What does the coefficient of determination equal if r = 0.89?
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A. B. C. D. E.E
The coefficient of determination is the r-squared.
The coefficient of determination, denoted as R-squared (R²), is a statistical measure that represents the proportion of the variance in the dependent variable that can be explained by the independent variable(s). In other words, it indicates the goodness of fit of a regression model.
To calculate R-squared, we square the correlation coefficient (r) between the independent and dependent variables. In this case, the question states that r = 0.89. Therefore, to find the coefficient of determination, we square 0.89.
R-squared = r² = 0.89² = 0.7921
So, the correct answer is E. 0.79.
It is important to note that R-squared values range from 0 to 1. An R-squared of 1 indicates that 100% of the variation in the dependent variable can be explained by the independent variable(s), while an R-squared of 0 means that none of the variation can be explained. In this case, an R-squared of 0.79 indicates that approximately 79% of the variation in the dependent variable can be explained by the independent variable(s).