How does signal attenuation relate to wire gauge and distance ?

Attenuation relates to wire gauge and distance (approximately) as follows:

wire gauge  thickness   @300kHz    @68kHz
22 AWG      .64 mm       8.62      4.62    db/km
24 AWG      .51 mm      11.90      6.65    dB/km
26 AWG      .40 mm      13.81      9.37    dB/km

A sensible formula, in common use, assuming 26AWG wire, is:
DS_Atn = 13.81 dB/km * distance

It is important to note that long loop wire thickness is not consistent, it tends to increase with distance from the CO. Thinner twisted pairs are often used underground near the CO while thicker wires are used on long loops in the regions closer to the subscriber location in order to minimize the total loop resistance.

Because most loops are made up of different gauges of wire the Atn/km ratio can decrease (stepwise) with distance and is not a linear function of the loop length.