I am trying to fit a multiple regression on a dataset with n=8619.
First of all, using an untransformed Y as the response variable (ie Y = aX + bX +..) resulted in a residual plot with increasing error variance.
I then tried transforming Y to sqrt(Y) which made the residual plot look better.
However, the residuals still exhibit a wide-tailed distribution (see QQ plot below).
My question is - to what extent does this affect the validity of the model? I am aware that non-normal residuals and variances will result in inaccurate p-values/standard errors, but if I recall correctly, the inaccuracy is much more pronounced with smaller samples.
With my sample size (n=8619), is it large enough to be resistant to such a wide-tailed residual distribution?