Zeros in Dependent Variable : Bad- Zeros in Independent Variables: Not Bad? I am an MBA Student taking courses in statistics.
We have been learning about regression models for count data. Recently, our professor has been talking about situations in which there are a lot of zeros in the response variable - our professor mentioned that when there are a lot of zeros in the response variable, this kind of data becomes difficult to model. He didn't really explain why this is difficult. While I somewhat get the idea he was trying to convey, he didn't quite clearly explain why modelling data with many zeros is difficult.
However, one distinction that he did make - he stated that if you are trying to fit a regression model to some data and the response variable has a lot of zeros: this could be a problem. But on the other hand, if the dependent variables have a lot of zeros, this is not necessarily a problem.
I can conceptually accept why modelling data with a lot of zeros in general might be difficult - but I would be really interested in specifically understanding why :

*

*"Many Zeros in Dependent Variable : Bad"

*" Many Zeros in Independent Variables:  Not Bad?"

Can anyone offer any insights and explain this distinction?
PS: After much reading, my guess is because regression models tend to make assumptions on the distribution of the dependent variable and not the independent variables, therefore large numbers of zeros in the independent variables are not as problematic as large numbers of zeros in the dependent variable. This leads me to the following idea: large number of zeros in the dependent variable are problematic, but large number of zeros in the independent variable is even more problematic. Am I correct about this?

In principle, zeros are just numbers as any other one, so to single them out, there needs to be some special property of zeros. And this is indeed the case here, as you explained in the comments to your question.
You mentioned zero-inflation models, and those are models with distributions that deliberately single out the zero to give extra probability mass to them.
In your example with the filing of complaints, you have two situations: the first one is that the customer doesn't file any complaints, even though he has complaints, it is just that he maybe doesn't have enough time to file them, or maybe doesn't have internet, or is afraid to bother people. The second situation is that the customer actually does file the complaints. So, clearly, it makes sense to use zero-inflation models, in which, as the name suggests, zeros are treated specially.
Thus, in a way, in this example, you could interpret zeros as missing data. And if you don't just want to model the number of filed complaints, but the actual complaints, as a function of money spent, then, of course, lots of zeros will be a problem. Imagine, that you are exclusively dealing with people that are too afraid to bother people to file complaints. Then you will never get any information about the actual complaints. Thus, in this special situation, zeros are a problem.
