/*
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package org.statcato.statistics.inferential;
import org.statcato.statistics.StudentTProbabilityDistribution;
import org.statcato.statistics.BasicStatistics;
import org.statcato.utils.HelperFunctions;
import java.util.Vector;
import java.util.ArrayList;
/**
* Linear correlation and regression
* between for two variables.
*
* @author Margaret Yau
* @version %I%, %G%
* @since 1.0
*/
public class CorrelationRegression {
private Vector x, y;
int n; // number of pairs of data values
double significance;
/**
* Constructor. The x and y variables are provided as vectors
* of double type of the same length. The values in the two vectors
* at the same position are considered to be a data point.
*
* @param x independent variable
* @param y dependent variable
* @param sig significance
*/
public CorrelationRegression(Vector x, Vector y, double sig) {
this.x = x;
this.y = y;
this.n = x.size();
this.significance = sig;
}
/**
* Returns the number of data pairs
*
* @return n
*/
public int N() {
return n;
}
/**
* Returns the degrees of freedom.
*
* @return DOF
*/
public int DOF() {
return n - 2;
}
/**
* Returns the linear correlation coefficient.
*
* @return r
*/
public double LinearCorrelationCoeff() {
double sumX = SumX();
double sumY = SumY();
return (n * SumXY() - sumX * sumY) /
Math.sqrt(n * SumXSq() - Math.pow(sumX, 2)) /
Math.sqrt(n * SumYSq() - Math.pow(sumY, 2));
}
/**
* Returns the test statistic t using the linear correlation correlation r.
* t = r / sqrt((1 - r^2)/(n - 2)).
*
* @return test statistic t
*/
public double TestStatistic_t() {
double r = LinearCorrelationCoeff();
return r / Math.sqrt((1 - r * r) / (n - 2));
}
/**
* Returns the slope of the regression equation b1.
*
* @return b1 slope
*/
public double RegressionEqSlope() {
double sumX = SumX();
double sumY = SumY();
return (n * SumXY() - sumX * sumY) /
(n * SumXSq() - sumX * sumX);
}
/**
* Returns the y-intercept of the regression equation b0.
*
* @return b0 y-intercept
*/
public double RegressionEqYInt() {
double sumX = SumX();
double sumY = SumY();
double sumXSq = SumXSq();
return (sumY * sumXSq - sumX * SumXY()) /
(n * SumXSq() - sumX * sumX);
}
/**
* Returns the sum of all the x values.
*
* @return sum of x
*/
private double SumX() {
return BasicStatistics.sum(x);
}
/**
* Returns the sum of all the y values.
*
* @return sum of y
*/
private double SumY() {
return BasicStatistics.sum(y);
}
/**
* Returns the sum of pairwise products between the x and y values.
*
* @return sum of x * y
*/
private double SumXY() {
double sum = 0;
for (int i = 0; i < x.size(); ++i) {
sum += ((Double)x.elementAt(i)).doubleValue() *
((Double)y.elementAt(i)).doubleValue();
}
return sum;
}
/**
* Returns the sum of sqaures of the x values.
*
* @return sum of x squares
*/
private double SumXSq() {
double sum = 0;
for (int i = 0; i < x.size(); ++i) {
sum += ((Double)x.elementAt(i)).doubleValue() *
((Double)x.elementAt(i)).doubleValue();
}
return sum;
}
/**
* Returns the sum of sqaures of the y values.
*
* @return sum of y squares
*/
private double SumYSq() {
double sum = 0;
for (int i = 0; i < y.size(); ++i) {
sum += ((Double)y.elementAt(i)).doubleValue() *
((Double)y.elementAt(i)).doubleValue();
}
return sum;
}
/**
* Returns the total variation (sum of differences between the y value
* and the mean).
*
* @return total variation
*/
public double TotalVariation() {
double total = 0;
double mean = BasicStatistics.mean(y).doubleValue();
for (int i = 0; i < y.size(); ++i) {
total += Math.pow((Double)y.elementAt(i).doubleValue() - mean, 2);
}
return total;
}
/**
* Returns the explained variation (sum of differences between the
* predicted y value and the mean).
*
* @return explained variation
*/
public double ExplainedVariation() {
double total = 0;
double mean = BasicStatistics.mean(y).doubleValue();
double xValue, yValue, yR;
double b0 = RegressionEqYInt();
double b1 = RegressionEqSlope();
for (int i = 0; i < y.size(); ++i) {
yValue = (Double)y.elementAt(i).doubleValue();
xValue = (Double)x.elementAt(i).doubleValue();
yR = b0 + b1 * xValue;
total += Math.pow(yR - mean, 2);
}
return total;
}
/**
* Returns the unexplained variation (sum of differences between the
* y value and the predicted y value).
