In any Research , suppose we have four independent variables and one dependent varibles. so apart of regression any other method we may use to establish relationship independent variables to dependent variables.
In general regression analysis is very appropriate in the case you describe.
But depending on (fi) the measurement level of the variables, or particular research questions, or particular experimental design, other methods may apply.
That is why I asked you:"which are your objections against regression?"
Answering that question will increase the probability of a relevant answer to your main question.