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The phrase "a higher level of correlation with" is correct and usable in written English.
It can be used when discussing the strength or degree of a relationship between two variables or sets of data.
Example: "The study found a higher level of correlation with the participants' exercise habits and their overall health outcomes."
Alternatives: "a stronger correlation with" or "an increased correlation with".
Exact(2)
The Cancer-Specific summary score was expected to achieve a higher level of correlation with the Breast Cancer Specific Concerns of the FACT-B, which is targeted for breast cancer patients.
These results are consistent with our prior experience in which conductivity was found to have a higher level of correlation with tumor presence than the corresponding permittivity values and would be expected to be the superior measure of tumor progression/regression [ 25].
Similar(58)
These parameters also showed a high level of correlation in between each other.
We observed a high level of correlation between methylation and expression levels.
Thus in spite of its high level of correlation with expression level, the breadth of expression shows, in the Arabidopsis genome, a prevalent effect toward sequence expansion.
As expected, the activity limitations scale scores had the highest level of correlations with responses to these two questions.
A higher level of education had a significant correlation with knowledge of generic medicines (P < 0.01).
Patients with osteoporosis presented a higher level of serum chemerin, which witnessed an inverse correlation with BMD.
With increasing host dispersal, a higher level of parasitoid dispersal was necessary to drive negative correlation between host populations.
"What we have found is a very strong correlation between the Yes vote and a higher level of unemployment.
Separability of these components was confirmed with a ω-correlation matrix showing that these seasonal components did not show high levels of correlation with other components.
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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