`scipy.stats._mstats_basic:linregress`

source: build-install/usr/lib/python3.14/site-packages/scipy/stats/_mstats_basic.py:1034

Signature

def linregress(x, y = None)

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. 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: Slope of the regression line.
intercept: Intercept of the regression line.
rvalue: The Pearson correlation coefficient. The square of rvalue is equal to the coefficient of determination.
pvalue: 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: Standard error of the estimated slope (gradient), under the assumption of residual normality.
intercept_stderr: Standard error of the estimated intercept, under the assumption of residual normality.

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)

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Perform the linear regression:

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

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Coefficient of determination (R-squared):

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

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R-squared: 0.764127

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()

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<matplotlib.legend.Legend object at 0x7f3f687dbcb0>

plt.show()

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Calculate 95% confidence interval on slope and intercept:

from scipy.stats import t
tinv = lambda p, df: abs(t.ppf(p/2, df))

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ts = tinv(0.05, len(x)-2)

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print(f"slope (95%): {res.slope:.6f} +/- {ts*res.stderr:.6f}")
print(f"intercept (95%): {res.intercept:.6f}"
      f" +/- {ts*res.intercept_stderr:.6f}")

✗

intercept (95%): 0.519583 +/- 0.409359

Aliases

scipy.stats._mstats_basic.linregress