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"having a positive correlation with" is correct and usable in written English
You use this phrase to describe a relationship between two or more variables where an increase in one variable corresponds to an increase in the other. For example, "Studies have shown that having a higher level of education is associated with having a higher income, having a positive correlation with one another."
Exact(5)
Most importantly, the magnitude of these changes correlated well with cognitive performance: increased Frontal activity having a positive correlation with cognitive tests, and decreased Basal Ganglia activity having a negative correlation with cognitive tests.
In contrast, for trees shorter than the average, rain duration (RD) was the most influential variable, having a positive correlation with SFFR.
It is found that within the main maturity range (2.5 % < EqR o < 3.5 %) of the shale, its porosity develops well, having a positive correlation with the TOC content, and its gas content is controlled mainly by the preservation conditions related to the tectonic deformation, but shale with a super high maturity (EqR o > 3.5 %) is considered a high risk for shale gas exploration.
However, the presence of SO4 2− in the aquifers of the studied river basin having a positive correlation with As in both the seasons (0.047 in the wet season and 0.283 in the dry seasons) could also be one of the possible sources of As mobilization through which As enters the water environment by the oxidation of the sulfide ores of As (Acharyya et al. 1999).
Evermann et al.[ 20] listed risk factors for reproductive disease in the bitch, and cycle stage was identified as one of 8 factors having a positive correlation with disease.
Similar(55)
As seen in Eq. (22), θ∞ has a positive correlation with a and P0, and is negatively correlated to Ks.
Researchers found that binge-watching had a positive correlation with poor mental and physical wellbeing.
Interestingly, Williams found that any direct student/faculty contact had a positive correlation with student learning.
Mason et al. also reported that prostaglandin E2, which has a positive correlation with ROS and PGE220,29,30, downregulated ABCG2 expression31.
The relationship with soil properties differed according families: Lampyridae, Aphodiidae and Formicidae had a positive correlation with soil macro-porosity (radius of the pores > 15 μm); Tenthredinidae and Tenebrionidae had a positive correlation with the micro-porosity (pores ≤ 15 μm).
Based on biological evaluation via a 3D organotypic cultural model, we found that α-SMA had a positive correlation with the NPM concentration.
More suggestions(17)
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having a negative correlation with
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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