Does this graph imply a violation of homoscedasticity? I assume that this graph doesn't support the assumption of homoscedasticity. Am I right? Does it make sense to carry out another test to be sure?
y-axis: Regression Standardized Residual, x-axis: Regression Standardized Predicted Value, dependent variable: Score of a questionnaire measuring rage attacks, n=156

 A: You have bigger problems than heteroskedasticity here
Based on the straight diagonal line forming the lower bound of the residuals on the lower-left side of the plot, it appears that you are using a linear regression to deal with a non-negative response variable (possibly a count variable?).  If this is the case then it would be usual to either use a count regression model or at least use a logarithmic transformation on your response variable in the model.  This would usually give you a more appropriate model for this kind of data and would typically deal with the heteroskedasticity at issue.
Before worrying about heteroskedasticity, I recommend that you reconsider whether you are using the correct model.  If your response is a count variable then I would recommend starting with a negative-binomial count regression.  If your response is not a count variable, but is some other non-negative variable, I would recommend that you consider a log-linear regression (with an adjustment for response values of zero).  You can also consider variations on these models, but that is where I would start.
A: Two essential assumptions of regression are being unbiased and variance independence with observations. Mathematically, $\varepsilon \in \mathbb{R}^{n}$ is: 
$$
\varepsilon  \sim \mathcal{N} (0, \sigma^{2} I_{n}).
$$
In your case, it seems that the estimated variance increase with observations. Two possibilities : the first one is a problem of heteroscedasticity and maybe a problem of sampling.
I hope it helps.
