If the coefficient of correlation is −0.50, the percentage of the variation in the dependent variable y that is explained by the variation in the independent variable x is:
A)− 50%.
B)25%.
C)50%.
D)− 25%.

Question

Quizplus · Accepted Answer

The coefficient of correlation (r) measures the degree and direction of the linear relationship between two variables. The value of r ranges from -1 to +1. A negative value of r indicates a negative linear relationship between the variables, while a positive value of r indicates a positive linear relationship. The closer the value of r is to -1 or +1, the stronger the relationship between the variables.

The coefficient of determination (r^2) represents the proportion of variation in the dependent variable y that can be explained by the variation in the independent variable x. We can calculate r^2 as follows:

r^2 = (r)^2

For a coefficient of correlation of -0.50, r^2 = (-0.50)^2 = 0.25

Therefore, 25% of the variation in the dependent variable y can be explained by the variation in the independent variable x. The best choice is B) 25%.

If the Coefficient of Correlation Is −0