from math import sqrt, pow
from operator import mul, sub

def mean(xs):
	
	if len(xs) == 0: return 0
	return sum(xs) / len(xs)
    
def stddev(xs):

    if len(xs) == 0: return 0
    m = mean(xs)
    return sqrt(sum([pow(x - m,2) for x in xs])/float(len(xs)))
    
def linreg(data):

    xs = [x for x,y in data]
    ys = [y for x,y in data]
    
    return (slope(xs, ys), intercept(xs, ys))
    
def linregs(data):

    return "f(x) = {0}x + {1}".format(*linreg(data))
    
def slope(xs, ys):

    n = len(xs)
    return (n * sum(map(mul,xs,ys)) - (sum(xs) * sum(ys)))/(n*sum(map(mul,xs,xs)) - pow(sum(xs),2))
                                                                
def intercept(xs, ys):
    
    return mean(ys) - (slope(xs,ys)* mean(xs))
    
def correlation(data):

    xs = [x for x,y in data]
    ys = [y for x,y in data]

    n = len(xs)
    xvar = map(sub, xs, [mean(xs)] * n)
    yvar = map(sub, ys, [mean(ys)] * n)
    return sum(map(mul, xvar, yvar))/(n*stddev(xs)*stddev(ys))