Interpreting the drop1 output in R

Question

In R, the drop1command outputs something neat.
These two commands should get you some output:
example(step)#-> swiss
drop1(lm1, test="F")

Mine looks like this:

> drop1(lm1, test="F")
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 

What does all of this mean? I'm assuming that the "stars" help in deciding which input variables are to be kept. Looking at the output above, I want to throw away the "Examination" variable and focus on the "Education" variable, is interpretation this correct?

Also, the AIC value, lower is better, yes?

Ed. Please note the Community Wiki answer below and add to it if you see fit, to clarify this output.

Answer 1

drop1 gives you a comparison of models based on the AIC criterion, and when using the option test="F" you add a "type II ANOVA" to it, as explained in the help files. As long as you only have continuous variables, this table is exactly equivalent to summary(lm1), as the F-values are just those T-values squared. P-values are exactly the same.

So what to do with it? Interprete it in exactly that way: it expresses in a way if the model without that term is "significantly" different from the model with that term. Mind the "" around significantly, as the significance here cannot be interpreted as most people think. (multi-testing problem and all...)

And regarding the AIC : the lower the better seems more like it. AIC is a value that goes for the model, not for the variable. So the best model from that output would be the one without the variable examination.

Mind you, the calculation of both AIC and the F statistic are different from the R functions AIC(lm1) resp. anova(lm1). For AIC(), that information is given on the help pages of extractAIC(). For the anova() function, it's rather obvious that type I and type II SS are not the same.

I'm trying not to be rude, but if you don't understand what is explained in the help files there, you shouldn't be using the function in the first place. Stepwise regression is incredibly tricky, jeopardizing your p-values in a most profound manner. So again, do not base yourself on the p-values. Your model should reflect your hypothesis and not the other way around.

Answer 2

For reference, these are the values that are included in the table:
Df refers to Degrees of freedom, "the number of degrees of freedom is the number of values in the final calculation of a statistic that are free to vary."

The Sum of Sq column refers to the sum of squares (or more precisely sum of squared deviations). In short this is a measure of the amount that each individual value deviates from the overall mean of those values.
RSS is the Residual Sum of Squares. These are a measure of how much the predicted value of the dependent (or output) variable varies from the true value for each data point in the set (or more colloquially: each "line" in the data table).

AIC is the Akaike information criterion which is generally regarded as "too complex to explain" but is, in short, a measure of the goodness of fit of an estimated statistical model. If you require further details, you will have to turn to dead trees with words on them (i.e., books). Or Wikipedia and the resources there.

The F value is used to perform what's called an F-test and from it is derived the Pr(F) value, which describes how likely (or Probable = Pr) that F value is. A Pr(F) value close to zero (indicated by ***) is indicative of an input variable that is in some way important to include in a good model, that is, a model that does not include it is "significantly" different than the one that does.

All of these values are, in the context of the drop1 command, calculated to compare the overall model (including all the input variables) with the model resulting from removing that one specific variable per each line in the output table.

Now, if this can be improved upon, please feel free to add to it or clarify any issues. My goal is only to clarify and provide a better "reverse lookup" reference from the output of an R command to the actual meaning of it.