import csv

# Provides only numerical data, without any additional comments which are in the first column in .csv file
with open('loss.csv', 'rb') as csvfile:
    data = [row[1:] for row in csv.reader(csvfile, delimiter='\t')]

# This nested horrible construct provides sum of products X*Y, where X is the j-th element of the first row
# and Y is the j-th element i-th row. Pairs data[0] and data[i] provide data to fit linear equation.
# len(data) provides number of lines, so len(data)-1 is the number of linear equations to obtain
sop = [sum(j) for j in [[float(x) * float(y) for x, y in zip(data[0], data[i])] for i in xrange(1, len(data))]]

# N is the number of X, Y pairs, instead of zero it can be any number from xrange(0, len(data))
n = len(data[0])

# Average of X
x_avg = sum([float(x) for x in data[0]]) / n

# Average of Y in i-th row
y_avg = [sum(j) / n for j in [[float(y) for y in data[i]] for i in xrange(1, len(data))]]

# sos is the sum of X**2
sos = sum([float(j)**2 for j in data[0]])

# list of b coeficients of linear equation
a = [(i - n * x_avg * j) / (sos - n * x_avg**2) for i, j in zip(sop, y_avg)]

# list of b coeficients of linear equation
b = [j - i * x_avg for i, j in zip(a, y_avg)]

# printing results
print 'Results of regression analysis:'
x = 1
for i, j in zip(a, b):
    print 'Equation ' + str(x) + ': y = %.4ex + %.4e' % (i, j)
    x += 1