GOAL: I have been running a multivariate linear regression to predict student outcomes (grades; at the individual student level) from several variables measures at the student level (age, and a few others), and also from 2 self-report teacher variables (stress, teaching experience). I have 10 classrooms and 250 kids; so the teacher variables (stress, and teaching experience) have a true N of 10; however, because the data is merged, each student within one classroom is associated with the same teacher value for stress and the same value for experience. I know that ideally, I would conduct this analysis as a nested model and enter the student variables as Level 1 variables and the Teacher variables as Level 2 variables. However, with 10 classrooms only, I don't have enough power to do that. Now, if I conduct this as a regular multiple regression, am I getting totally biased results? I am trying to understand this before going ahead.

It would be just like entering the school's SES, in a regression predicting student level outcomes (e.g. grades), where each student within the classroom (or school) would be associated with the same SES. Let me know if you have thoughts! And sorry if this is obvious and I am not getting it.