Setting column name in "group by" operation with data.table

DT[,list(z=sum(y)+3,a=mean(y*z)),by=x]
   x  z  a
1: a  6  9
2: b 15 60

Since you are new to data.table, I recommend that you also study the help page of the setnames function as well as ?data.table and the data.table vignettes.

For conciseness, you can now use .() instead of list()

DT[, .(z=sum(y)+3, a=mean(y*z)), by=x]