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from math import sqrt

def mean(a):
    return float(sum(a))/len(a)

def regression_linear(data):
    vx,vy = list(zip(*data))
    mx = mean(vx)
    my = mean(vy)
    sx = sum((x-mx)**2 for x in vx)
    sy = sum((y-my)**2 for y in vy)
    sxy = sum((x-mx)*(y-my) for [x,y] in data)

    a = sxy/sx
    b = my-a*mx
    return {
        "rxy": sxy/sqrt(sx*sy),
        "center": [mx,my],
        "a": a, "b": b,
        "f": lambda x: a*x+b,
    }

def regression(data,X,step):
    from numpy import arange
    import matplotlib.pyplot as plot

    t = regression_linear(data)

    print("y = a*x+b")
    print("a = {}".format(t["a"]))
    print("b = {}".format(t["b"]))

    [x,y] = zip(*data)
    plot.plot(x,y,'o',color='black')

    x = arange(X[0],X[1],step)
    plot.plot(x,t["f"](x),color='black')

    plot.show()

# Ausreisser:
# [2,219]

data = [
    [1,375], [3,335], [4,322],
    [5,310], [6,302], [7,299], [8,269], [9,260]
]

regression(data,X=[0,10],step=0.1)