Which of the following is the correct interpretation for 0.60 coefficient of determination? a. 60% of the variation in the X values is explained by the variation in the Y values. b. 40% of the variation in the Y values is explained by the variation in the X values. c. The relationship between Y and X is very weak d. 60% of the variation in the Y values is explained by the variation in the X values.
Question
Which of the following is the correct interpretation for 0.60 coefficient of determination?
a.
60% of the variation in the X values is explained by the variation in the Y values.
b.
40% of the variation in the Y values is explained by the variation in the X values.
c.
The relationship between Y and X is very weak
d.
60% of the variation in the Y values is explained by the variation in the X values.
Solution
The correct interpretation for a 0.60 coefficient of determination is:
d. 60% of the variation in the Y values is explained by the variation in the X values.
This is because the coefficient of determination, often denoted as R^2, measures the proportion of the variance in the dependent variable (Y) that is predictable from the independent variable(s) (X). So, in this case, 60% of the variation in Y can be explained by its relationship with X.
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