Pulling remote hostname into variable

I'm trying to write a shell script using bash that connects to a remote server, runs a command that generates a file, pulls the file over, then renames it with the hostname of the remote server and a an extension.

So far, I'm able to everything but pull the hostname of the remote server into a variable.

REMHOST='ssh root@192.168.1.1 hostname'
echo $REMHOST

returns:
ssh root@192.168.1.1 hostname

When I run the command from the prompt, it returns what I am looking for. I also tried:

REMHOST='ssh root@192.168.1.1 hostname 2>$1'
echo $REMHOST

and i had similar results, where the contents of the ' were returned.

Thanks in advance for the help

You should use (`) - backtick, not (') - single quote:

REMHOST=`ssh root@192.168.1.1 hostname`

nice, no wonder I was having problems. Thanks.

Tested, Problem resolved.