# For all datasets with a binary outcome, will linear regression always yield betas with a smaller standard error compared to logistic regression?

Any cases where the betas' standard errors from logistic regression will be smaller than linear regression, after converting from log odds space to probability space?

• It's not a good way to frame the question. Linear regression will result in poor model fit in this situation. Use a method that has a chance of fitting and that yields probabilities constrained to be in [0,1]. Apr 28 at 12:18
• Thanks Frank - yes, linear regression will lead to poor model fit. However, just out of mathematical curiosity, are there any edge cases where linear regression will lead to standard errors greater than those estimated by logistic regression? Apr 28 at 12:21
• "Standard error" of what, exactly? Could you point to a parameter of one model that has the same meaning as a parameter in the other model? If you cannot, then your question makes no sense.
– whuber
Apr 28 at 12:22
• So in a regression of form y ~ ax + b, where the outcome is always 0 or 1, would the standard error of "a" using linear regression ever be larger than the standard error of "a" using logistic regression? After converting the standard error from logistic regression from log odds to probability space. Apr 28 at 12:26