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The phrase "negative correlation between" is correct and can be used in written English.
It is typically used to describe a relationship between two variables where as one variable increases, the other variable decreases. Example: There is a negative correlation between smoking and lung health, meaning that as a person smokes more, their lung health decreases.
Exact(60)
The 2014 index illustrates the negative correlation between armed conflicts and freedom of information.
The report underlines the negative correlation between low wages and education.
"There's a nearly perfect negative correlation between high yield and low expense ratio," Mr. Tjornehoj said.
"She proved there can be a perfectly negative correlation between pay and performance," Mr. Crystal said.
Our research finds that the negative correlation between structured management and inequality is driven by a strong negative correlation between the use of structured monitoring practices and inequality.
Regarding the liver, there was a negative correlation between fat intake and liver glycogen.
Results showed a negative correlation between practical intelligence (knowledge of medical remedies) and academic achievement.
By contrast, a negative correlation between genome size and the density of SSR loci was revealed.
We observed a significant negative correlation between leukocytosis and hypokalemia.
Moreover, a negative correlation between MT and salinity was found.
This negative correlation between the dollar and stock prices, she added, was generally strong during the last eight years.
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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