Business Degree Certification Practice Test

If the coefficient of determination is 0.94, what can we conclude?

1. The strength of the relationship is 0.94

2. The direction of the relationship is positive

3. 94% of variation in one variable is explained by the other

4. All options are correct

The correct answer is: 94% of variation in one variable is explained by the other

When the coefficient of determination, commonly represented as R², is 0.94, it indicates that 94% of the variability in the dependent variable can be explained by the independent variable in the regression model. This high percentage suggests a very strong explanatory power in the relationship; the independent variable does a good job of capturing the differences in the dependent variable's values. Although the other options might imply certain characteristics of the data, they do not accurately capture the meaning of the coefficient of determination. The coefficient itself does not measure the strength of the relationship as a pure value, nor does it inherently specify the direction of the relationship (whether positive or negative)--these aspects would typically be interpreted from the regression coefficients or the general context of the data. Therefore, option C is correct because it succinctly expresses a clear conclusion drawn directly from the definition of the coefficient of determination, which quantifies how much of the variance in the dependent variable is accounted for by the independent variable in the model.