Multivariate Linear Regression

The skeletal structure of this application is the figure below:-

The application in action looks like this:-

This application is powered my the Math.Net Numerics library. The code typed-in during the ML tutorial is as follows:-

    using System;
    using System.Collections.Generic;
    using System.ComponentModel;
    using System.Data;
    using System.Diagnostics;
    using System.Drawing;
    using System.IO;
    using System.Linq;
    using System.Text;
    using System.Text.RegularExpressions;
    using System.Threading.Tasks;
    using System.Windows.Forms;
    using Microsoft.Office.Interop.Excel;
    using ExcelApp = Microsoft.Office.Interop.Excel;
    using MathNet.Numerics.LinearAlgebra.Double;

    namespace Tutorials
    {
        public partial class Form1 : Form
        {
            public Form1()
            {
                InitializeComponent();
            }

            Random rand = new Random();
            double[] xCoords;
            double[] yCoords;

            private void button1_Click(object sender, EventArgs e)
            {
                xCoords = new double[Convert.ToInt32(numericUpDown1.Value)];
                yCoords = new double[Convert.ToInt32(numericUpDown1.Value)];

                chart1.Titles.Clear();
                chart1.Series.Clear();

                chart1.Titles.Add("Linear Regression");

                for (var i = 0; i < Math.Floor(xCoords.GetLength(0) / 2.0); i++)
                    xCoords[i] = rand.Next(i - xCoords.Length / 10, i + xCoords.Length / 10);

                for (var i = Convert.ToInt32(Math.Floor(xCoords.GetLength(0) / 2.0)); i < xCoords.GetLength((0)); i++)
                    xCoords[i] = rand.Next(i + xCoords.Length / 5, i + xCoords.Length / 2);

                for (var i = 0; i < Math.Floor(yCoords.GetLength(0) / 2.0); i++)
                    yCoords[i] = rand.Next(i, i + yCoords.Length / 5);

                for (var i = Convert.ToInt32(Math.Floor(yCoords.GetLength(0) / 2.0)); i < yCoords.GetLength((0)); i++)
                    yCoords[i] = rand.Next(i - yCoords.Length / 10, i);

                chart1.Series.Add("Data Points");
                chart1.Series["Data Points"].ChartType = System.Windows.Forms.DataVisualization.Charting.SeriesChartType.Point;

                for (var i = 0; i < xCoords.Length; i++)
                    chart1.Series["Data Points"].Points.AddXY(xCoords[i], yCoords[i]);

                chart1.Series["Data Points"].Color = Color.DarkOrange;

                chart1.Series.Add("QR Line");
                chart1.Series["QR Line"].ChartType = System.Windows.Forms.DataVisualization.Charting.SeriesChartType.Line;
                chart1.Series["QR Line"].Color = Color.DarkGreen;

                chart1.Series.Add("Calc Line");
                chart1.Series["Calc Line"].ChartType = System.Windows.Forms.DataVisualization.Charting.SeriesChartType.Line;
                chart1.Series["Calc Line"].Color = Color.DarkRed;


            }

            private void button2_Click(object sender, EventArgs e)
            {
                chart1.Series["QR Line"].Points.Clear();
                chart1.Series["Calc Line"].Points.Clear();

                var degree = Convert.ToInt32(numericUpDown2.Value);
                var X = new DenseMatrix(xCoords.Length, degree + 1);
                X.SetColumn(0, DenseVector.Create(xCoords.Length, i => 1));

                if (degree != 0)
                    X.SetColumn(1, xCoords);

                for (int i = 2; i <= degree; i++)
                    X.SetColumn(i, X.Column(1).PointwiseMultiply(X.Column(i - 1)));

                var y = DenseMatrix.OfColumns(yCoords.Length, 1, new[] { new DenseVector(yCoords) });

                var qrTheta = X.QR().Solve(y).ToColumnWiseArray();

                //(XTX)-1 * (XTy).
                var calcTheta = (X.Transpose().Multiply(X)).Inverse()
                    .Multiply(X.Transpose()).Multiply(y).ToColumnWiseArray();

                var xMax = xCoords.Max();
                var xMin = xCoords.Min();
                var interval = (xMax - xMin) / Convert.ToDouble(numericUpDown1.Value);

                for (var i = xMin; i < xMax; i += interval)
                {
                    chart1.Series["QR Line"].Points.AddXY(i, yPrediction(i, qrTheta));
                    chart1.Series["Calc Line"].Points.AddXY(i, yPrediction(i, calcTheta));
                }


            }

            private static double yPrediction(double xPlot, double[] theta)
            {
                var yPlot = 0.0;

                for (var i = 0; i < theta.Length; i++)
                    yPlot += theta[i] * Math.Pow(xPlot, i);

                return yPlot;
            }
        }
    }


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