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Variable A is either 0 or 1. It is 0 if the sum of variables a + b + c + d … is less than some constant threshold, and is 1 if the sum of variables a + b + c + d … is greater than some constant threshold. Let’s call the sum of these variables “Variable B.”

a, b, c, and d can be, for example, can be 0, 0.5, 1, 2, or 3.

The sum of variables a, b, c, d might be the sum of 0.5, 0, 2, 0.5, which is 4. Here, Variable B is 4.

If the threshold is, for example, 3, then Variable A would be 1 (as it is above the threshold).

Let’s say we have many observations, and for each of which, we have Variable A, Variable B, Variable C, and Variable D. Variable D is what we’re predicting in a linear regression analysis. Variable C is a covariate.

Under what circumstances would Variable A be much more relevant (higher associated p-value and beta coefficient) in predicting Variable D compared to Variable B? Can you give an example to make this intuitive of why it is possible?

It is unintuitive as Variable A is produced from Variable B.

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    $\begingroup$ Maybe I don't understand, but if the truth is D=A (or A+2*C), then of course A should be identified as more important. $\endgroup$
    – Ben Reiniger
    Nov 2, 2023 at 21:45

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