Linear Regression in C#/.NET Using Least Squares

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

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)
                Add(point);
        }

        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)
                    Add(Xs.ElementAt(i), Ys.ElementAt(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);
                ComputeSums(p, SumMode.Add);
                ComputeMinAndMax();
                ComputeSlopeAndYIntercept();
            }
        }

        public void Add(double x, double y) {
            Add(new PointD(x, y));
        }

        public void Add(PointD p) {
            _internalList.Add(p);
            RSquare = double.NaN;

            ComputeSums(p, SumMode.Add);
            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;

            ComputeSums(p, SumMode.Add);
            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) {
            if (mode == SumMode.Add) {
                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;
        }

    }
}