using System;

public static class Program

    {

        public static void Main()

        {

            var xValues = new double[]

                              {

                                  1,2,3,4,5,6,7,8

                              };

            var yValues = new double[]

                              {

                                 900,800,1000,1050,900,998,895,1100

                              };

​

            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 * 9) + 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;

        }

    }