The coefficient of determination measures the amount of:

A) variation in y that is explained by variation in x
B) variation in x that is explained by variation in y
C) variation in y that is unexplained by variation in x
D) variation in x that is unexplained by variation in y
E) all of these

The coefficient of determination, also known as R-squared, measures the proportion of the variance in the dependent variable (y) that is explained by the independent variable (x). Therefore, option A is the correct choice as it states the variation in y that is explained by the variation in x. Option B is incorrect as the coefficient of determination doesn't measure the variation in x, but rather how much of the variation in y can be accounted for by the variation in x. Option C and D are also incorrect as they refer to unexplained variation, while R-squared measures explained variation. Option E is incorrect as it includes all options, but only A is the correct one.