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@NikolayIT
Created March 17, 2017 13:43
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Linear regression implementation in pure C# with example of Bulgarian population prediction
namespace LinearRegression
{
using System;
using System.Diagnostics;
public static class Program
{
public static void Main()
{
var xValues = new double[]
{
1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004,
2005, 2006, 2007, 2008, 2009
};
var yValues = new double[]
{
8669269, 8595500, 8484900, 8459800, 8427400, 8384700, 8340900, 8283200, 8230400, 8190900,
8149468, 7932984, 7845841, 7801273, 7761049, 7720000, 7679290, 7640238, 7606551,
7563710
};
double rSquared, intercept, slope;
LinearRegression(xValues, yValues, out rSquared, out intercept, out slope);
Console.WriteLine($"R-squared = {rSquared}");
Console.WriteLine($"Intercept = {intercept}");
Console.WriteLine($"Slope = {slope}");
var predictedValue = (slope * 2017) + intercept;
Console.WriteLine($"Prediction for 2017: {predictedValue}");
}
/// <summary>
/// Fits a line to a collection of (x,y) points.
/// </summary>
/// <param name="xVals">The x-axis values.</param>
/// <param name="yVals">The y-axis values.</param>
/// <param name="rSquared">The r^2 value of the line.</param>
/// <param name="yIntercept">The y-intercept value of the line (i.e. y = ax + b, yIntercept is b).</param>
/// <param name="slope">The slop of the line (i.e. y = ax + b, slope is a).</param>
public static void LinearRegression(
double[] xVals,
double[] yVals,
out double rSquared,
out double yIntercept,
out double slope)
{
if (xVals.Length != yVals.Length)
{
throw new Exception("Input values should be with the same length.");
}
double sumOfX = 0;
double sumOfY = 0;
double sumOfXSq = 0;
double sumOfYSq = 0;
double sumCodeviates = 0;
for (var i = 0; i < xVals.Length; i++)
{
var x = xVals[i];
var y = yVals[i];
sumCodeviates += x * y;
sumOfX += x;
sumOfY += y;
sumOfXSq += x * x;
sumOfYSq += y * y;
}
var count = xVals.Length;
var ssX = sumOfXSq - ((sumOfX * sumOfX) / count);
var ssY = sumOfYSq - ((sumOfY * sumOfY) / count);
var rNumerator = (count * sumCodeviates) - (sumOfX * sumOfY);
var rDenom = (count * sumOfXSq - (sumOfX * sumOfX)) * (count * sumOfYSq - (sumOfY * sumOfY));
var sCo = sumCodeviates - ((sumOfX * sumOfY) / count);
var meanX = sumOfX / count;
var meanY = sumOfY / count;
var dblR = rNumerator / Math.Sqrt(rDenom);
rSquared = dblR * dblR;
yIntercept = meanY - ((sCo / ssX) * meanX);
slope = sCo / ssX;
}
}
}
@ianpowell2017
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Hi,
If we removed the last value of each of the above arrays (2009 & 7563710).
What formulae would I use to calculate the x-result (approx. 2009) when the y-input is 7563710?

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