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The phrase "substantially correlated" is correct and can be used in written English.
It means that there is a strong connection or relationship between two things. Example: The study found that there is a substantially correlated increase in air pollution and respiratory illnesses in urban areas.
Exact(47)
The chewing function score and the OHIP-J14 summary score were substantially correlated (Pearson correlation coefficient: -0.46, 95% CI: -0.52 to -0.38), indicating that better chewing ability was associated with better OHRQoL (R2 = 0.21, p < 0.001).
Individual unobtrusive knowledge scales and ASVAB tests were substantially correlated with sample correlations ranging to.39 and population correlation estimates to.66 after correcting for range restriction.
There is little doubt that performance at MRCGP and MRCP UK) are substantially correlated, with disattenuated correlations of.748 and.698 between the knowledge exams, and.636 between the clinical assessments.
Anxiety and depression are known to be substantially correlated so that moderate positive correlations of self-report instruments for depression with measures of anxiety are a common phenomenon.
The validity of scales are substantiated when conceptually related scales are substantially correlated with each other (r > 0.40).
As a consequence, the CFI will be high if the observed items are substantially correlated with each other.
Similar(13)
Construct validity was also examined using the interscale correlations between Haem-A-QoL and SF-36, conceptually related scales would substantially correlate (>0.40) and scales with less in common would show lower correlations.
This introduces the possibility of substantially correlating squared returns.
Simply put, English scores of ninth graders will substantially correlate (in the majority of cases, if not always) with those of eighth graders.
Meanwhile, parent ratings of behavioral inhibition and social anxiety symptoms did substantially correlate with the number of words used during the speech tasks implying that these characteristics were better indicators of children's actual speech behavior than symptoms of SM.
Lieb and colleagues, using a genome-wide competition ChIP assay in yeast, show that thermodynamic quantities are substantially less well correlated with gene expression than kinetic quantities [ 23].
More suggestions(15)
basically correlated
substantially attributed
essentially correlated
considerably correlated
markedly correlated
substantially associated
far correlated
substantially connected
substantially interconnected
much correlated
distinctly correlated
substantially constrained
fundamentally correlated
considerable correlated
greatly correlated
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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