If $(x_1,y_1),(x_2,y_2),$dots,$(x_n,y_n)$

be a random sample taken from a logistic regression, then

the log$-$likelihood equation is$,$

${\displaystyle \underset{i=1}{\overset{n}{}}}{y}_{i}ln(\frac{{}_i}{1-{}_i})+{\displaystyle \underset{i=1}{\overset{n}{}}}ln(1-{}_i)$

${\displaystyle \underset{i=1}{\overset{n}{}}}{y}_{i}ln(1-{}_i)+{\displaystyle \underset{i=1}{\overset{n}{}}}ln(\frac{{}_i}{1-{}_i})$

${\displaystyle \underset{i=1}{\overset{n}{}}}{y}_{i}ln(\frac{{}_i}{1-{}_i})+{\displaystyle \underset{i=1}{\overset{n}{}}}ln({}_i)$

${\displaystyle \underset{?}{\overset{?}{}}}n{y}_{i}ln(\frac{1-{}_i}{-})+{\displaystyle \underset{?}{\overset{?}{}}}nln(1-{}_t)$