Using the drop1 command in R and AIC While using the drop1 command in R for model building, it is said the variable with the lowest AIC value must be dropped. What could be the reason for the same? I know AIC talks about information loss and a lower AIC value is better, but dropping a variable with low AIC seems counter intuitive. Can someone please explain the reason for doing so?
 A: The given AIC from drop1 relates to the whole model - not to a variable, so the output tells you which variable to remove in order to yield the model with the lowest AIC. For example, with the built-in dataset swiss
lm1 <- lm(Fertility ~ ., data = swiss)
drop1(lm1, test = "F")  # So called 'type II' anova

Single term deletions

Model:
Fertility ~ Agriculture + Examination + Education + Catholic + 
    Infant.Mortality
                 Df Sum of Sq    RSS    AIC F value    Pr(>F)    
<none>                        2105.0 190.69                      
Agriculture       1    307.72 2412.8 195.10  5.9934  0.018727 *  
Examination       1     53.03 2158.1 189.86  1.0328  0.315462    
Education         1   1162.56 3267.6 209.36 22.6432 2.431e-05 ***
Catholic          1    447.71 2552.8 197.75  8.7200  0.005190 ** 
Infant.Mortality  1    408.75 2513.8 197.03  7.9612  0.007336 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Here, the removal of Examination will yield the model with the lowest AIC
On a related note, while it may be better to use AIC than p values, it is considered bad practice to use any automatic model selection algorithms:
Algorithms for automatic model selection
