"To show a correlation" means to demonstrate a relationship or connection between two or more things. It suggests that there is a pattern or tendency that suggests when one thing happens, the other thing also tends to happen. Full definition
A group of researchers recently reviewed the literature on the effect of skipping breakfast on obesity and found a great number of studies showing a correlation between the two. (fitnessandpower.com)
Recent studies show a correlation of salt restriction with increased heart failure and with insulin resistance leading to diabetes. (westonaprice.org)
This corresponds with a wide body of research showing correlations between early father - involvement and positive child outcomes. (fatherhoodinstitute.org)