Cleaned up from http://www.answermysearches.com/how-to-do-a-simple-linear-regression-in-python/124/

linregress.py

def linregress(X, Y):
    """
    Summary
        Linear regression of y = ax + b
    Usage
        real, real, real = linreg(list, list)
    Returns coefficients to the regression line "y=ax+b" from x[] and y[], and R^2 Value
    """
    if len(X) != len(Y):
        raise ValueError('unequal length')
    N = len(X)
    Sx = Sy = Sxx = Syy = Sxy = 0.0
    for x, y in zip(X, Y):
        Sx = Sx + x
        Sy = Sy + y
        Sxx = Sxx + x*x
        Syy = Syy + y*y
        Sxy = Sxy + x*y
    det = Sxx * N - Sx * Sx
    a, b = (Sxy * N - Sy * Sx)/det, (Sxx * Sy - Sx * Sxy)/det
    meanerror = residual = 0.0
    for x, y in zip(X, Y):
        meanerror = meanerror + (y - Sy/N)**2
        residual = residual + (y - a * x - b)**2
    RR = 1 - residual/meanerror
    ss = residual / (N-2)
    Var_a, Var_b = ss * N / det, ss * Sxx / det
    return a, b, RR


if __name__ == '__main__':
    X = range(0, 5)
    Y = [3, 33, 45, 88, 3]
    print linregress(X, Y)

From the comments on that post, line 13 could be:

for x, y in zip(X, Y):

Oh, and line 22.

@lroggendorff, nice spot. Updated.