I am unable to comment as somehow I need to have 50 reputation points and this answer (by Fawkes Meteor) should not have a -1 as his is the correct answer !!
What we need to know is if you look at the permissions for this file you will see the following:
pi@raspberrypi:~ $ ls -la /etc/dhcpcd.conf
-rw-rw-r-- 1 root netdev 1876 Jan 24 23:41 /etc/dhcpcd.conf
What you will see here is that 'root' owns the file and is part of the 'netdev'group
If you run (assuming you are user pi)
pi@raspberrypi:~$ groups
You will see that user 'pi' belongs to the group 'netdev'
I would, with 99% certainty, assume all people who have this issue (The dhcpcd configuration file is not writeable") is because they have logged in (or created) another user which is not belonging to the 'netdev' group, hence do not have permissions to write to this file.
What Fawkes Meteor is saying is add all the groups that pi belongs to, to the new user they have logged in as.
To do this:
1) Switch user to pi:
sudo -pi
sudo usermod -aG adm,dialout,cdrom,sudo,audio,video,plugdev,games,users,input,netdev,spi,i2c,gpio (your new user account name)
eg: sudo usermod -aG adm,dialout,cdrom,sudo,etc, montypython
Log back in as the new user and run"
groups
You should see that the new user now belongs to 'netdev' group
- Reboot
All good and you now should be able to connect to your wireless SSID. If not connect directly with Ethernet cable and leave for 20min and your wireless will be available.
sudo
before dealing with configuration files? – fcm Jul 22 '16 at 15:00