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 <erlend.aasland@innova.no>

* Update signature in main docs

* Fix missing comma

Co-authored-by: Erlend Egeberg Aasland <erlend.aasland@innova.no>

4 files changed, 42 insertions, 8 deletions

diff --git a/Doc/library/statistics.rst b/Doc/library/statistics.rst
index bb03a2ce6e..8638abfb69 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
    <https://en.wikipedia.org/wiki/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 4f3ab49b40..5c3f77df15 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 fbc6a071cf..c0e427d935 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 0000000000..b2e9c7e2f0
--- /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`.