regression

A tiny Javascript toolkit for regression analysis.

Be warned that I am neither an expert on linear algebra nor numerical stability: this toolkit should be perfectly adequate for prototyping and experimentation, but you should use a real linear algebra toolkit for production applications. (Unfortunately, none seem to exist in Javascript. We at The Dark Sky Company use this toolkit for prototyping, but switch to NumPy for production applications.)

API

• regression.linear(x,y,n): Calculates the ordinary least squares linear regression on a dataset. x should be an N×M matrix, while y should be an N×1 column vector. Usage is straightforward:

  /* Find the best fit for the overdetermined system of equations:
   * 
   *     1 * a[1] + 0 * b[1] =  1
   *     1 * a[2] + 1 * b[2] = -1
   *     1 * a[3] + 2 * b[3] = -3
   *     1 * a[4] + 3 * b[4] = -5
   *     1 * a[5] + 4 * b[5] = -7
   * 
   * The answer is a=1 and b=-2 (which, in this case, solves each
   * equation exactly). */
  console.log(
    regression.linear(
      [
        1, 0,
        1, 1,
        1, 2,
        1, 3,
        1, 4
      ],
      [
         1,
        -1,
        -3,
        -5,
        -7
      ],
      2
    )
  );
  /* => [1, -2] */
  

• regression.sinusoidal(x,y,frequency[,phase]): Calculates the best fit sinusoidal model with the given frequency for the given dataset. x and y should both be N×1 column vectors. Usage is similarly straightforward:

  /* This finds the following sinusoidal model:
   * 
   *     f(x) = 0 + 1 * sin(x * Math.PI + 0.5 * Math.PI)
   * 
   * That is, the function returns the constant, amplitude, phase, and
   * frequency of the model, respectively. */
  console.log(
    regression.sinusoidal(
      [ 0,  1,  2,  3],
      [+1, -1, +1, -1],
      Math.PI
    );
  );
  /* => [0, 1, 0.5 * Math.PI, Math.PI] */
  

  Phase is optional. If not provided, the best phase will be determined automatically; if provided, it will be assumed in the model.