If I understand correctly I would be approximating value of "women" at which the "minimum effect" were to be found:
idx <- which.min( predict(prestige.mod, newdata= data.frame(
women=seq(min(Prestige$women), max(Prestige$women), length=100),
income=mean(Prestige$income, na.rm=TRUE),
education=mean(Prestige$education, na.rm=TRUE) ) ) )
idx
#37
#37
# Just copy the argument to the newdata argument in predict call above
# and get the value that produced the minimum
seq(min(Prestige$women), max(Prestige$women), length=100)[idx]
#[1] 35.45818
The use of the predict
function on value sequences contained in "newdata" dataframes is undoubtedly happening "underneath the hood" for the plotting of those "effects".