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In logistic regression, we learn coefficients which have magnitude and direction (positive or negative). If the direction of a coefficient is negative, we say that the variable associated with the coefficient has a "protective effect". Is there a similar term or phrase to describe a coefficient that is positive?

This term, "protective effect," might be context-dependent, depending on what the outcome variable represents. In my case, the binary outcome (dependent) variable is death (1 = death, 0 = not-death). So one of my independent variables is average hours of exercise per week, and the associated coefficient is negative, I can say "the average hours of exercise per week has a protected effect on death," meaning, that as the average hours of exercise per week increase, the probability of death decreases.

One of my independent variables is average number of cigarette packs smoked per week and the associated coefficient is positive, what would I say? e.g. "the average number of cigarette packs smoked per week has a [something] effect on death"

I looked up antonyms to "protective" and found such things as "harmful", but substituting that into the sentence does not make sense. Is there jargon around describing this relationship? I want to use "encouraging effect", but that does not seem right either.

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"Confers an increased risk of ...." or "Increases the risk of ...." (If you are claiming a causal relationship.)

"Is associated with an increased risk of ...." (If you are claiming merely a statistical relationship.)

Avoid "implies an increased risk of ....", because "implies" can mean both "suggests" and "necessitates".

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A positive association for a positive outcome would be a protective or preventative effect, both of which are common in the biomedical and epidemiological literature. The opposite would be described as harmful.

In your case, the effect is positive but the outcome is negative. In other words, smoking more increases the odds of death, so it would be harmful.

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