I'm modeling traffic accidents (1) vs. no accident (0) on the highway for the day. I have a binary rain variable that is precipitation (1) or no precipitation (0).

I have only 30 days with a value of 1 for that variable, however when it does occur 28 of the 30 times there is an accident. My coefficient for that variable is very low though. I think this is because 90% of the time I have a 0 for weather, and there are still many accidents. The regression is showing a weak correlation because I have 9 times as many no-weather days where there may or may not be an accident.

I'm guessing that I have to treat this variable differently since it's such low frequency.

Would I just model accidents 1/0 and with a single variable, and only use days where it rained, and then find the coefficient to manually use in my regression with multiple variables?