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Most of teaching videos and materials about binary logistic are using more than one predictor in their examples.

My question can you run binary logistic regression (for smoking or not outcome) with only one predictor whether it is continuous or dichotomous such as age and gender respectively and separately

Then i run another model where i put multiple predictors together to predict smoking. Is that okay?

And when reporting should i call the results from the first as simple logistic regression and from the second as multiple logistic regression? or better call them unadjusted and adjusted logistic regressions respectively?

Thank you for your help

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You can certainly run logistic regression with only one predictor.

Both your choices of name are correct.

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