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I understand that you need to reference the intercept of the linear regression model to explain how each independent variables (or covariates) of the model affects the overall dependent variable of interest.

But it sounds too technical to write, "the intercept of linear regression model starts at X (\* indicates the intercept is not at zero), and the estimate/slope of the model is X."

I was told that I wouldn't need to report on the intercept (neither its estimate, standard error, t-value, p-value, etc.). And just focus on the effects of my covariates on the outcome of interest.

If it's for a lay biology journal, I wonder if reviewers would want to see an explanation of what intercepts are. At least for the first table of the models I show.

What have you all seen as a best practice in reporting this?
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No, you do not need to explain the intercept.

The only exception is that if you're writing about regression itself, or demonstrating how using regression would be advantageous, for example.
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Biologists only care about the effect size and the p-value of the variables of interest. They also care about what variables are included in the models. Look at other papers in the journal you'd like to publish and set up your tables in a similar fashion.
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If the aim of the manuscript is to educate people, I think it’s vital that you explain the intercept. Specifically, helping them understand intercept models and no intercept models.

I’ve always explained the intercept to the business clients as the baseline outcome - where the effect of all other factors that you haven’t considered in the model is captured. The baseline value of the outcome when all your factors are set to a value of zero is still non zero, because there might be some other factors you haven’t included in the study / model.

That means, if you have reason to believe that you have considered all the factors affecting your outcome, you can suppress the intercept and build a no intercept model instead.
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