While writing in C is one way to speed up R code, you can also get pretty close to compiled speed by writing fully vectorized R code and pre-allocating vectors. The R REPL is just a thin wrapper over a bunch of C functions, and a careful programmer can ensure that allocation and copy operations (the slow bits) are kept to a minimum.
This is good if your code can be expressed in vectorized operations and doesn't gain benefits from problem structure exploited by multiple dispatch. With R the best you can is the speed of someone else's (or your) C code while Julia can beat C.