Here's the technical definition for a Host Precedence Violation (under RFC-1812): "Sent by the first hop router to a host to indicate that a requested precedence is not permitted for the particular combination of source/destination host or network, upper layer protocol and source/destination port."
Keep in mind, this is just a reference; there is a much-easier-to-digest explanation.
Let's go back to your Test History page. Find a Line Quality test then open it. Go down and look at the "your first hop ping" row. Check your gateway's IP. Most likely, it is between 10.0.0.0 & 10.255.255.255, 172.16.0.0 & 172.31.255.255 or 192.168.0.0 & 192.168.255.255, correct?
Those three domain ranges are in something dubbed the "Private IP Network" domains. With the way the Internet works, your ISP has set up an "exclusive LAN." Your ISP has your gateway set up so that it is dedicated to only Internet traffic coming from you and going to you. The DSLreports servers are not recognized within your ISP's network, so your gateway doesn't respond to any packets being sent directly to it. Your first hop ping is then estimated. Nearly all of the time, it shows up as way higher than it really is.
Do you want to know what your first hop ping really is?
With your Windows PC, go to "Start" - "Run" - then type "ping -t Your Gateway's IP here."
With your Mac OS X PC, open Terminal and type "ping IP here."
Open the Network Utility and fill in the text box.
With your Linux PC, go to a shell, then type "ping Your Gateway's IP here."
Since the gateway recognizes you as a part of your ISP's "happy family," it will correctly respond to a ping and return accurate results.