What is the term used for saying if something increases/decreases it has no effect on another thing
Solution 1:
Orthogonal
Solution 2:
"Is not dependent on" and "is independent of" are both common usage in statistics.
I'd also suggest "X and Y are not correlated." This is also a commonly used term in stats.
Alternatively, you could use "X and Y are uncorrelated" (as was suggested by Alain), which means the same thing, but might sound a bit more sophisticated.
Solution 3:
I believe it's actually independent. X is an independent variable if it does not depend on Y.
Solution 4:
I would use depend, as in:
Y does not depend on X.