# Interpreting the ANOVA output for hierarchical linear regression

I followed this tutorial to learn Hierarchical Linear Regression (HLR) in R, but couldn't understand how to interpret its sample output of >anova(model1,model2,model3)

The tutorial simply says

each predictor added along the way is making an important contribution to the overall model.

But I would like some more details to quantify the contribution of each explanatory variable, like:

1. "UNEM" explains X (or X%) variance

2. Adding the "HGRAD" variable explains Y (or Y%) more variance

3. Adding the "INC" variable further explains Z (or Z%) more variance

So, can I get the value of X, Y, and Z using the above ANOVA table? How? Specifically, what do Res.Df, RSS, Sum of Sq mean in this ANOVA table?

Look at % variance farther up in the tutorial where the R-squared values are reported. You look at the model for the quantity of variance explained and the test (anova) for whether the increase across model complexity is significant.
• So you are suggesting that I can use >summary(model) for each individual model to see its R-squared (which is the variance explained), and compared the differences between R-squared. Then using >anova(model1, model2, model3), I can further evaluate whether the differences of R-squared are significant. Is this correct? – Ida Jun 25 '14 at 2:33
• Sorry I'm a bit confused about variance and deviance. I already revised my question. – Ida Jun 25 '14 at 2:36