I'd be interested to understand a bit more, if you don't mind humouring a noob? Why does this work? Are the line voltages the same in the US/UK, etc?
A noisy condition can be caused when there is oxidation at a splice point or terminal connection. See the attached graph showing the initial very noisy SNR conditions on my line. Passing a current through the line can clear this if there is not too much corrosion. My SNR graph is a smooth line now since having installed the resistor a couple of weeks ago.
You can actually hear this effect if you have phone service on the ADSL line: when you pick up the receiver you may initially hear some crackle, which then goes away. This is because current flows through the line only when you lift the receiver. At other times there is no appreciable current through the line, even with the ADSL modems operating.
Placing a resistor across the line will allow a current to flow at all times, not just while the handset is lifted. This constant current can "seal" a line from noise caused by oxidized terminals or splices, which will improve the SNR figure and, eventually, the sync speeds.
The value of the resistor should be small enough to allow a few ma of current to flow through the line: if the open line voltage is 50v (typical) a 15,000 Ohm resistor will pass about 3 ma of current (I=E/R); smaller resistor values will pass greater current through the line. If the resistor value is too low the phone may fail to ring on incoming calls... I have about 5 ma of current on my line now. I expect that 10 or 20 ma may be the reasonable limit if the condition is really bad. The resistor should be rated 1 or 2 watts for these currents.
I suppose the line could deteriorate further if there is a junction or terminal exposed to the elements somewhere along the way. But at that time I will either decrease the resistor value further (increase the current) or hope that the noise level becomes bad enough so that the telco people will be prompted to fix it. I am interested to see how long the line will hold up. So far it has been rock solid even during recent downpours.
BTW, after getting rid of the noise on my line it took several days for the sync speeds to be re-negotiated back to top speed.