Is this Residual-vs-Fitted-Plot showing homoscedasticity or heteroscedasticity? I have a regression model. I checked it with  hettest (test for heteroscedasticity) in Stata and it gave me an insignificant result; thus no heteroscedasticity. But when I use rvfplot for a residual versus fitted plot, it shows me the graph below and I'm not sure how to interpret it. The dependent variable is a categorical one, with ten categories. I already checked if there are outliers, but there are none. 
 A: Despite apparently different titles and focus, the issues this raises are very similar to those in the recent thread Deleting outliers based on diagnostic plots is not working as intended (regression model) - data added 
If you smooth say the absolute residuals you may well find its pattern approximately flat, indicating rough homoscedasticity. (In Stata, rvfplot does not support this directly, but search rvfplot2 for an alternative.) 
There are, however, three bigger deals here:  


*

*As your outcome is categorical, it's an open question whether plain regression is a really good idea. If the outcome is a nominal variable, the regression is nonsense. It is an ordinal variable, the regression is dubious. If it's a count, but the bounds are 0 to 10, or 1 to 10, or there are bounds to what count is possible, other models will make more sense. If it's a count without an upper bound, yet other models will make more sense. 

*It's important to understand the structure in your plot. As you are asking for an interpretation, it seems that it is puzzling you. From the definition residual $\equiv$ observed response $-$ fitted response, it follows that all the residuals for observed values of (say) 7 lie on the line $$\text{residual} = 7 - \text{fitted}$$ with intercept $7$ and gradient of $-1$, and the same is true for any other value of $7$ (to recycle a mild joke attributed to William Feller). That is why you have a structure of parallel lines. 

*Loosely as in the cited thread, not seeing outliers here doesn't rule out there being outliers among your predictors. 
