For the school data set (again, using math score as the outcome variable) fit the following models:

a) A random intercept model with random intercepts for schools and both the raw SES scores and the respective school means as fixed effects.

b) The same model as in

(a) except using SES centered around its respective school mean (instead of the raw SES scores) as well as school mean SES as fixed effects.

c) Consider model (a). Does school mean SES contribute significantly to explaining the child’s math score?Would your conclusions change if you based them on model

(b) instead? Why or why not?