We are assuming here that the “regression” in the question is of a linear form.
Correlation is the measure of how strong a linear relationship between two variables is. There are several correlation coefficient standards (Pearson, Spearman, etc).
The correlation coefficient ranges between -1.0 and 1.0. Zero correlation means there is no linear relationship between the variables. The greater the correlation coefficient, the stronger the relationship, meaning that when one variable goes up, the other also goes up (or down, depending on the sign of the correlation coefficient).
It’s worth noting that the order of the comparison does not affect the correlation coefficient (symmetry) :
Regression, on the other hand, analyses the linear relationship between a dependent variable and one or more independent variables.
In its basic form, a linear regression equation is expressed as
, also called the intercept, is the value of when .
, or the regression coefficient, represents the change in for each unit of .
It is important to note that the relationship is not symmetrical.