From d2b55b07d2b503dcd3b5c0e2753efa835cff8e8f Mon Sep 17 00:00:00 2001 From: Raymond Hettinger Date: Sun, 21 Nov 2021 08:39:26 -0600 Subject: bpo-45766: Add direct proportion option to linear_regression(). (#29490) * bpo-45766: Add direct proportion option to linear_regression(). * Update 2021-11-09-09-18-06.bpo-45766.dvbcMf.rst * Use ellipsis to avoid round-off issues. * Update Misc/NEWS.d/next/Library/2021-11-09-09-18-06.bpo-45766.dvbcMf.rst Co-authored-by: Erlend Egeberg Aasland * Update signature in main docs * Fix missing comma Co-authored-by: Erlend Egeberg Aasland --- Doc/library/statistics.rst | 12 ++++++++- Lib/statistics.py | 31 +++++++++++++++++----- Lib/test/test_statistics.py | 6 +++++ .../2021-11-09-09-18-06.bpo-45766.dvbcMf.rst | 1 + 4 files changed, 42 insertions(+), 8 deletions(-) create mode 100644 Misc/NEWS.d/next/Library/2021-11-09-09-18-06.bpo-45766.dvbcMf.rst diff --git a/Doc/library/statistics.rst b/Doc/library/statistics.rst index bb03a2c..8638abf 100644 --- a/Doc/library/statistics.rst +++ b/Doc/library/statistics.rst @@ -643,7 +643,7 @@ However, for reading convenience, most of the examples show sorted sequences. .. versionadded:: 3.10 -.. function:: linear_regression(x, y, /) +.. function:: linear_regression(x, y, /, *, proportional=False) Return the slope and intercept of `simple linear regression `_ @@ -677,8 +677,18 @@ However, for reading convenience, most of the examples show sorted sequences. >>> round(slope * 2019 + intercept) 16 + If *proportional* is true, the independent variable *x* and the + dependent variable *y* are assumed to be directly proportional. + The data is fit to a line passing through the origin. + Since the *intercept* will always be 0.0, the underlying linear + function simplifies to: + + *y = slope \* x + noise* + .. versionadded:: 3.10 + .. versionchanged:: 3.11 + Added support for *proportional*. Exceptions ---------- diff --git a/Lib/statistics.py b/Lib/statistics.py index 4f3ab49..5c3f77d 100644 --- a/Lib/statistics.py +++ b/Lib/statistics.py @@ -937,13 +937,13 @@ def correlation(x, y, /): LinearRegression = namedtuple('LinearRegression', ('slope', 'intercept')) -def linear_regression(x, y, /): +def linear_regression(x, y, /, *, proportional=False): """Slope and intercept for simple linear regression. Return the slope and intercept of simple linear regression parameters estimated using ordinary least squares. Simple linear regression describes relationship between an independent variable - *x* and a dependent variable *y* in terms of linear function: + *x* and a dependent variable *y* in terms of a linear function: y = slope * x + intercept + noise @@ -961,21 +961,38 @@ def linear_regression(x, y, /): >>> linear_regression(x, y) #doctest: +ELLIPSIS LinearRegression(slope=3.09078914170..., intercept=1.75684970486...) + If *proportional* is true, the independent variable *x* and the + dependent variable *y* are assumed to be directly proportional. + The data is fit to a line passing through the origin. + + Since the *intercept* will always be 0.0, the underlying linear + function simplifies to: + + y = slope * x + noise + + >>> y = [3 * x[i] + noise[i] for i in range(5)] + >>> linear_regression(x, y, proportional=True) #doctest: +ELLIPSIS + LinearRegression(slope=3.02447542484..., intercept=0.0) + """ n = len(x) if len(y) != n: raise StatisticsError('linear regression requires that both inputs have same number of data points') if n < 2: raise StatisticsError('linear regression requires at least two data points') - xbar = fsum(x) / n - ybar = fsum(y) / n - sxy = fsum((xi - xbar) * (yi - ybar) for xi, yi in zip(x, y)) - sxx = fsum((d := xi - xbar) * d for xi in x) + if proportional: + sxy = fsum(xi * yi for xi, yi in zip(x, y)) + sxx = fsum(xi * xi for xi in x) + else: + xbar = fsum(x) / n + ybar = fsum(y) / n + sxy = fsum((xi - xbar) * (yi - ybar) for xi, yi in zip(x, y)) + sxx = fsum((d := xi - xbar) * d for xi in x) try: slope = sxy / sxx # equivalent to: covariance(x, y) / variance(x) except ZeroDivisionError: raise StatisticsError('x is constant') - intercept = ybar - slope * xbar + intercept = 0.0 if proportional else ybar - slope * xbar return LinearRegression(slope=slope, intercept=intercept) diff --git a/Lib/test/test_statistics.py b/Lib/test/test_statistics.py index fbc6a07..c0e427d 100644 --- a/Lib/test/test_statistics.py +++ b/Lib/test/test_statistics.py @@ -2527,6 +2527,12 @@ class TestLinearRegression(unittest.TestCase): self.assertAlmostEqual(intercept, true_intercept) self.assertAlmostEqual(slope, true_slope) + def test_proportional(self): + x = [10, 20, 30, 40] + y = [180, 398, 610, 799] + slope, intercept = statistics.linear_regression(x, y, proportional=True) + self.assertAlmostEqual(slope, 20 + 1/150) + self.assertEqual(intercept, 0.0) class TestNormalDist: diff --git a/Misc/NEWS.d/next/Library/2021-11-09-09-18-06.bpo-45766.dvbcMf.rst b/Misc/NEWS.d/next/Library/2021-11-09-09-18-06.bpo-45766.dvbcMf.rst new file mode 100644 index 0000000..b2e9c7e --- /dev/null +++ b/Misc/NEWS.d/next/Library/2021-11-09-09-18-06.bpo-45766.dvbcMf.rst @@ -0,0 +1 @@ +Added *proportional* option to :meth:`statistics.linear_regression`. -- cgit v0.12