Definition of Coefficient of Correlation
In simple linear regression analysis, the coefficient of correlation (or correlation coefficient) is a statistic which indicates an association between the independent variable and the dependent variable. The coefficient of correlation is represented by "r" and it has a range of -1.00 to +1.00.
When the coefficient of correlation is a positive amount, such as +0.80, it means the dependent variable is increasing when the independent variable is increasing. It also means that the dependent variable is decreasing when the independent variable is decreasing. However, a high positive correlation does not guarantee there is a cause and effect relationship. (A negative amount indicates an inverse association...the dependent variable is decreasing when the independent variable is increasing and vice versa.)
A coefficient of correlation of +0.8 or -0.8 indicates a strong correlation between the independent variable and the dependent variable. An r of +0.20 or -0.20 indicates a weak correlation between the variables. When the coefficient of correlation is 0.00 there is no correlation.
Relationship of Coefficient of Correlation to Coefficient of Determination
When the coefficient of correlation is squared, it becomes the coefficient of determination. This means that a coefficient of correlation of +0.80 will result in a coefficient of determination of 0.64 or 64%. (The coefficient of determination of 0.64 tells you that 64% of the change in the total of the dependent variable is associated with the change in the independent variable.) An r of +0.20 or -0.20 will result in an r-squared of only 4% (0.20 x 0.20), which means that only 4% of the change in the dependent variable is explained by the change in the independent variable.