How do I calculate a trendline for a graph?

Question

Google is not being my friend - it's been a long time since my stats class in college...I need to calculate the start and end points for a trendline on a graph - is there an easy way to do this? (working in C# but whatever language works for you)

Answer 1

I'm not too sure I understand what you mean by 'trendline' here... Could you please specify a bit (available input, required output)?

Edit: is linear regression what you're after?

Answer 2

ok, here's my best pseudo math:

the equation for your line is:

Y = a + bX

where:

b = (sum(xy) - sum(x)sum(y)/n) / (sum(x^2) = sum(x)^2/n)

a = sum(y)/n - b(sum(x)/n)

where sum(xy) is the sum of all x*y etc. Not particularly clear I concede, but it's the best I can do without a sigma symbol :)

Answer 3

Given that the trendline is straight, find the slope by choosing any two points and calculating:

(A) slope = (y1-y2)/(x1-x2)

Then you need to find the offset for the line. The line is specified by the equation:

(B) y = offset + slope*x

So you need to solve for offset. Pick any point on the line, and solve for offset:

(C) offset = y/(slope*x)

Now you can plug slope and offset into the line equation (B) and have the equation that defines your line. If your line has noise you'll have to decide on an averaging algorithm, or use curve fitting of some sort.

If your line isn't straight then you'll need to look into Curve fitting, or Least Squares Fitting - non trivial, but do-able. You'll see the various types of curve fitting at the bottom of the least squares fitting webpage (exponential, polynomial, etc) if you know what kind of fit you'd like.

Also, if this is a one-off, use Excel.

Answer 4

If you have access to Excel, look in the "Statistical Functions" section of the Function Reference within Help. For straight-line best-fit, you need SLOPE and INTERCEPT and the equations are right there.

Oh, hang on, they're also defined online here: http://office.microsoft.com/en-us/excel/HP052092641033.aspx for SLOPE, and there's a link to INTERCEPT. OF course, that assumes MS don't move the page, in which case try Googling for something like "SLOPE INTERCEPT EQUATION Excel site:microsoft.com" - the link given turned out third just now.

Answer 5

Thanks to all for your help - I was off this issue for a couple of days and just came back to it - was able to cobble this together - not the most elegant code, but it works for my purposes - thought I'd share if anyone else encounters this issue:

public class Statistics
{
    public Trendline CalculateLinearRegression(int[] values)
    {
        var yAxisValues = new List<int>();
        var xAxisValues = new List<int>();

        for (int i = 0; i < values.Length; i++)
        {
            yAxisValues.Add(values[i]);
            xAxisValues.Add(i + 1);
        }

        return new Trendline(yAxisValues, xAxisValues);
    }
}

public class Trendline
{
    private readonly IList<int> xAxisValues;
    private readonly IList<int> yAxisValues;
    private int count;
    private int xAxisValuesSum;
    private int xxSum;
    private int xySum;
    private int yAxisValuesSum;

    public Trendline(IList<int> yAxisValues, IList<int> xAxisValues)
    {
        this.yAxisValues = yAxisValues;
        this.xAxisValues = xAxisValues;

        this.Initialize();
    }

    public int Slope { get; private set; }
    public int Intercept { get; private set; }
    public int Start { get; private set; }
    public int End { get; private set; }

    private void Initialize()
    {
        this.count = this.yAxisValues.Count;
        this.yAxisValuesSum = this.yAxisValues.Sum();
        this.xAxisValuesSum = this.xAxisValues.Sum();
        this.xxSum = 0;
        this.xySum = 0;

        for (int i = 0; i < this.count; i++)
        {
            this.xySum += (this.xAxisValues[i]*this.yAxisValues[i]);
            this.xxSum += (this.xAxisValues[i]*this.xAxisValues[i]);
        }

        this.Slope = this.CalculateSlope();
        this.Intercept = this.CalculateIntercept();
        this.Start = this.CalculateStart();
        this.End = this.CalculateEnd();
    }

    private int CalculateSlope()
    {
        try
        {
            return ((this.count*this.xySum) - (this.xAxisValuesSum*this.yAxisValuesSum))/((this.count*this.xxSum) - (this.xAxisValuesSum*this.xAxisValuesSum));
        }
        catch (DivideByZeroException)
        {
            return 0;
        }
    }

    private int CalculateIntercept()
    {
        return (this.yAxisValuesSum - (this.Slope*this.xAxisValuesSum))/this.count;
    }

    private int CalculateStart()
    {
        return (this.Slope*this.xAxisValues.First()) + this.Intercept;
    }

    private int CalculateEnd()
    {
        return (this.Slope*this.xAxisValues.Last()) + this.Intercept;
    }
}

Answer 6

Regarding a previous answer

if (B) y = offset + slope*x

then (C) offset = y/(slope*x) is wrong

(C) should be:

offset = y-(slope*x)

See: http://zedgraph.org/wiki/index.php?title=Trend

Answer 7

matt

Your code really helped me,thanks very much.