# Linear Regression in C#/.NET Using Least Squares

I had a class that handled the regression of my data sets, but it had too many business rules. It was necessary for me to refactor the code.

Here's how you can use it:

double[] X = { 75.0, 83, 85, 85, 92, 97, 99 };
double[] Y = { 16.0, 20, 25, 27, 32, 48, 48 };
var ds = new XYDataSet(X, Y);

Console.WriteLine(Math.Round(ds.Slope,2)); //1.45
Console.WriteLine(Math.Round(ds.YIntercept,2)); //-96.85
ConsoleWriteLine(Math.Round(ds.ComputeRSquared(), 3)); //0.927


The source is in my .NET CommonLib library. XYDataSet.cs: https://github.com/jprichardson/CommonLib/blob/master/CommonLib/Numerical/XYDataSet.cs XYDataSetTest.cs: https://github.com/jprichardson/CommonLib/blob/master/TestCommonLib/Numerical/XYDataSetTest.cs

Here is the source for XYDataSet.cs:

using System;
using System.Collections.Generic;
using System.Collections;
using System.Collections.ObjectModel;
using System.Linq;
using System.Text;
using CommonLib.Geometry;

namespace CommonLib.Numerical
{
public class XYDataSet : IList<PointD>
{

private List<PointD> _internalList = new List<PointD>();

public XYDataSet() : this(null, null) { }

public XYDataSet(IEnumerable<PointD> points) {
ResetValues();

foreach (var point in points)
}

public XYDataSet(IEnumerable<double> Xs, IEnumerable<double> Ys) {
ResetValues();

if (Xs != null || Ys != null) {
if (Xs.Count() != Ys.Count())
throw new Exception("X count must be the same as the Y count.");

for (int i = 0; i < Xs.Count(); ++i)
}
}

public int Count { get { return _internalList.Count; } }

public bool IsReadOnly { get { return false; } }

private double _maxX = Double.NegativeInfinity;
public double XMax { get { return _internalList[XMaxIndex].X; } }
private double _minX = Double.PositiveInfinity;
public double XMin { get { return _internalList[XMinIndex].X; } }
public int XMaxIndex { get; protected set; }
public int XMinIndex { get; protected set; }

private double _maxY = Double.NegativeInfinity;
public double YMax { get { return _internalList[YMaxIndex].Y; } }
private double _minY = Double.PositiveInfinity;
public double YMin { get { return _internalList[YMinIndex].Y; } }
public int YMaxIndex { get; protected set; }
public int YMinIndex { get; protected set; }

public double XMean { get { return XSum / Count; } }
public double YMean { get { return YSum / Count; } }

public double RSquare { get; protected set; }

public PointD RegressionPoint0 { get; protected set; }
public PointD RegressionPointN { get; protected set; }

public double Slope { get; protected set; }

public double XSum { get; set; }
public double YSum { get; set; }
public double XSquaredSum { get; set; }
public double XYProductSum { get; set; }

public double XIntercept { get { return -YIntercept / Slope; } }
public double YIntercept { get; protected set; }

public PointD this[int index] {
get { return _internalList[index]; }
set {
var p = value;
var old = _internalList[index];
_internalList[index] = p;

ComputeSums(old, SumMode.Subtract);
ComputeMinAndMax();
ComputeSlopeAndYIntercept();
}
}

public void Add(double x, double y) {
}

RSquare = double.NaN;

ComputeMinAndMax(Count - 1, p);
ComputeSlopeAndYIntercept();
}

public void Clear() {
_internalList.Clear();
ResetValues();
}

public void ComputeSlopeAndYIntercept() {
double delta = Count * XSquaredSum - Math.Pow(XSum, 2.0);
YIntercept = (1.0 / delta) * (XSquaredSum * YSum - XSum * XYProductSum);
Slope = (1.0 / delta) * (Count * XYProductSum - XSum * YSum);

RegressionPoint0.X = XMin;
RegressionPoint0.Y = Slope * XMin + YIntercept;
RegressionPointN.X = XMax;
RegressionPointN.Y = Slope * XMax + YIntercept;
}

public double ComputeRSquared() {
var SStot = _internalList.Sum(p => Math.Pow(p.Y - YMean, 2.0));
var SSerr = _internalList.Sum(p => Math.Pow(p.Y - (Slope * p.X + YIntercept), 2.0));
RSquare = 1.0 - SSerr / SStot;
return RSquare;
}

public bool Contains(PointD p) {
return _internalList.Contains(p);
}

public void CopyTo(PointD[] points, int index) {
_internalList.CopyTo(points, index);
}

public IEnumerator<PointD> GetEnumerator() {
return _internalList.GetEnumerator();
}

IEnumerator IEnumerable.GetEnumerator() {
return _internalList.GetEnumerator();
}

public int IndexOf(PointD p) {
return _internalList.IndexOf(p);
}

public void Insert(int index, PointD p) {
_internalList.Insert(index, p);
RSquare = double.NaN;

ComputeMinAndMax();
ComputeSlopeAndYIntercept();
}

public bool Remove(PointD p) {
var success = _internalList.Remove(p);
if (success) {
RSquare = double.NaN;
ComputeSums(p, SumMode.Subtract);
ComputeMinAndMax();
ComputeSlopeAndYIntercept();
}
return success;
}

public void RemoveAt(int index) {
var old = _internalList[index];
_internalList.RemoveAt(index);
RSquare = double.NaN;

ComputeSums(old, SumMode.Subtract);
ComputeMinAndMax();
ComputeSlopeAndYIntercept();
}

protected void ComputeMinAndMax() { //methods that call this, Insert,
ResetMinAndMax();

for (int i = 0; i < _internalList.Count; ++i)
ComputeMinAndMax(i, _internalList[i]);
}

protected void ComputeMinAndMax(int index, PointD newPoint) {
if (newPoint.X <= _minX) {
_minX = newPoint.X;
XMinIndex = index;
}

if (newPoint.X >= _maxX) {
_maxX = newPoint.X;
XMaxIndex = index;
}

if (newPoint.Y <= _minY) {
_minY = newPoint.Y;
YMinIndex = index;
}

if (newPoint.Y >= _maxY) {
_maxY = newPoint.Y;
YMaxIndex = index;
}
}

protected enum SumMode { Add, Subtract };
protected void ComputeSums(PointD p, SumMode mode) {
XSum += p.X;
YSum += p.Y;
XSquaredSum += Math.Pow(p.X, 2.0);
XYProductSum += (p.X * p.Y);
}
else if (mode == SumMode.Subtract) {
XSum -= p.X;
YSum -= p.Y;
XSquaredSum -= Math.Pow(p.X, 2.0);
XYProductSum -= (p.X * p.Y);
}
}

protected void ResetMinAndMax() {
_maxX = double.NegativeInfinity;
_maxY = double.NegativeInfinity;
_minX = double.PositiveInfinity;
_minY = double.PositiveInfinity;
}

protected void ResetValues() {
ResetMinAndMax();

RegressionPoint0 = new PointD();
RegressionPointN = new PointD();

RSquare = double.NaN;

Slope = double.NaN;
YIntercept = double.NaN;

XSum = 0.0;
YSum = 0.0;
XSquaredSum = 0.0;
XYProductSum = 0.0;

XMaxIndex = -1;
YMaxIndex = -1;
XMinIndex = -1;
YMinIndex = -1;
}

}
}