If you increase the internet speed itself automatically the Youtube download will also increase.It is just that the videos take quite a lot of bytes to stream....To increase internet speed
* Check to see if faster internet connections are in your area:
Fiber optic and cable internet tend to be faster than DSL and dial-Up.
*Do some basic maintenance on your PC:
a scan disk, a virus scan, a malware scan, and clear your recycle bin.Delete old files and temporary files.
* Reset Your Modem
Sometimes switching OFF and ON your modem helps you to speed the internet.
* Optimize your cache or temporary Internet files.
These files improve your Internet connection performance by not downloading the same file over and over.
After you have tried some of this,try your connection again using http://www.scanmyspeed.com/ and see if it's running any faster. If you are not satisfied Call your Internet service provider (ISP) and check whether upgradation of your plan is necessary.