What type of regression model do I use, if I have one dependent variable and five independent variables, but each observation was gathered in groups?

In this case I have a test score as the dependent variable and a bunch of independent variables measured for each student, but the students are in 10 different classes (two different schools). I don't really have any class specific or school specific data.

Do I use a regular linear regression and just ignore the grouped data structure or do I introduce a class_id variable as a level two variable in a hierarchical regression?