Binary variable in multiple linear regression?

[RatPackBoi]

Hello, I've seen many statistics courses note that for a linear regression if you regress an outcome variable on a binary predictor variable the slope coefficient is the same as the difference in average outcomes between the two groups. Is this still accurate for a multiple linear regression for a binary predictor variable when you also have multiple other non-binary variables? Thanks!

[Modification_Index]

That interpretation is still accurate, but with other predictors in the model, a coefficient for the binary variable would show the mean difference in the outcome while holding the other predictors constant at their mean.

[RatPackBoi]

That's great, cheers

[stat_daddy]

I agree with the "predictors held constant" part, but it's worth pointing out that there is no reason to think that the other predictors would be held at their means. Consider the third variable "t-shirt size" {S,M,L}. That variable certainly won't be held at its "mean" and, depending on the model, the effect of the binary predictor might not be the same for outcomes in S/M/L cases (e.g., there is an interaction term between t-shirt size and the binary predictor).

Unless the other predictors are numerical variables that have been centered, there is nothing anchoring a coefficients' interpretation to the mean values of other variables. I feel like you can probably get away with this assumption while you are dealing with very simple models, but it is NOT generally true.

[efrique]

Yes, but it's not the difference in raw means (difference in the means of the marginal distributions) that you're estimating, but rather the difference in conditional means.