"why change in the independent variable should affect the dependent variable in a particular way. " Does it used to emphasize "affect"? Thanks.
It's epistemic "should", that is to say it relates to the writer's knowledge, understanding, or presumption.
Here the implication is that it does have an effect, and the writer is speculating or theorising on why it does so.
Nothing to do with "affect".
I can't find a statement of this meaning in dictionary.com, but in the OED it is s.v. shall, sense 22d: " d. In clause dependent on sentence (negative, interrogative, or hypothetical) expressing possibility, probability, or expectation."