A collection of functions for performing and evaluating polynomial regression in JavaScript.

regression.coffee

# Find the best-fit curve for an nth order polynomial.
# Credit: https://stackoverflow.com/a/28301054/1544937
# Requirement: https://github.com/sloisel/numeric/blob/master/src/numeric.js
polyfit = (xArray, yArray, order) ->

    matrix = []

    if xArray.length <= order

        console.warn "Warning: Polyfit may be poorly conditioned."

    for value in xArray

        powers = []

        for power in [0 ... order + 1]

            powers.push Math.pow value, power

        matrix.push powers

    xMatrixT = numeric.transpose matrix
    yMatrixT = numeric.transpose [yArray]

    dot1 = numeric.dot xMatrixT, matrix
    dot2 = numeric.dot xMatrixT, yMatrixT

    dotInv = numeric.inv dot1

    coefficients = numeric.dot dotInv, dot2

    return coefficients

# Evaluate model accuracy.
rSquared = (xArray, yArray, coefficients) ->

    yMean = yArray.reduce((a, b) -> a + b) / yArray.length

    regressionSquaredError = 0
    totalSquaredError = 0

    for index in [0 ... xArray.length]

        regressionSquaredError += Math.pow yArray[index] - predict(xArray[index], coefficients), 2
        totalSquaredError += Math.pow yArray[index] - yMean, 2

    return 1 - (regressionSquaredError / totalSquaredError)

# Predict y given x.
predict = (x, coefficients) ->

    prediction = 0

    for coefficient, index in coefficients

        prediction += coefficient * Math.pow x, index

    return prediction

regression.js

// Generated by CoffeeScript 2.7.0

var polyfit, predict, rSquared;

// Find the best-fit curve for an nth order polynomial.
// Credit: https://stackoverflow.com/a/28301054/1544937
// Requirement: https://github.com/sloisel/numeric/blob/master/src/numeric.js
polyfit = function(xArray, yArray, order) {
  var coefficients, dot1, dot2, dotInv, i, j, len, matrix, power, powers, ref, value, xMatrixT, yMatrixT;
  matrix = [];
  if (xArray.length <= order) {
    console.warn("Warning: Polyfit may be poorly conditioned.");
  }
  for (i = 0, len = xArray.length; i < len; i++) {
    value = xArray[i];
    powers = [];
    for (power = j = 0, ref = order + 1; (0 <= ref ? j < ref : j > ref); power = 0 <= ref ? ++j : --j) {
      powers.push(Math.pow(value, power));
    }
    matrix.push(powers);
  }
  xMatrixT = numeric.transpose(matrix);
  yMatrixT = numeric.transpose([yArray]);
  dot1 = numeric.dot(xMatrixT, matrix);
  dot2 = numeric.dot(xMatrixT, yMatrixT);
  dotInv = numeric.inv(dot1);
  coefficients = numeric.dot(dotInv, dot2);
  return coefficients;
};

// Evaluate model accuracy.
rSquared = function(xArray, yArray, coefficients) {
  var i, index, ref, regressionSquaredError, totalSquaredError, yMean;
  yMean = yArray.reduce(function(a, b) {
    return a + b;
  }) / yArray.length;
  regressionSquaredError = 0;
  totalSquaredError = 0;
  for (index = i = 0, ref = xArray.length; (0 <= ref ? i < ref : i > ref); index = 0 <= ref ? ++i : --i) {
    regressionSquaredError += Math.pow(yArray[index] - predict(xArray[index], coefficients), 2);
    totalSquaredError += Math.pow(yArray[index] - yMean, 2);
  }
  return 1 - (regressionSquaredError / totalSquaredError);
};

// Predict y given x.
predict = function(x, coefficients) {
  var coefficient, i, index, len, prediction;
  prediction = 0;
  for (index = i = 0, len = coefficients.length; i < len; index = ++i) {
    coefficient = coefficients[index];
    prediction += coefficient * Math.pow(x, index);
  }
  return prediction;
};