apache.org/viewvc/commons/proper/math/trunk/src/test/java/org/apache/commons/math/stat/regression/OLSMultipleLinearRegressionTest.java?rev=987983&r1=987982&r2=987983&view=diff
==============================================================================
---
commons/proper/math/trunk/src/test/java/org/apache/commons/math/stat/regression/OLSMultipleLinearRegressionTest.java
(original)
+++
commons/proper/math/trunk/src/test/java/org/apache/commons/math/stat/regression/OLSMultipleLinearRegressionTest.java
Mon Aug 23 02:55:01 2010
@@ -109,7 +109,7 @@ public class OLSMultipleLinearRegression
assertEquals(0.0,
errors.subtract(referenceVariance).getNorm(),
5.0e-16 * referenceVariance.getNorm());
-
+ assertEquals(1, ((OLSMultipleLinearRegression)
regression).calculateRSquared(), 1E-12);
}
@@ -186,6 +186,10 @@ public class OLSMultipleLinearRegression
// Check regression standard error against R
assertEquals(304.8540735619638,
model.estimateRegressionStandardError(), 1E-10);
+ // Check R-Square statistics against R
+ assertEquals(0.995479004577296, model.calculateRSquared(), 1E-12);
+ assertEquals(0.992465007628826, model.calculateAdjustedRSquared(),
1E-12);
+
checkVarianceConsistency(model);
}
@@ -294,6 +298,10 @@ public class OLSMultipleLinearRegression
// Check regression standard error against R
assertEquals(7.73642194433223,
model.estimateRegressionStandardError(), 1E-12);
+ // Check R-Square statistics against R
+ assertEquals(0.649789742860228, model.calculateRSquared(), 1E-12);
+ assertEquals(0.6164363850373927, model.calculateAdjustedRSquared(),
1E-12);
+
checkVarianceConsistency(model);
}
