Hypothesis testing: association with raw data

If you have only one response variable, but multiple explanatory variables, multiple linear regression (MLR) may be sufficient. Note, this method assumes that the explanatory variables linearly influence the response variable and that this relationship is not reversible.

If you would like to test for linear associations between multiple response variables and multiple explanatory variables, consider redundancy analysis (RDA).

If you believe that your response variables respond unimodally (reaching a maximum and then decreasing in value) to an environmental gradient expressed in your explanatory variables, consider canonical correspondence analysis (CCA). If you are unsure which variables are responding to which, consider canonical correlation analysis (CCorA).