Consider a linear regression model

y = beta_{0} + beta_{1}*x

with N data points D = \{x_{i}, y_{i}\} i = 1, 2, 3 ,...,N

Show that the unbiased estimate of the model parameters are given by using python

beta 0 = ( sum i = 1 to N x i )( sum i=1 ^ N x i y i )-( sum i=1 ^ N x i ^ 2 ) sum i=1 ^ N y i N sum i=1 ^ N x i ^ 2 -( sum i=1 ^ N x i )^ 2

beta 1 = ( sum i = 1 to N x i )( sum i=1 ^ N y i )-N( sum i=1 ^ N x i y i ) ( sum i=1 ^ N x i )^ 2 -N( sum i=1 ^ N x i ^ 2 )