How do I use regular expressions in bash scripts?

I want to check if a variable has a valid year using a regular expression. Reading the bash manual I understand I could use the operator =~

Looking at the example below, I would expect to see "not OK" but I see "OK". What am I doing wrong?

i="test"
if [ $i=~"200[78]" ]
then
  echo "OK"
else
  echo "not OK"
fi