Thanks Hong, that was exactly the problem I was running into. The error you get suggests that the number of rows is wrong, but the problem is actually that the model has been trained using a command that ends up with the wrong names for parameters.
This is really a critical detail that is entirely non-obvious for lm and so on. Some of the tutorial make reference to doing lines like lm(olive$Area@olive$Palmitic) - ending up with variable names of olive$Area NOT Area, so creating an entry using anewdata<-data.frame(Palmitic=2) can't then be used. If you use lm(Area@Palmitic,data=olive) then the variable names are right and prediction works.
The real problem is that the error message does not indicate the problem at all:
Warning message: 'anewdata' had 1 rows but variable(s) found to have X rows