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What is the coefficient of correlation?

In simple linear regression analysis, the coefficient of correlation (or correlation coefficient) is a statistic which indicates the relationship 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 an increase in the independent variable will result in an increase in the dependent variable. (Also, a decrease in the independent variable will mean a decrease in the dependent variable.) When the coefficient of correlation is negative, such as -0.80, there is an inverse relationship. (An increase in the independent variable will mean a decrease in the dependent variable. A decrease in the independent variable will mean an increase in the dependent variable.)

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.

When the coefficient of correlation is squared, it becomes the coefficient of determination. This means that an r of +0.80 or -0.80 will result in a coefficient of determination of 0.64 or 64%. (This 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 indicates that only 4% (0.20 x 0.20) of the change in the dependent variable is explained by the change in the independent variable.

It is important to realize that correlation does not guarantee that a cause-and-effect relationship exists between the independent variable and the dependent variable. However, a cause-and-effect relationship will mean there is correlation. It is also important to plot the data/observations used in the regression analysis in order to detect and review any outlier.