linear_regression.py

class LinearRegression:
    """
    >>> lr = LinearRegression()
    >>> lst = [(0., 0.)]
    >>> lr.add(lst[0][0], lst[0][1])
    >>> lr.get()
    >>> lr.error()
    >>> for nxt in [(1., 1.), (2., 2.), (4., 3.), (-1., -0.5)]:
    ...     lst.append(nxt)
    ...     lr.add(nxt[0], nxt[1])
    ...     m, b = lr.get()
    ...     print len(lr), (m, b), lr.error()
    2 (1.0, -0.0) 0.0
    3 (1.0, -0.0) 0.0
    4 (0.7428571428571429, 0.2) 0.171428571429
    5 (0.7364864864864865, 0.21621621621621623) 0.172297297297
    >>> import pprint
    >>> pprint.pprint([(x, y, m * x + b) for x, y in lst])
    [(0.0, 0.0, 0.21621621621621623),
     (1.0, 1.0, 0.9527027027027027),
     (2.0, 2.0, 1.6891891891891893),
     (4.0, 3.0, 3.1621621621621623),
     (-1.0, -0.5, -0.5202702702702703)]
    """

    def __init__(self):
        self._count = 0
        self._sum_x = 0.
        self._sum_y = 0.
        self._sum_xx = 0.
        self._sum_xy = 0.
        self._sum_yy = 0.
        self._last_computed = -1

    def __len__(self):
        return self._count

    def add(self, x, y):
        self._count += 1
        self._sum_x += x
        self._sum_y += y
        self._sum_xx += x ** 2
        self._sum_xy += x * y
        self._sum_yy += y ** 2

    def get(self):
        if self._count < 2:
            return None
        if self._count > self._last_computed:
            det = self._sum_x ** 2 - self._count * self._sum_xx
            assert abs(det) > 1.e-12
            self._m = (self._sum_x * self._sum_y - self._count * self._sum_xy) / det
            self._b = (-self._sum_xx * self._sum_y + self._sum_x * self._sum_xy) / det
            self._last_computed = self._count
        return (self._m, self._b)

    def error(self):
        if self._count < 2:
            return None
        m, b = self.get()
        return (
            self._sum_yy
            - 2 * (m * self._sum_xy + b * self._sum_y)
            + m**2 * self._sum_xx + 2 * m * b * self._sum_x + b**2 * self._count
        )


if __name__ == "__main__":
    import doctest
    doctest.testmod()