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Module « scipy.stats.mstats »

Fonction linregress - module scipy.stats.mstats

Signature de la fonction linregress

def linregress(x, y=None) 

Description

help(scipy.stats.mstats.linregress)

Calculate a linear least-squares regression for two sets of measurements.

Parameters
----------
x, y : array_like
    Two sets of measurements.  Both arrays should have the same length N.  If
    only `x` is given (and ``y=None``), then it must be a two-dimensional
    array where one dimension has length 2.  The two sets of measurements
    are then found by splitting the array along the length-2 dimension. In
    the case where ``y=None`` and `x` is a 2xN array, ``linregress(x)`` is
    equivalent to ``linregress(x[0], x[1])``.

Returns
-------
result : ``LinregressResult`` instance
    The return value is an object with the following attributes:

    slope : float
        Slope of the regression line.
    intercept : float
        Intercept of the regression line.
    rvalue : float
        The Pearson correlation coefficient. The square of ``rvalue``
        is equal to the coefficient of determination.
    pvalue : float
        The p-value for a hypothesis test whose null hypothesis is
        that the slope is zero, using Wald Test with t-distribution of
        the test statistic. See `alternative` above for alternative
        hypotheses.
    stderr : float
        Standard error of the estimated slope (gradient), under the
        assumption of residual normality.
    intercept_stderr : float
        Standard error of the estimated intercept, under the assumption
        of residual normality.

See Also
--------
scipy.optimize.curve_fit :
    Use non-linear least squares to fit a function to data.
scipy.optimize.leastsq :
    Minimize the sum of squares of a set of equations.

Notes
-----
Missing values are considered pair-wise: if a value is missing in `x`,
the corresponding value in `y` is masked.

For compatibility with older versions of SciPy, the return value acts
like a ``namedtuple`` of length 5, with fields ``slope``, ``intercept``,
``rvalue``, ``pvalue`` and ``stderr``, so one can continue to write::

    slope, intercept, r, p, se = linregress(x, y)

With that style, however, the standard error of the intercept is not
available.  To have access to all the computed values, including the
standard error of the intercept, use the return value as an object
with attributes, e.g.::

    result = linregress(x, y)
    print(result.intercept, result.intercept_stderr)

Examples
--------
>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> from scipy import stats
>>> rng = np.random.default_rng()

Generate some data:

>>> x = rng.random(10)
>>> y = 1.6*x + rng.random(10)

Perform the linear regression:

>>> res = stats.mstats.linregress(x, y)

Coefficient of determination (R-squared):

>>> print(f"R-squared: {res.rvalue**2:.6f}")
R-squared: 0.717533

Plot the data along with the fitted line:

>>> plt.plot(x, y, 'o', label='original data')
>>> plt.plot(x, res.intercept + res.slope*x, 'r', label='fitted line')
>>> plt.legend()
>>> plt.show()

Calculate 95% confidence interval on slope and intercept:

>>> # Two-sided inverse Students t-distribution
>>> # p - probability, df - degrees of freedom
>>> from scipy.stats import t
>>> tinv = lambda p, df: abs(t.ppf(p/2, df))

>>> ts = tinv(0.05, len(x)-2)
>>> print(f"slope (95%): {res.slope:.6f} +/- {ts*res.stderr:.6f}")
slope (95%): 1.453392 +/- 0.743465
>>> print(f"intercept (95%): {res.intercept:.6f}"
...       f" +/- {ts*res.intercept_stderr:.6f}")
intercept (95%): 0.616950 +/- 0.544475

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