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"inverse correlation with" is a grammatically correct phrase and can be used in written English.
It is typically used to describe a relationship between two variables where one increases while the other decreases. Example: "There is an inverse correlation between exercise and weight gain. The more a person exercises, the less weight they tend to gain."
Exact(60)
For a decade from 2000, the fate of airlines' profits had an inverse correlation with the fuel price as rising oil costs savaged the bottom line.
Mg concentrations exhibit a weak inverse correlation with Cl.
Wall Street maintained its inverse correlation with the U.S. currency, slumping in the early going Friday.
Such an effect was specifically driven by novelty and showed an inverse correlation with accuracy performance.
The research highlighted how WTP has an inverse correlation with age.
However, PSF- and TOF-related deviations showed an inverse correlation with the lesions' TBR.
Augmentation of the axial diffusivity shows inverse correlation with the cumulative headache day in lifetime.
CES2 activity has a strong inverse correlation with HOMA-IR and liver DG concentration.
Both Dcx and PSA-NCAM showed a similar inverse correlation with EGFr immunohistochemistry (Fig. 4B E).
On the other hand, fat uridine concentrations showed an inverse correlation with plasma concentrations.
There was also an inverse correlation with IL6 mRNA levels (r = −0.67, p = 0.05).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com