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The phrase "demonstrates the correlation" is grammatically correct and can be used in written English.
It is typically used to describe how two variables or factors are related to each other. Example: The study, conducted by a team of researchers, demonstrates a strong correlation between exercise and mental well-being.
Exact(11)
Kate Hunter, executive director of Case, says: "The survey demonstrates the correlation between the size of the fundraising workforce and the amount of philanthropy raised.
On average for the season, it ranks ahead of "Pawn Stars" on History and "Duck Dynasty" on A&E, another program that demonstrates the correlation between shows featuring men with ridiculously long beards and high television ratings.
Correlogram is a figure that demonstrates the correlation between two series.
Figure 6a demonstrates the correlation between the exit rate and theta.
Figure 1 demonstrates the correlation between the background rareness and the over-representation for 10 datasets.
Figure 2 demonstrates the correlation between vitamin D and DAS28-ESR (r square = 0.077, P = 0.014).
Similar(49)
Table 3 shows the regression results of quadratic model for the removal efficiency of diazinon; Fig. 2 demonstrates the correlations between the actual and predicted removal of diazinon.
Table 4 demonstrates the correlations of the WHOQOL-Bref with SF-36, QOLS and clinical variables.
Table 3 demonstrates the correlations between socio-environmental variables and suicide ASM by gender.
Table 2 demonstrates the correlations among SIRT1, DBC1, H4K16Ac, H3K9Ac, and p53 expressions, which were mutually related.
1– 5 This study demonstrates the correlations of changes in abdominal fat distribution with ΔFBG, ΔHDL-C, and ΔTG in women.
More suggestions(16)
demonstrates the interdependence
denotes the correlation
demonstrates the proportion
demonstrates the interplay
confirms the correlation
demonstrates the concordance
demonstrates the interaction
demonstrates the link
determines the correlation
demonstrates the interrelationship
illuminates the correlation
demonstrates the interconnectedness
demonstrates the relevance
validates the correlation
determining the correlation
determine the correlation
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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