The answer depends on the properties of you DVs which you haven't mentioned. You probably don't want a bivariate regression unless your research question is strange(you don't say). My guess is, assuming you do the usual thing you would want an ordinal logistic regression in a predictive model(assuming your questions were Likert type). I have recently done something that I believe is similar to what you want except my case was binary logistic regression. I have attached a copy of that paper in case it would be helpful. Assuming a similar research question to mine for ordinal logistic regression I would suggest for finding the best predictor variables the adaptive lasso procedure. Reasons for and how to do are described in the attached. Further, adaptive lasso for ordinal regression is now available and you can find details at this link: https://www.google.com/search?q=Adaptive+lasso+for+an+ordinal+logistic+regression&rlz=1C1CHBF_enUS874US874&oq=Adaptive+lasso+for+an+ordinal+logistic+regression&aqs=chrome..69i57.30702j0j1&sourceid=chrome&ie=UTF-8

In case you are not familiar with ordinal logistic regression, I have attached my fav. reference. HTH, Good luck. Best wishes, David Booth PS should I have guessed incorrectly and your DVs are binary. you should be able to use what we did in the attached paper. BTW I assumed Likert type questions in the above case for ordinal logistic regression.

The analysis will change depending on the type of response you used (whether it was dichotomous or ordinal). But, regardless of this, you should extract from your model an estimator that expresses the chance (odds ratio, for example). Thus, depending on the reference response alternative, you will be able to observe whether a different response category increases or not the chance of the variable depends on occurring.