Original post by: Minho ,
You probably have a defective screen and that is certainly the first thing to try, whether you try and replace it [guide|30265|yourself] or have it done by a shop. If a replacement screen doesn't solve the problem, then you may have a logic board issue. The iPhone 6 Plus does suffer from [https://www.refectio.ca/blog/touch-disease|Touch Disease] however the typical symptoms are more lack of touch or grey bars at the top of the screen. So I would start by replacing the screen and if that doesn't solve your problem, you will need to consider a micro-soldering repair.