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The part of the sentence "a positive correlation between" is correct and usable in written English.
You can use it when referring to the relationship between two variables that have a direct, positive relationship. For example, "A positive correlation between exercise and good health has been proven in numerous studies."
Exact(60)
(A recent study found a positive correlation between chili-eating and "sensation-seeking" behavior).
These results suggest a positive correlation between genetic diversity and geographic distance.
Research shows a positive correlation between need-based aid like the Pell grant and college completion.
Linear regression analysis indicates a positive correlation between the values (R2 = 0.633).
There was a positive correlation between WSS and time (r = 0.97; P < 0.001).
We find a positive correlation between a high number of minority-appointed directors and large dividends.
I would expect a positive correlation between tons of fertilizer used and crop yields.
There is a positive correlation between energy intensity and carbon intensity.
There is a positive correlation between the various economic and development indices.
Several studies have shown a positive correlation between gene expression and the DNA methylation level of genic regions11.
This is consistent with previous observations indicating a positive correlation between genome size, TE content and genomic methylation levels36.
More suggestions(12)
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a positive concordance between
a favorable correlation between
a positive link between
a positive interaction between
a positive relationship between
a positive interrelationship between
a positive alignment between
a positive feedback between
a positive association between
a positive relation between
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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