# Coefficient of determination

1. The coefficient of determination is a way of describing the strength of the relationship between two variables.

2. The coefficient of determination is computed by squaring the correlation coefficient (i.e., it is r2).

• Because the coefficient of determination is the result of squaring the correlation coefficient, the coefficient of determination cannot be negative. (Even if the correlation is negative, squaring it will result in a positive number.)
• Because the coefficient of determination is the result of squaring the correlation coefficient, a large negative correlation coefficient (e.g., -.9) will produce a larger coefficient than a small positive correlation. For example, -.8 squared is +64 whereas +.2 squared is .04.
• Because the smallest a correlation can be is 0, the smallest a coefficient of determination can be is 0. Because the biggest a correlation can be is -1 (or +1), the biggest a coefficient of determination can be is +1  because -1 * -1 = 1, as does +1 * +1).

3. Because the coefficient of determination is computed by squaring the correlation coefficient, the coefficient of determination, like the absolute value of the correlation coefficient, ranges from 0 to 1 and bigger values indicate stronger relationships.

4. The coefficient of determination  (r2) is a more accurate measure of the strength of a relationship than the absolute value of r. For example, you  might think that an r of .2 indicates a relationship that is twice as strong as an r of .1. However, you would be wrong. In fact, an r of .2 indicates a relationship that is four times as strong as an r of .1--a fact that would have been clear to you had you compared their coefficients of determination. That is, the r2 for .2 is .04 whereas the r2 for .1 is only .01. Similarly, whereas a correlation of .8 does not seem that much bigger than a correlation of .5, comparing their  r2 values reveals that the .8 correlation with its r2 of .64 is more than twice the strength of the .5 correlation with its  r2of only .25.