*
* @return unexplained variation
*/
public double UnexplainedVariation() {
double total = 0;
double mean = BasicStatistics.mean(y).doubleValue();
double xValue, yValue, yR;
double b0 = RegressionEqYInt();
double b1 = RegressionEqSlope();
for (int i = 0; i < y.size(); ++i) {
yValue = (Double)y.elementAt(i).doubleValue();
xValue = (Double)x.elementAt(i).doubleValue();
yR = b0 + b1 * xValue;
total += Math.pow(yValue - yR, 2);
}
return total;
}
/**
* Returns a list of residual values in order.
*
* @return ArrayList object containing the residuals
*/
public ArrayList Residuals() {
ArrayList residualList = new ArrayList();
ArrayList predictedList = PredictedValues();
double yValue, yR;
for (int i = 0; i < y.size(); ++i) {
yR = predictedList.get(i);
yValue = (Double)y.elementAt(i).doubleValue();
residualList.add(new Double(yValue - yR));
}
return residualList;
}
/**
* Returns a list of predicated values in order.
*
* @return ArrayList object containing the predicted values
*/
public ArrayList PredictedValues() {
ArrayList valueList = new ArrayList();
double xValue, yValue, yR;
double b0 = RegressionEqYInt();
double b1 = RegressionEqSlope();
for (int i = 0; i < y.size(); ++i) {
yValue = (Double)y.elementAt(i).doubleValue();
xValue = (Double)x.elementAt(i).doubleValue();
yR = b0 + b1 * xValue;
valueList.add(new Double(yR));
}
return valueList;
}
/**
* Returns the coefficient of determination r^2, the amount of the variation
* in y that is explained by the regression line.
*
* @return r^2 coefficient of determination
*/
public double CoefficientOfDetermination() {
return ExplainedVariation() / TotalVariation();
}
public double StandardError() {
double b0 = RegressionEqYInt();
double b1 = RegressionEqSlope();
return Math.sqrt((SumYSq() - b0 * SumY() - b1 * SumXY()) / (n - 2));
}
/**
* Returns the critical value for r corresponding to the given significance.
*
* @param significance significance
* @return critical value (positive)
*/
public double CriticalValue_r(double significance) {
double t = CriticalValue_t(significance);
double tSq = t * t;
return Math.sqrt(tSq / (n - 2 + tSq));
}
public double CriticalValue_t(double significance) {
StudentTProbabilityDistribution dist =
new StudentTProbabilityDistribution(DOF());
return dist.inverseCumulativeProbability(1 - significance / 2);
}
/**
* Returns the p-Value corresponding to the test statistic.
*
* @return p-Value
*/
public double PValue() {
double ts = TestStatistic_t();
StudentTProbabilityDistribution dist =
new StudentTProbabilityDistribution(DOF()); // t distribution
double area = dist.cumulativeProbability(ts);
if (area > 0.5)
area = 1 - area;
return 2 * area;
}
@Override
public String toString() {
String text = "";
text += "Sample size n = " + N() + "
";
text += "Degrees of freedom = " + DOF() + "
";
text += "Correlation:
";
text += "H0: ρ = 0 (no linear correlation)
";
text += "H1: ρ ≠ 0 (linear correlation)
";
text += "";
text += " Test Statistic Critical Value r ";
text += "" +
HelperFunctions.formatFloat(LinearCorrelationCoeff(), 4) + " ";
text += "±" +
HelperFunctions.formatFloat(CriticalValue_r(significance), 4) + " ";
text += "t ";
text += "" +
HelperFunctions.formatFloat(TestStatistic_t(), 4) + " ";
text += "±" +
HelperFunctions.formatFloat(CriticalValue_t(significance), 4) + " ";
text += "
";
text += "p-Value = " +
HelperFunctions.formatFloat(PValue(), 4) + "
";
text += "Regression:
";
text += "Regression equation Y = b0 + b1x
";
text += "b0 = " +
HelperFunctions.formatFloat(RegressionEqYInt(), 4) + "
";
text += "b1 = " +
HelperFunctions.formatFloat(RegressionEqSlope(), 4) + "
";
text += "Variation:
";
text += "Explained variation = " +
HelperFunctions.formatFloat(ExplainedVariation(), 4) + "
";
text += "Unexplained variation = " +
HelperFunctions.formatFloat(UnexplainedVariation(), 4) + "
";
text += "Total variation = " +
HelperFunctions.formatFloat(TotalVariation(), 4) + "
";
text += "Coefficient of determination r2 = " +
HelperFunctions.formatFloat(CoefficientOfDetermination(), 4)
+ "
";
text += "Standard error of estimate = " +
HelperFunctions.formatFloat(StandardError(), 4) + "
";
return text;
}
}
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