2. The coefficient of determination is computed by squaring the
correlation coefficient (i.e., it is *r*^{2}).^{
}

- 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 (*r*^{2})
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 *r*^{2} for .2 is
.04 whereas the *r*^{2 }for .1 is only .01. Similarly, whereas a
correlation of .8 does not seem that much bigger than a correlation of .5,
comparing their *r*^{2} values reveals that the .8
correlation with its *r*^{2} of .64 is more than twice the strength
of the .5 correlation with its *r*^{2}of only .25.