# scipy.stats.siegelslopes#

scipy.stats.siegelslopes(y, x=None, method='hierarchical')[source]#

Computes the Siegel estimator for a set of points (x, y).

`siegelslopes` implements a method for robust linear regression using repeated medians (see ) to fit a line to the points (x, y). The method is robust to outliers with an asymptotic breakdown point of 50%.

Parameters:
yarray_like

Dependent variable.

xarray_like or None, optional

Independent variable. If None, use `arange(len(y))` instead.

method{‘hierarchical’, ‘separate’}

If ‘hierarchical’, estimate the intercept using the estimated slope `slope` (default option). If ‘separate’, estimate the intercept independent of the estimated slope. See Notes for details.

Returns:
result`SiegelslopesResult` instance

The return value is an object with the following attributes:

slopefloat

Estimate of the slope of the regression line.

interceptfloat

Estimate of the intercept of the regression line.

`theilslopes`

a similar technique without repeated medians

Notes

With `n = len(y)`, compute `m_j` as the median of the slopes from the point `(x[j], y[j])` to all other n-1 points. `slope` is then the median of all slopes `m_j`. Two ways are given to estimate the intercept in  which can be chosen via the parameter `method`. The hierarchical approach uses the estimated slope `slope` and computes `intercept` as the median of `y - slope*x`. The other approach estimates the intercept separately as follows: for each point `(x[j], y[j])`, compute the intercepts of all the n-1 lines through the remaining points and take the median `i_j`. `intercept` is the median of the `i_j`.

The implementation computes n times the median of a vector of size n which can be slow for large vectors. There are more efficient algorithms (see ) which are not implemented here.

For compatibility with older versions of SciPy, the return value acts like a `namedtuple` of length 2, with fields `slope` and `intercept`, so one can continue to write:

```slope, intercept = siegelslopes(y, x)
```

References

 (1,2)

A. Siegel, “Robust Regression Using Repeated Medians”, Biometrika, Vol. 69, pp. 242-244, 1982.



A. Stein and M. Werman, “Finding the repeated median regression line”, Proceedings of the Third Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 409-413, 1992.

Examples

```>>> import numpy as np
>>> from scipy import stats
>>> import matplotlib.pyplot as plt
```
```>>> x = np.linspace(-5, 5, num=150)
>>> y = x + np.random.normal(size=x.size)
>>> y[11:15] += 10  # add outliers
>>> y[-5:] -= 7
```

Compute the slope and intercept. For comparison, also compute the least-squares fit with `linregress`:

```>>> res = stats.siegelslopes(y, x)
>>> lsq_res = stats.linregress(x, y)
```

Plot the results. The Siegel regression line is shown in red. The green line shows the least-squares fit for comparison.

```>>> fig = plt.figure()