Linear Regession 3 methods different results

Question

Morning,

So I use a package called Ninja Trader that has a linear regression method, I have also written my own method and compared the results to excels linear regression method. All three are giving different results and I an trying to understand why.

If we look at one example maybe someone will be able to shed some light one why this is.

EXAMPLE

Y vals 165.05 165.02 165.03 165.07 165.02 165.07 165.04 165.03 165.02 165.01 165 165.02 165.03 165.02 165.02 165.01 165.03 165.04 165.04 165.07

x vals 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

The results I have from the three different methods are:

Ninja Trader method : 165.034571428572
My own method:        165.036842105263
Excels method:        165.025578947368000

Here is My linea regression method, in C#:

public static double LinearRegression(double[] xVals, double[] yVals, int inclusiveStart, int inclusiveEnd)
        {

                double sumOfX = 0;
                double sumOfY = 0;
                double sumOfXSq = 0;
                double sumOfYSq = 0;
                double ssX = 0;
                double ssY = 0;
                double sumCodeviates = 0;
                double sCo = 0;
                double count = xVals.Length;
                double x;
                double y;

                for (int ctr = inclusiveStart; ctr < count; ctr++)
                {
                    x = xVals[ctr];
                    y = yVals[ctr];
                    sumCodeviates += x * y;
                    sumOfX += x;
                    sumOfY += y;
                    sumOfXSq += x * x;
                    sumOfYSq += y * y;
                }

            double slope = ((count * sumCodeviates) - (sumOfX * sumOfY)) / ( (count * sumOfXSq) - (sumOfX * sumOfX));
            double yIntercept = ((sumOfXSq * sumOfY) - (sumOfX * sumCodeviates)) / ((count * sumOfXSq) - (sumOfX * sumOfX));

            return yIntercept + slope * (xVals.Length + 1);
        }

I hope that someone can help me out getting to the bottom of this. Thx ; )

Answer 1

It is a common problem due to floating point arithmetics. For example you cast variables to double type, whereas Excel uses a limited precision.

Here you can find more info about the numeric precision in Excel: https://en.wikipedia.org/wiki/Numeric_precision_in_Microsoft_Excel

I don't know anything about NinjaTrader, but I think the results are slightly different from your implementation because of the precision used.