Coefficient of Determination

A

The coefficient of determination is r-squared.

The coefficient of determination, denoted as R^2, is a statistical measure that represents the proportion of the variance in the dependent variable that can be explained by the independent variable(s). It ranges from 0 to 1, where 0 indicates that the independent variable(s) does not explain any of the variance in the dependent variable, and 1 indicates that the independent variable(s) completely explains the variance.

In this case, the given value is r = 0.65. It's important to note that the coefficient of determination, R^2, is equal to the square of the correlation coefficient (r). Therefore, we need to square the value of r to calculate R^2.

Calculating R^2: R^2 = r^2 = (0.65)^2 = 0.4225

Now, let's look at the given answer choices:

A. 0.423: This answer is very close to the calculated value of 0.4225, suggesting it could be a possible match.

B. None of these answers: This option implies that none of the answer choices provided are correct. However, we have found a close match in option A, so this answer choice can be eliminated.

C. 0.577: This answer does not match the calculated value of 0.4225, so it can be eliminated.

D. 0.806: This answer also does not match the calculated value of 0.4225, so it can be eliminated.

E. 0.194: This answer does not match the calculated value of 0.4225, so it can be eliminated.

Therefore, based on the calculations, the correct answer is:

A. 0.423