To have regard for means to respect, pay attention to. If you are regardless, you do something despite everything; you do it anyway, nevertheless. Regardless also means not taking into account.
We’ll go fishing, regardless of the weather.
Regardless of the time of day, he would promptly come to help me.
Regardless of the threat, they went on.
Another way of expressing that something is not affected by something else is to use irrespective of.
This applies to all students, irrespective of nationality.
We came to the same result, irrespective of what method we used.
Irrespective of whether a text is long or short, it needs copyediting.
The meaning of not being affected by something may lead Swedish writers to use the word independent (Swedish oberoende) in sentences like the ones above. However, independent means separate, unrelated, autonomous or self-sufficient. Use irrespective of instead.