#include <lregress.h>
Public Methods | |
| lregress () | |
| ~lregress () | |
| double | meanX (std::vector< point > &data) const |
| Calculate the mean of the x values in a vector of point objects. More... | |
| double | meanY (std::vector< point > &data) const |
| Calculate the mean of the y values in a vector of point objects. More... | |
| void | lr (std::vector< point > &data, lineInfo &info) const |
| Calculate the linear regression on a set of N points, {Xi, Yi}. More... | |
Private Methods | |
| lregress (const lregress &rhs) | |
The lregress class packages the lr function, which calculates a linear regression line given paired vectors of X and Y points.
You may use this source code without limitation and without fee as long as you include:
This software was written and is copyrighted by Ian Kaplan, Bear Products International, www.bearcave.com, 2001.
This software is provided "as is", without any warranty or claim as to its usefulness. Anyone who uses this source code uses it at their own risk. Nor is any support provided by Ian Kaplan and Bear Products International.
Please send any bug fixes or suggested source changes to:
iank@bearcave.com
Definition at line 40 of file lregress.h.
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Definition at line 46 of file lregress.h. 00046 {}
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Definition at line 47 of file lregress.h. 00047 {}
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Calculate the linear regression on a set of N points, {Xi, Yi}. A regression line is described by the equation y' = a + bx. The coefficients a and b are returned in a lineInfo object, along with the other values. Formally, linear regression of a set of {x,y} points is described in terms of independent and dependent variables. The array x contains the independent variable, which is exactly known. The array y contains the dependent variable, which is "measured". The y values are assumed to be random values, dependent on the x values. Definition at line 64 of file lregress.cpp. Referenced by autocorr::acorrSlope(), and main().
00066 {
00067 const size_t N = data.size();
00068 if (N > 0) {
00069
00070 double muX = meanX( data );
00071
00072 double muY = meanY( data );
00073
00074 // N-1
00075 // ---
00076 // \ (Xi - meanX)(Yi - meanY)
00077 // /__
00078 // i=0
00079 // b = -----------------------------
00080 // N-1
00081 // --- 2
00082 // \ (Xi - meanX)
00083 // /__
00084 // i=0
00085 //
00086
00087 double SSxy = 0;
00088 double SSxx = 0;
00089 double SSyy = 0;
00090 double Sx = 0;
00091 double Sy = 0;
00092 double Sxy = 0;
00093 double SSy = 0;
00094 double SSx = 0;
00095 for (size_t i = 0; i < N; i++) {
00096 Sx = Sx + data[i].x();
00097 Sy = Sy + data[i].y();
00098 Sxy = Sxy + (data[i].x() * data[i].y());
00099 SSx = SSx + (data[i].x() * data[i].x());
00100 SSy = SSy + (data[i].y() * data[i].y());
00101 double subX = (data[i].x() - muX);
00102 double subY = (data[i].y() - muY);
00103 SSyy = SSyy + subY * subY;
00104 SSxy = SSxy + subX * subY;
00105 SSxx = SSxx + subX * subX;
00106 }
00107
00108 // slope
00109 double b = SSxy / SSxx;
00110 // intercept
00111 double a = muY - b * muX;
00112
00113 // standard deviation of the points
00114 double stddevPoints = sqrt( (SSyy - b * SSxy)/(N-2) );
00115
00116 // Error of the slope
00117 double bError = stddevPoints / sqrt( SSxx );
00118
00119 double r2Numerator = (N * Sxy) - (Sx * Sy);
00120 double r2Denominator = ((N*SSx) - (Sx * Sx))*((N*SSy) - (Sy * Sy));
00121 double r2 = (r2Numerator * r2Numerator) / r2Denominator;
00122
00123 double signB = (b < 0) ? -1.0 : 1.0;
00124
00125 double r = signB * sqrt( r2 );
00126
00127 info.corr( r );
00128 info.stddev( stddevPoints );
00129 info.slopeErr( bError );
00130 info.slope( b );
00131 info.intercept( a );
00132 } // if N > 0
00133
00134 } // lineInfo
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Calculate the mean of the x values in a vector of point objects.
Definition at line 13 of file lregress.cpp. Referenced by lr().
00014 {
00015 double mean = 0.0;
00016 double sum = 0.0;
00017
00018 const size_t N = data.size();
00019 size_t i;
00020 for (i = 0; i < N; i++) {
00021 sum = sum + data[i].x();
00022 }
00023 mean = sum / N;
00024 return mean;
00025 } // meanX
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Calculate the mean of the y values in a vector of point objects.
Definition at line 32 of file lregress.cpp. Referenced by lr().
00033 {
00034 double mean = 0.0;
00035 double sum = 0.0;
00036
00037 const size_t N = data.size();
00038 size_t i;
00039 for (i = 0; i < N; i++) {
00040 sum = sum + data[i].y();
00041 }
00042 mean = sum / N;
00043 return mean;
00044 } // meanY
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1.2.8.1 written by Dimitri van Heesch,
© 1997-2001