# AI Insights

## Linear Regression C#

When looking at time series data, such as a stream of prices, it can often be useful to establish a general trend and represent this with a single number. This can be achieved using a linear regression calculation.

Take this series of prices:
4.8, 4.8, 4.5, 3.9, 4.4, 3.6, 3.6, 2.9, 3.5, 3.0, 2.5, 2.2, 2.6, 2.1, 2.2

If you plot on an Excel graph and add a linear trend line, you should get something like this:

We can do the same thing in code:

1. using System;
2. class Regression
3. {
4.     static void Main(string[] args)
5.     {
6.         double[] values = { 4.8, 4.8, 4.5, 3.9, 4.4, 3.6, 3.6, 2.9, 3.5, 3.0, 2.5, 2.2, 2.6, 2.1, 2.2 };
7.         double xAvg = 0;
8.         double yAvg = 0;
9.         for (int x = 0; x < values.Length; x++)
10.         {
11.             xAvg += x;
12.             yAvg += values[x];
13.         }
14.         xAvg = xAvg / values.Length;
15.         yAvg = yAvg / values.Length;
16.         double v1 = 0;
17.         double v2 = 0;
18.         for (int x = 0; x < values.Length; x++)
19.         {
20.             v1 += (x – xAvg) * (values[x] – yAvg);
21.             v2 += Math.Pow(x – xAvg, 2);
22.         }
23.         double a = v1 / v2;
24.         double b = yAvg – a * xAvg;
25.         Console.WriteLine(“y = ax + b”);
26.         Console.WriteLine(“a = {0}, the slope of the trend line.”, Math.Round(a, 2));
27.         Console.WriteLine(“b = {0}, the intercept of the trend line.”, Math.Round(b, 2));
29.     }
30. }

Now you have the slope of the trend line, this can be used as an input for neural networks analysing time series data.

For a complete explanation of linear regression see Wikipedia.