# Bio.Statistics.lowess module¶

Implements the Lowess function for nonparametric regression.

Functions: lowess Fit a smooth nonparametric regression curve to a scatterplot.

William S. Cleveland: “Robust locally weighted regression and smoothing scatterplots”, Journal of the American Statistical Association, December 1979, volume 74, number 368, pp. 829-836.

William S. Cleveland and Susan J. Devlin: “Locally weighted regression: An approach to regression analysis by local fitting”, Journal of the American Statistical Association, September 1988, volume 83, number 403, pp. 596-610.

`Bio.Statistics.lowess.``lowess`(x, y, f=0.6666666666666666, iter=3)

Lowess smoother: Robust locally weighted regression.

The lowess function fits a nonparametric regression curve to a scatterplot. The arrays x and y contain an equal number of elements; each pair (x[i], y[i]) defines a data point in the scatterplot. The function returns the estimated (smooth) values of y.

The smoothing span is given by f. A larger value for f will result in a smoother curve. The number of robustifying iterations is given by iter. The function will run faster with a smaller number of iterations.

x and y should be numpy float arrays of equal length. The return value is also a numpy float array of that length.

e.g.

```>>> import numpy
>>> x = numpy.array([4,  4,  7,  7,  8,  9, 10, 10, 10, 11, 11, 12, 12, 12,
...                 12, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 16, 16,
...                 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 20, 20, 20, 20,
...                 20, 22, 23, 24, 24, 24, 24, 25], numpy.float)
>>> y = numpy.array([2, 10,  4, 22, 16, 10, 18, 26, 34, 17, 28, 14, 20, 24,
...                 28, 26, 34, 34, 46, 26, 36, 60, 80, 20, 26, 54, 32, 40,
...                 32, 40, 50, 42, 56, 76, 84, 36, 46, 68, 32, 48, 52, 56,
...                 64, 66, 54, 70, 92, 93, 120, 85], numpy.float)
>>> result = lowess(x, y)
>>> len(result)
50
>>> print("[%0.2f, ..., %0.2f]" % (result[0], result[-1]))
[4.85, ..., 84.98]
```