// Copyright 2003, Paul Meagher 
// Distributed under GPL 
class SimpleLinearRegression { 
var n; 
var X = array(); 
var Y = array(); 
var ConfInt; 
var Alpha; 
var XMean; 
var YMean; 
var SumXX; 
var SumXY; 
var SumYY; 
var Slope; 
var YInt; 
var PredictedY = array(); 
var Error = array(); 
var SquaredError = array(); 
var TotalError; 
var SumError; 
var SumSquaredError; 
var ErrorVariance; 
var StdErr; 
var SlopeStdErr; 
var SlopeVal; // T value of Slope 
var YIntStdErr; 
var YIntTVal; // T value for Y Intercept 
var R; 
var RSquared; 
var DF; // Degrees of Freedom 
var SlopeProb; // Probability of Slope Estimate 
var YIntProb; // Probability of Y Intercept Estimate 
var AlphaTVal; // T Value for given alpha setting 
var ConfIntOfSlope; 
var RPath = "/usr/local/bin/R"; // Your path here 
var format = "%01.2f"; // Used for formatting output 
} 
?> 

 
// Copyright 2003, Paul Meagher 
// Distributed under GPL 
function SimpleLinearRegression(X, Y, ConfidenceInterval="95") { 
numX = count(X); 
numY = count(Y); 
if (numX != numY) { 
die("Error: Size of X and Y vectors must be the same."); 
} 
if (numX <= 1) { 
die("Error: Size of input array must be at least 2."); 
} 
this->n = numX; 
this->X = X; 
this->Y = Y; 
this->ConfInt = ConfidenceInterval; 
this->Alpha = (1 + (this->ConfInt / 100) ) / 2; 
this->XMean = this->getMean(this->X); 
this->YMean = this->getMean(this->Y); 
this->SumXX = this->getSumXX(); 
this->SumYY = this->getSumYY(); 
this->SumXY = this->getSumXY(); 
this->Slope = this->getSlope(); 
this->YInt = this->getYInt(); 
this->PredictedY = this->getPredictedY(); 
this->Error = this->getError(); 
this->SquaredError = this->getSquaredError(); 
this->SumError = this->getSumError(); 
this->TotalError = this->getTotalError(); 
this->SumSquaredError = this->getSumSquaredError(); 
this->ErrorVariance = this->getErrorVariance(); 
this->StdErr = this->getStdErr(); 
this->SlopeStdErr = this->getSlopeStdErr(); 
this->YIntStdErr = this->getYIntStdErr(); 
this->SlopeTVal = this->getSlopeTVal(); 
this->YIntTVal = this->getYIntTVal(); 
this->R = this->getR(); 
this->RSquared = this->getRSquared(); 
this->DF = this->getDF(); 
this->SlopeProb = this->getStudentProb(this->SlopeTVal, this->DF); 
this->YIntProb = this->getStudentProb(this->YIntTVal, this->DF); 
this->AlphaTVal = this->getInverseStudentProb(this->Alpha, this->DF); 
this->ConfIntOfSlope = this->getConfIntOfSlope(); 
return true; 
} 
?> 

 
PredictedY[i] = YIntercept + Slope * X[i] 

 
// Copyright 2003, Paul Meagher 
// Distributed under GPL 
class SimpleLinearRegression { 
var RPath = "/usr/local/bin/R"; // Your path here 
function getStudentProb(T, df) { 
Probability = 0.0; 
cmd = "echo 'dt(T, df)' | this->RPath --slave"; 
result = shell_exec(cmd); 
list(LineNumber, Probability) = explode(" ", trim(result)); 
return Probability; 
} 
function getInverseStudentProb(alpha, df) { 
InverseProbability = 0.0; 
cmd = "echo 'qt(alpha, df)' | this->RPath --slave"; 
result = shell_exec(cmd); 
list(LineNumber, InverseProbability) = explode(" ", trim(result)); 
return InverseProbability; 
} 
} 
?>

 
// BurnoutStudy.php 
// Copyright 2003, Paul Meagher 
// Distributed under GPL 
include "SimpleLinearRegression.php"; 
// Load data from burnout study 
Concentration = array(20,60,38,88,79,87, 
68,12,35,70,80,92, 
77,86,83,79,75,81, 
75,77,77,77,17,85,96); 
ExhaustionIndex = array(100,525,300,980,310,900, 
410,296,120,501,920,810, 
506,493,892,527,600,855, 
709,791,718,684,141,400,970); 
slr = new SimpleLinearRegression(Concentration, ExhaustionIndex); 
YInt = sprintf(slr->format, slr->YInt); 
Slope = sprintf(slr->format, slr->Slope); 
SlopeTVal = sprintf(slr->format, slr->SlopeTVal); 
SlopeProb = sprintf("%01.6f", slr->SlopeProb); 
?> 
Equation: 
T: 
Prob > T: