I presume if the coin price plummets then people will lose interest and move to other profitable coin and as a result, falling coin's difficulty would decrease but so far I havent quite noticed that with zcash. Sometimes it seems opposite is happening.
But I'd really need to capture long term data over long enough time range to see any relationship and/or pattern being observed.
No, there is no direct relationship between the two.
There IS a direct relationship between both of those and PROFITABILITY though.
Price rises DO tend to fuel higher difficulty over time indirectly, as PROFITABILITY increases and folks build more rigs to take advantage of the profitability increase.
Many folks "chase the profitability" into coins that briefly spike on profitability - it tends to even out most coins over time fairly closely but often takes a day or two and sometimes might take a week.
Folks that don't "chase the profits" STILL benefit some as hashrate leaves the coin they're on to "chase the profitability" - and they don't lose any mining income while they are switching their rigs over to another coin.
When I look at whattomine, I NEVER look at "current profit" - I normally look at 24 hour average as a minimum, and more commonly at 1 week average, before I decide if it's worthwhile moving my farm to something else.
Other folks are more "gotta max out to the limit"....
To be explicit, as it's been asked before - difficulty does NOT cause price rises, it's the other way around but not directly, and there is a lag factor involved (a really BIG one the past year and some on Bitcoin and Litecoin due to limits of ASIC manufacturing, a lesser but significant one for some months this spring when most GPU coins shot WAY up and rig-building couldn't keep pace).