The phrase "demonstrate a positive correlation" is correct and usable in written English.
You can use it when referring to two things that are connected in some way and share a relationship with one another. For example: "The data obtained from the study demonstrated a positive correlation between the number of hours of studying and the student's final grade."
Our results demonstrate a positive correlation between maintenance of normal LINE methylation and HPV-positivity.
Our study results demonstrate a positive correlation between patients' education and level of awareness for potentially vision-robbing sequelae of sarcoidosis.
Being intensive consumers of phytoplankton in Omani waters (Haleem et al. 2011), through fluctuations of landings, sardines demonstrate a positive correlation with monthly fluctuations of chlorophyll-a concentrations (Piontkovski et al. 2014).
Our data demonstrate a positive correlation between concentrations of circulating VEGF levels and BMI in healthy male subjects under highly controlled conditions.
Taken together, these results demonstrate a positive correlation between pyrvinium treatment and tissue organization, proliferation, and vascularity during granulation tissue formation.
Our data demonstrate a positive correlation between plasma VEGF concentrations and BMI over a large range of BMI between 17.6 kg/m2 and 43.6 kg/m2.
Furthermore, mRNA expression of Bim, Bid and Bak demonstrated a positive correlation with procalcitonin, although Bim and Bid correlated with serum IL-6 (Table 2).
Human tissue microarrays stained for CD164 demonstrated a positive correlation with prostate-specific antigen levels, while its expression was negatively correlated with the expression of androgen receptor.
The study further demonstrates a positive correlation between active and attitudinal acceptability.
Several studies have demonstrated a positive correlation between breast cancer and increased breast vascularity [4, 5, 6, 7, 8].
The results of the study demonstrated a positive correlation between the growth of urban areas and CO2 emission levels.
