# Does the normality assumption hold? Is this an outlier?

I am trying to fit a multiple linear regression (OLS) model with IPO underpricing as dependent variable. As part of my master thesis I would like to analyze the effect of venture capital certification (dummy) on IPO underpricing (raw returns - not transformed). My sample consists of 199 IPOs.

Up to now I got the following plots. However, I am concerned about the residuals at the upper end of the qq-plot. Is the assumption of normality in the residuals violated in this case? I would report robust standard errors in order to control for the observed heteroscedasticity.

Further, I am not sure how to deal with the observation at the upper right in the qq-plot (represents first-day return of 63% vs. 51% the next smaller). Could this be an outlier or may it be simply the result of a misspecified model?. The studentized residual for this particular observation is 5.36 (all others below 3) and it has a Cook's D of 0.16. I run the regression twice: with and without this particular observation. It turns out that, if removed, the coefficients are getting larger in absolute values. The variables of interest (VC reputation and VC type) turned from weakly significant (at 10% level) into significant (at the 5% level). Running a robust regression, both the coefficients as well as the p-values are even more significant. However, the robust regression excludes 4 observations. Hence, should I simply stick with OLS and remove this potential outlier (and mention that I did so)? Or would it be better to report both results (with and without the observation)?

Thank you!

• The worst of all solutions is to remove the outlier just because it is awkward. You need to report what you've reported here. Saying as much as you can about the substantive context of the outlier is likely to be expected. You don't say which kind of robust regression you used. That's essential. It's likely that it downweighted 4 observations to zero weight; that's not quite the same as excluding them. Their values were considered! – Nick Cox Jan 28 '18 at 10:59
• Running a robust regression, both the coefficients as well as the p-values are even more significant. Which other regression analysis you have conducted ? – Subhash C. Davar Jan 28 '18 at 15:40
• @NickCox Sorry, I should be clearer. I used the robust regression implemented in stata (rreg command) with M-estimators (combination of Huber-weights and Tukey's biweights). Indeed, no observation were excluded, 4 received a weight of 0. Compared to OLS, the coefficients do not change dramatically, only the SE decrease which makes the main variable of interest highly significant (1% level). Following your suggestions, I won't exclude any values but will report the circumstances, instead. So, am I fine proceeding with the OLS regression (regarding normality)? – dtribus Jan 28 '18 at 20:09
• @subhashc.davar Sorry for not clearly specifying. I meant robust regression with M-estimators. Thus, weighting resiuals according to their size. – dtribus Jan 28 '18 at 20:15
• rreg in Stata is arguably best ignored. See statalist.org/forums/forum/general-stata-discussion/general/… and its references for arguments why. – Nick Cox Jan 28 '18 at 21:20