If two variables are perfectly negatively correlated, their coefficient of determination would be…
A) -1.00
B) 1.00
C) 0.00
D) .50

Question

Quizplus · Accepted Answer

The coefficient of determination (r-squared) measures the proportion of variability in one variable (dependent) that can be explained by the other variable (independent). If two variables are perfectly negatively correlated, as one variable increases, the other variable decreases in an exact linear relationship. Therefore, all the variability in one variable can be explained by the other variable. The coefficient of determination in this case would be 1.00, indicating a perfect fit between the two variables. A coefficient of determination of -1.00 is not possible since the value must fall between 0 and 1. A coefficient of determination of 0.00 indicates no relationship between the two variables, while a coefficient of determination of 0.50 indicates that 50% of the variability in one variable can be explained by the other variable.

If Two Variables Are Perfectly Negatively Correlated, Their Coefficient of Determination