$.[3$ pts$]$ Explain using the reason linear regression as a classifier is very sensitive to outliers

$[5$ pts$]$ Logistic regression is to maximize the following formula.

prod$\_($i$)=1^($N$)$p$\_(1)($x$\_($i$)$;w$)^($y$\_($i$))$p$\_(0)($x$\_($i$)$;w$)^(1-$y$\_($i$))$

If we change above formula to below, does it still work? Explain exactly what is going to happen.

prod$\_($i$)=1^($N$)$p$($x$\_($i$)$;w$)^($y$\_($i$))$