It can't possibly be linear: my first guess would be exponential.
Correlation between study time and rating

Idiots need to study more. The chess geniuses understand quicker, so you can't treat it like studying for a test. If you got the skills, you can kung pao your opponent into submission without the cramming the night before.

As some with a Master's in Chemistry and Bachelor's, in Physics, I often look for mathematical relationships. I was also a high school teacher and varsity sports coach and both in sports and chess, ability seems to move to plateaus where they remain for a while then, for some often unclear reason, jump up after a period of hard work. Below is an example: it's my Chess Tactics rating over at chesstempo.com in 2017. I had been away from semi-serious chess for years before return at the beginning of 2017. I do tactics problems most days for about 1/2 hour or more. At first I hit a plateau around 1500, then beginning around the 2nd week of February there was a surge that temporarily reached 1700 then settled back to a new plateau around 1600. In April another surge to 1700 occurred that settled into a new plateau around 1650. Around August - surprising right after a one-week Caribbean Cruise vacation - I made another surge to 1700 and stayed at a plateau around 1700. Around the beginning of November I surged again to a max. of 1778.9 and stay mostly in the upper 1700's for while. Then, I got a bad sinus infection that took most of the month to cure, and I didn't do tactics problems every day and the rating has fallen back around 1700.
Hello
Being a math teacher I am curious to know how study time and chess rating correlate, and if the rating increase is linear or not.
To find out I'd appreciate if some of you would kindly give a realistic estimate of study hours (including play) and tell what your FIDE rating is. Then I'll try to find out if we can tell anything from the numbers you have given.
Thanks!