Coefficient of Determination
Another number that can be helpful in understanding the relationship between two variables is the coefficient of determination. The coefficient of determination is the amount of variability that can be accounted for in one variable by knowing a second variable. Think for a moment of all the things that can have an impact on an exam score: amount of time spent studying, how you feel the day of the exam, amount of sleep the previous night, whether you were sick or felt well, as well as a host of other factors. This means that the variability in your exam scores (as they are usually not all the exact same score) is due to many factors. A certain amount of the variability may be due to the number of hours you studied for the exam. Suppose that you compute the Pearson correlation between the number of hours a group of students spent studying for the exam and their scores on the exam and find a correlation of +.70. To get the coefficient of determination you simply square the Pearson correlation, which in this case is the square of .70, or .49. If you multiply this result by 100 percent, you end up with 49 percent. This indicates that of all of the things that can affect exam scores, 49 percent of the influence is due to the amount of time spent studying.
Learning Check #19:
Given the correlation coefficients in Learning Check #18 of +.71 and +.30, explain what you can determine with respect to the coefficient of determination.
Learning Check #20:
Suppose that the correlation coefficient between two variables is -.80. Would this lead to a different conclusion based on the coefficient of determination than a correlation of +.80?