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"why change in the independent variable should affect the dependent variable in a particular way. " Does it used to emphasize "affect"? Thanks.

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  • The entire quote is a bit strange. The relation being explained is built in to the definitions of independent and dependent variables. The only added bit is in a particular way. It really wants a definite, not indefinite determiner, ie., in this particular way. Otherwise, you ought to use a stronger word than should, such as will or must.
    – Phil Sweet
    Dec 11, 2017 at 15:15

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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."

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