I always enjoy this questionThe simple answer is: sort of but not really.
You will always be limited by you own physical connection however there are things you can do using your VPS to make things happen faster.
E.g.
Running OpenVPN on your VPS with lzo compression 'can' deliver a perceived faster experience, the reality is your own connection has not changed the data is just being -de/compressed.
Analogy: You could never physically carry 10000 feathers from point A to point B in 5 minutes unless you somehow compressed them all together and made them more efficient to carry.
So if your downloading a file if your connection speed is 200 KB/s it will stay at 200 KB/s but your download may finish faster, strange thing happens in chrome though in the download manager it will look like your downloading at 500 KB/s as the data is coming down faster.
Another thing to consider is that if your in New York and your VPS is in Spain then you will get zero advantage as the introduced latency between you and your VPS will far outweigh any gains, so your VPS needs to be as close to you as possible.
So instead of your local ISP? No that's ridiculous, you need something to initially get you from Point A (your PC) to your VPS
With your ISP to get a slightly better quality (not bandwidth) of connection... sort of
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