# Interpreting Residual and Null Deviance in GLM (using R)

I am using a glm function for regression analysis. And I have one question about interpreting residual / null deviance in GLM.

First, here is the result.

Call:  glm(formula = cbind(using, notUsing) ~ age + hiEduc + noMore,
family = binomial, data = cuse)

Coefficients:
(Intercept)     age25-29     age30-39     age40-49   hiEducTRUE   noMoreTRUE
-1.9662       0.3894       0.9086       1.1892       0.3250       0.8330

Degrees of Freedom: 15 Total (i.e. Null);  10 Residual
Null Deviance:      165.8
Residual Deviance: 29.92    AIC: 113.4


To see significance, I obtained the p-value as follows:

pchisq(29.92, 10, lower.tail = FALSE)
[1] 0.0008828339


Because this p-value is smaller than 0.05, is it OK to say that our model is appropriate?

On the other hand, the model does explains a deviance of $$165.8 - 29.92 = 135.9$$ on 5 degrees of freedom, which is most ($$135.9 / 165.8 = 82$$%) of what can be explained. So the model explains a lot but not quite everything.