How to upgrade R in linux?
Now it is very simple. Just make:
install.packages("ropenblas")
ropenblas::rcompiler()
Note: I now keep on GitHub (here) an up-to-date guide to upgrading R on Linux Mint or Ubuntu Linux, which also includes a bit of extra information about system dependencies for tidyverse, the popular set of data-wrangling packages, as well as devtools, the popular R package development... package.
The link provided by FedRo is a good resource, however a slight change would need to be made since you're using Linux Mint 18.1 which uses Xenial repositories rather than Trusty repositories (see here). I also typically use the approach here to deal with packages I've already installed when I upgrade R rather than the approach offered by FedRo. So, for completeness, these are all the steps you'd need to take:
Step 1
Go to CRAN's list of mirrors and find the URL of the mirror that is closest to you. The terminal commands below assume you choose http://cran.wustl.edu/
Step 2
Open a terminal and enter the following commands1 (replacing http://cran.wustl.edu/ with whichever CRAN mirror URL you chose in step 1):
sudo apt-key adv --keyserver keyserver.ubuntu.com --recv-keys E298A3A825C0D65DFD57CBB651716619E084DAB9
sudo echo "deb http://cran.wustl.edu/bin/linux/ubuntu xenial/" | sudo tee -a /etc/apt/sources.list
sudo apt update
sudo apt upgrade r-base r-base-dev
sudo apt update
sudo apt upgrade
Note also that I have put to upgrade r-base and r-base-dev, but I don't know if you have r-base-dev installed. If not, I highly recommend you install it via sudo apt install r-base-dev.
Step 3
Start a new R session and run the following:
update.packages(checkBuilt=TRUE, ask=FALSE)
Then you should be good to go.
Update: Linux Mint 19 and R 3.6.x
Since both Linux Mint and R have seen upgrades since I answered this question, I'm updating for those who come to this answer needing the info for Linux Mint 19 and R 3.6.x.
The only difference is that instead of the command
sudo echo "deb http://cran.wustl.edu/bin/linux/ubuntu xenial/" | sudo tee -a /etc/apt/sources.list
you need to use
sudo echo "deb http://cran.wustl.edu/bin/linux/ubuntu bionic-cran35/" | sudo tee -a /etc/apt/sources.list
(replacing http://cran.wustl.edu/ with whichever CRAN mirror URL you chose in step 1)
1 I put here the full key, though many other guides you may see will use only the "short key." I have updated this guide to use the full key out of security concerns (see here, for example).