For the school data set (again, using math score as the outcome variable) start with fitting a model with the following fixed effects: SES centered around its respective school mean, school mean SES, public school (vs. private), hours spent on homework, race, gender, and the following random effects: SES centered around its respective school mean and hours spent on homework. Select a final model to explain how you arrived at the final model, and justify any decisions made in the process. Also graph the between and within schools regressions.