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The phrase "a very modest correlation" is correct and usable in written English.
It can be used when discussing the strength or significance of a relationship between two variables in a statistical context.
Example: "The study revealed a very modest correlation between exercise frequency and overall happiness levels among participants."
Alternatives: "a slight correlation" or "a weak correlation".
Exact(1)
Magnetic resonance imaging and spectroscopy studies show a very modest correlation between inflammation, depicted by Gd-enhancement (a marker of inflammation), and progressive brain and spinal cord atrophy (markers for neurodegeneration) (Bielekova et al., 2005; Filippi and Rocca, 2005; Anderson et al., 2006; Zivadinov and Cox, 2007).
Similar(58)
The Women's Health Initiative observed a statistically significant but very modest correlation between reported diet and supplement intake and measured 25(OH D concentrations (r = 0.19; P < 0.001) (18).
The total score had only very modest correlation with Themes A and C.
This finding indicates that even with very modest correlations such as these, homozygotes that differ at a single locus could provide biological clues into understanding the etiology of g.
I asked for a very modest £700.
He's a very modest, efficient mover.
"Both come from a very modest background," Mostert said.
"My dad was a very modest man," Cook said.
In response, he gets what seems a very modest punishment.
I grew up in a very modest home.
I am the beneficiary of a very modest trust.
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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