I've seen this post but I have still some additional questions. I have a ordinary linear regression model with more then 300 predictors (which represents different conditions). I want to know which conditions have a positive effect on the outcome. So I look at the pvalues and select the ones below 0.01 (after correcting for multiple testing) I have 300 coefficients and a s I used the default Gaussian family function. sample size of 1200 with at least 3 df for each term).
But after building the model and looking at the residuals. I see that they are heavy tailed. So what does this mean for the standard error estimates of the coefficients? Are they too conservative (which is safe) or too liberal(change of picking up more false positives)?
Here plots from the glm output.