What sort of equation produces this upside-down hockey stick shaped curve?

Question

I have a dataset that I'm trying to model with an equation. The points when connected produce a curve much like an upside down hockey stick:

I've been experimenting with an inverse square root equation y = b - a/sqrt(x). Below model uses a=100 and b=10. However I can't get the curve to turn sharply enough.

Am I on the right track? How can improve the fit?

Looks like it could be logarithmic to me, try $y = a + b\log(x).$ — Stephen Donovan, Apr 27 '21 at 14:35
Use a higher negative exponent on $x$ in the second term, maybe? — Oscar Lanzi, Apr 27 '21 at 14:36
Have you tried plotting your data on a semi-log or log-log plot? — Charlie S, Apr 27 '21 at 14:47
something like this? https://www.desmos.com/calculator/brkxdclthl — David P, Apr 27 '21 at 14:50
https://www.desmos.com/calculator/k05plkvo4p is the closest i've been able to get so far. — Erich, Apr 27 '21 at 14:56

score 1 · Answer 1 · answered Apr 27 '21 at 20:02

Part of what was throwing me off was the upside-down-ness of the curve. This is also what was preventing Excel from coming up with a regression equation.

After realizing this, I made a new plot with the Y values subtracted from 10 which flipped it back over. Excel was then able to fit it to a power regression curve with equation y = a * x^b, where b was negative.

What sort of equation produces this upside-down hockey stick shaped curve?

1 Answers1