any correlation?

Well, as you use more and more space, your hard drive's read/write times will slightly improve (this just has to do with the way your hard drive reads its spinning disc). Once you start dipping below about 10 gigabytes, however, you'll notice performance degradations. Getting below 1GB is dangerous and should not be done unless absolutely necesary.
 
is there any correlation between how much of my hard drive is used up with how smoothly or how fast my computer runs?
The rule of thumb is that you should maintain at least 10% of your hard drive capacity as free space so that the virtual memory system has sufficient headroom to work properly.
 
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