Where two variables are completely unrelated, then their correlation coeffcient will be zero; where two variables are perfectly related, then their correlation would be one. A high correlation coefficient between two variables merely indicates that the two generally vary together - it does not imply causality in the sense of changes in one variable causing changes in the other.
Where high values of one variable are associated with high values of the other (and vice-versa), then they are said to be positively correlated. Where high values of one variable are associated with low values of the other (and vice-versa), then they are said to be negatively correlated. Thus correlation coefficients can range from +1 for perfect positive association to -1 for perfect negative association, with zero representing the case where there is no association between the two.
The correlation coefficient also serves to measure the goodness of fit of a regression line (see REGRESSION ANALYSIS) which has been fitted to a set of sample observations by the technique of ordinary least squares. A large positive correlation coefficient will be found when the regression line slopes upward from left to right and fits closely with the observations; a large negative correlation coefficient will be found when the regression line slopes downward from left to right and closely matches the observations. Where the regression equation contains two (or more) independent variables, a multiple correlation coefficient can be used to measure how closely the three-dimensional plane, representing the multiple regression equation, fits the set of data points.