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bundles / scipy latest / scipy / stats / _stats_py / linregress

function

scipy.stats._stats_py:linregress

source: /scipy/stats/_stats_py.py :10394

Signature

def   linregress ( x ,  y ,  alternative = two-sided ,  * ,  axis = 0 ,  nan_policy = propagate ,  keepdims = False )

Summary

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.

alternative : {'two-sided', 'less', 'greater'}, optional

Defines the alternative hypothesis. Default is 'two-sided'. The following options are available:

  • 'two-sided': the slope of the regression line is nonzero

  • 'less': the slope of the regression line is less than zero

  • 'greater': the slope of the regression line is greater than zero

axis : int or None, default: 0

If an int, the axis of the input along which to compute the statistic. The statistic of each axis-slice (e.g. row) of the input will appear in a corresponding element of the output. If None, the input will be raveled before computing the statistic.

nan_policy : {'propagate', 'omit', 'raise'}

Defines how to handle input NaNs.

  • propagate: if a NaN is present in the axis slice (e.g. row) along which the statistic is computed, the corresponding entry of the output will be NaN.

  • omit: NaNs will be omitted when performing the calculation. If insufficient data remains in the axis slice along which the statistic is computed, the corresponding entry of the output will be NaN.

  • raise: if a NaN is present, a ValueError will be raised.

keepdims : bool, default: False

If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the input array.

Returns

result : ``LinregressResult`` instance

The return value is an object with the following attributes:

slope

slope

intercept

intercept

rvalue

rvalue

pvalue

pvalue

stderr

stderr

intercept_stderr

intercept_stderr

Notes

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)

Beginning in SciPy 1.9, np.matrix inputs (not recommended for new code) are converted to np.ndarray before the calculation is performed. In this case, the output will be a scalar or np.ndarray of appropriate shape rather than a 2D np.matrix. Similarly, while masked elements of masked arrays are ignored, the output will be a scalar or np.ndarray rather than a masked array with mask=False.

Array API Standard Support

linregress has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

====================  ====================  ====================
Library               CPU                   GPU
====================  ====================  ====================
NumPy                 ✅                     n/a                 
CuPy                  n/a                   ⛔                   
PyTorch               ⛔                     ⛔                   
JAX                   ⛔                     ⛔                   
Dask                  ⛔                     n/a                 
====================  ====================  ====================

See dev-arrayapi for more information.

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.linregress(x, y)
✓
Coefficient of determination (R-squared): 
print(f"R-squared: {res.rvalue**2:.6f}")
✗
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()
✓
fig-9f5655d22bde1c8f.png
Calculate 95% confidence interval on slope and intercept: 
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}")
print(f"intercept (95%): {res.intercept:.6f}"
      f" +/- {ts*res.intercept_stderr:.6f}")
✗

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.

Aliases

  • scipy.stats.linregress

Referenced by

This package