# interpreting HLM coefficients

I have created the following model of longitudinal observations in HLM7:

Level-1 Model
Level-2 Model
π0jk = β00k + β01k*(FEMALEjk) + β02k*(SESjk) + r0jk
π1jk = β10k + β11k*(SESjk) + r1jk
π2jk = β20k + β21k*(SESjk) + r2jk
Level-3 Model
β00k = γ000 + γ001(RURALk) + u00k
β01k = γ010
β02k = γ020
β10k = γ100 + u10k
β11k = γ110
β20k = γ200 + u20k
β21k = γ210

• GRADE is a continuous variable, years of schooling
• FEMALE is dummy variable (0 = male)
• SES is a continuous variable, centred to sample mean
• RURAL is a dummy variable (0=urban/suburban)

I get the following results:

I interpret these as:

• mean initial reading achievement of average-SES male (that is, all vars 0): 48.24
• on average, mean initial reading achievement of average-SES males in rural schools is 3.6 points lower.
• mean female achievement is 2.47 points higher on average, controlling for school and SES
• the initial growth rate of reading achievement is 31.83 points per year. For every unit increase in SES is associated with an increase in initial growth is 2.15 points.

Does that interpretation make sense? Or am I erring somewhere?