Replicate Excel Power Trendline values with c#

Question

I need to replicate this Excel graph in code

Given a list of [x, y] values, how can I obtain a new list of values to graph the power trendline?

I've found people referring to this http://mathworld.wolfram.com/LeastSquaresFittingPowerLaw.html formula. But don't know how to generate a new list of values from this.

Answer 1

Follow the formula from the link:

function getFittedPoints(data) {
  var log = Math.log,
    pow = Math.pow,

    sums = [
        0, // sum of the logarithms of x ( sum(log(x)) )
        0, // sum of the logarithms of y ( sum(log(y)) )
        0, // sum of the logarithms of the products of x and y ( sum(log(x) * log(y)) )
        0 // sum of the powers of the logarithms of x ( sum((log(x))^2 )
    ],
    fittedPoints = [], // return fitted points
    a, // a coefficient
    b, // b coefficient

    dataLen = data.length,
    i,
    logX,
    logY;

  for (i = 0; i < dataLen; i++) {
    sums[0] += logX = log(data[i][0]);
    sums[1] += logY = log(data[i][1]);
    sums[2] += logX * logY;
    sums[3] += pow(logX, 2);
  }

  b = (i * sums[2] - sums[0] * sums[1]) / (i * sums[3] - pow(sums[0], 2));
  a = pow(Math.E, (sums[1] - b * sums[0]) / i);

  for (i = 0; i < dataLen; i++) {
    fittedPoints.push([
        data[i][0],
        a * pow(data[i][0], b)
    ]);
  }

  return fittedPoints;
}

And then apply the function to the data.

example: http://jsfiddle.net/fa3m4Lvf/

Of course if your data are not clean then you can improve the function with handling null values,etc.