How to use bash(3.2.25)'s An additional binary operator：=~

I feel confused about how to use "=~" when I read the info of bash(3.2.25) at rhel5.5

# match the IP, and return true
[kevin@server1 shell]# [[ 192.168.1.1 =~ "^[0-9]{1,3}\.[0-9]{1,3}\.[0-9]{1,3}\.[0-9]{1,3}$" ]] && echo ok || echo fail
ok

# add double qoute
# return false, en ... I know.
[kevin@server1 shell]# [[ 192.168 =~ "^[0-9]{1,3}\.[0-9]{1,3}\.[0-9]{1,3}\.[0-9]{1,3}$" ]] && echo ok || echo fail
fail

# remove double qoute
# return ture ? Why ?
[kevin@server1 shell]# [[ 192.168 =~ ^[0-9]{1,3}\.[0-9]{1,3}\.[0-9]{1,3}\.[0-9]{1,3}$ ]] && echo ok || echo fail
ok 

So, should I qoute the string to the right of the operator ? And why the second command return true，apparently it should return false !

Here is what the info said:

An additional binary operator, =~', is available, with the same precedence as==' and !='. When it is used, the string to the right of the operator is considered an extended regular expression and matched accordingly (as in regex3)). The return value is 0 if the string matches the pattern, and 1 otherwise. If the regular expression is syntactically incorrect, the conditional expression's return value is 2. If the shell optionnocasematch' (see the description of shopt' in *Note Bash Builtins::) is enabled, the match is performed without regard to the case of alphabetic characters. Substrings matched by parenthesized subexpressions within the regular expression are saved in the array variableBASH_REMATCH'. The element of BASH_REMATCH' with index 0 is the portion of the string matching the entire regular expression. The element ofBASH_REMATCH' with index N is the portion of the string matching the Nth parenthesized subexpression.