# What to report from hierarchical regression?

Here are three regression equations:

\begin{align} Y &= \beta_1Z_{\text{math}}\qquad (1)\\ Y &= \beta_2Z_{\text{math}} + \beta_3Z_{\text{science}}\qquad (2)\\ Y &= \beta_4Z_{\text{department}} + \beta_5Z_{\text{math}} + \beta_6Z_{\text{science}} + \beta_7Z_{\text{university}} + \beta_8Z_{\text{gender}}\qquad (3) \end{align}

I have 3-level regression model. I want to control the effect of maths achievement alone for (maths and science achievement in model 2), and model 3 includes gender, university and department.

B1math is SS in Model 1, B2science is SS in model 2, and B7university and B6science is SS in model three. I have 15, 25, and 35 R-squared estimates.

I am not sure what to report, besides increase in R-squared? Should I report the standardized Beta weight of university alone (because science was controlled) or should I also report B of science?

Do structure coefficient play a role in interpreting B?

If you are writing for a journal, they will probably have a style guide. I, personally, would make a table with each model and the associated $\beta$s, their SEs, and CIs. Most places will require p-values (but by choice I would leave them out). Standardized betas are required by the Am. Psychological Association style, but I don't like them.