///<summary>
///This subroutine determines the best fit line by minimizing the sum of the squares
///of the perpendicular distances of the points to the line.
///This was initially reported by Kermack and Haldane (1950) Biometrika, 37, 30.
///However I found it in York, D. (1966) Canadian Journal of Physics, vol 44, p 1079.
///</summary>
public static LinearRegression LinearRegressionWithErrorsInBothCoordinates(Statistics a, Statistics b)
{
double meanA = a.Mean();
double meanB = b.Mean();
double sA2 = 0;
double sB2 = 0;
double sAb = 0;
for (int i = 0; i < a.Length; i++)
{
double dA = a._list[i] - meanA;
double dB = b._list[i] - meanB;
sA2 += dA * dA;
sB2 += dB * dB;
sAb += dA * dB;
}
LinearRegression result = new LinearRegression();
if (sA2 > 0 && sB2 > 0 && sAb > 0)
{
result.Correlation = sAb / Math.Sqrt(sA2 * sB2);
result.Slope = (sB2 - sA2 + Math.Sqrt((sB2 - sA2) * (sB2 - sA2)
+ 4 * (sAb * sAb))) / 2 / sAb;
result.Intercept = meanB - result.Slope * meanA;
if (result.Correlation < 1)
{
result.SlopeError = (result.Slope / result.Correlation) * Math.Sqrt((1 - (result.Correlation * result.Correlation)) / a.Length);
}
else
{
result.SlopeError = 0;
}
}
else
{
result.Correlation = 0;
result.Slope = 0;
result.SlopeError = 0;
result.Intercept = 0;
}
return(result);
}
public LinearRegressionEntry(double startTime, double endTime, LinearRegression linearRegression)
{
StartTime = startTime;
EndTime = endTime;
LinearRegression = linearRegression;
}
///<summary>
///This subroutine determines the best fit line by minimizing the sum of the squares
///of the perpendicular distances of the points to the line.
///This was initially reported by Kermack and Haldane (1950) Biometrika, 37, 30.
///However I found it in York, D. (1966) Canadian Journal of Physics, vol 44, p 1079.
///</summary>
public static LinearRegression LinearRegressionWithErrorsInBothCoordinates(Statistics a, Statistics b)
{
double meanA = a.Mean();
double meanB = b.Mean();
double sA2 = 0;
double sB2 = 0;
double sAb = 0;
for (int i = 0; i < a.Length; i++)
{
double dA = a._list[i] - meanA;
double dB = b._list[i] - meanB;
sA2 += dA * dA;
sB2 += dB * dB;
sAb += dA * dB;
}
LinearRegression result = new LinearRegression();
if (sA2 > 0 && sB2 > 0 && sAb > 0)
{
result.Correlation = sAb / Math.Sqrt(sA2 * sB2);
result.Slope = (sB2 - sA2 + Math.Sqrt((sB2 - sA2) * (sB2 - sA2)
+ 4 * (sAb * sAb))) / 2 / sAb;
result.Intercept = meanB - result.Slope * meanA;
if (result.Correlation < 1)
{
result.SlopeError = (result.Slope / result.Correlation) * Math.Sqrt((1 - (result.Correlation * result.Correlation)) / a.Length);
}
else
{
result.SlopeError = 0;
}
}
else
{
result.Correlation = 0;
result.Slope = 0;
result.SlopeError = 0;
result.Intercept = 0;
}
return result;
}