From a Unix (or Mac) command line, you can use the 'ping' command with the 'count' option to check the response from the server as many times as you like.
For example:
ping -c 50 www.google.com
This will ping www.google.com 50 times. The final two lines of output will give you the packet loss, minimum, average, maximum, and standard deviation:
50 packets transmitted, 48 packets received, 4.0% packet loss
round-trip min/avg/max/stddev = 19.347/21.268/25.521/1.268 ms
On Windows you can do the same thing in the Command Prompt (command.exe) using -n for the count instead of -c:
ping -n 50 www.google.com
For more detailed response time information, you might like to Google for 'load testing services'. To create more detailed response tests in situations where, for example, you need to log in to the site first, you could code your own tests using a headless browser such as PhantomJS or ZombieJS, which also uses node.js.