Find a good linear relationship between data using the 3 Median Method.

Best median-fit line

My 11 year-old son is learning about regression in his 9th grade math class.   
For them regression is two tables of data and a calculator button.  
The graphing calculators also provide a button to find the best "median-fit" line and
the students were asked to find it as well as the regression line.   The regression line can
easily be found with numpy.polyfit(x, y, 1).   

I did not know of a function to calculate the best "median-fit" line.  I had to review a few
online videos to learn exactly what a best "median-fit" line is and found the 3-median method 
for determining the best "median-fit" line.   It's sometimes called the median median fit. 

I wrote this implementation to be sure that we understood how the calculator median-fit function
was actually working.   Someone else might find it useful.  

linefit.py

def median(values):
    svalues = sorted(values)
    N = len(values)
    n, r = divmod(N, 2)
    if r == 1:
        return float(svalues[n])
    else:
        return (svalues[n-1]+svalues[n])/2.0


def medfit(x, y):
    # Create 3 groups
    N = len(x)
    assert N == len(y)
    n, r = divmod(N, 3)
    n1 = n + (1 if r > 0 else 0)
    n2 = n
    n3 = n + (1 if r > 1 else 0)
    assert (n1 + n2 + n3 == N)

    grp1 = x[:n1], y[:n1]
    grp2 = x[n1:n1+n2], y[n1:n1+n2]
    grp3 = x[N-n3:], y[N-n3:]
    
    # Summarize the three groups with 3 points
    # defined as the median of the x points and the y points
    # in each group.
    pt1 = median(grp1[0]), median(grp1[1])
    pt2 = median(grp2[0]), median(grp2[1])
    pt3 = median(grp3[0]), median(grp3[1])
    
    # Calculate the slope from the outer summary points
    m = (pt3[1] - pt1[1]) / (pt3[0] - pt1[0])
    # Intercept of that line
    b0 = pt1[1] - m * pt1[0]
    
    
    # Correct the intercept using the point 2
    # by moving 1/3 of the way towards point 2
    y2 = m*pt2[0] + b0
    b = b0 + (pt2[1]-y2)/3.0
    
    # The slobe and intercept of the best median-fit line to the data
    return m, b