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The phrase "primarily influences" is correct and usable in written English
It can be used when discussing the main or most significant impact that something has on another thing. Example: "The economic policies of the government primarily influence the job market."
Exact(29)
The equivalence ratio primarily influences the temperature distribution of the wall and pollutant emissions.
Meanwhile, in countries where women's labour force participation rates are high, costing studies show that violence primarily influences absenteeism and productivity loss in the workplace.
However, it is still unclear whether oxytocin primarily influences attention towards positive or negative valence social stimuli.
These data indicate that increased 5-HT neurotransmission, following neonatal 6-OHDA treatment, primarily influences PPT-containing neurons of the direct striatal output pathway.
The functions of growth hormone and prolactin secreted by the pituitary overlap considerably, although prolactin usually regulates water and salt balance, whereas growth hormone primarily influences protein metabolism and hence growth.
Empirical analysis results show that the urban income rises have weak spillover effects, while rural income growth primarily influences land use efficiency changes when urban-rural ecological intercorrelation is weak.
Similar(31)
Community assembly was primarily influenced by stochastic processes.
Social mobility was primarily influenced by the state.
Hamas, he said, was a popular movement primarily influenced by Palestinian public opinion.
Before, the accent was prestigious, as was the dialect that has primarily influenced it, British English.
Early on, he was a Neo-Classicist, primarily influenced by Stravinsky and Hindemith.
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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