What can we say if the coefficient of determination is 0.94?
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A. B. C. D. E.B
We cannot tell anything about the direction of the relationship from the coefficient of determination or r- squared.
The coefficient of determination, denoted as R², is a statistical measure that represents the proportion of the total variation in one variable that can be explained by the variation in another variable. It is commonly used in regression analysis to assess the goodness of fit of a regression model.
In this specific question, the coefficient of determination is given as 0.94. Let's analyze each answer choice to determine the correct interpretation:
A. Direction of relationship is positive: The coefficient of determination does not provide information about the direction of the relationship between the variables. It only measures the proportion of variation explained, so this answer is not correct.
B. 94% of total variation in one variable is explained by variation in another variable: This answer is correct. When the coefficient of determination is 0.94, it means that approximately 94% of the total variation in the dependent variable (the variable being explained or predicted) can be explained by the independent variable (the variable used to explain or predict the dependent variable). In other words, 94% of the variation in the dependent variable can be attributed to the independent variable, while the remaining 6% may be due to other factors or random error.
C. All of these answers are correct: This answer is incorrect because answer choice A is incorrect.
D. Strength of relationship is 0.94: The coefficient of determination, R², measures the goodness of fit of a regression model but does not directly represent the strength of the relationship. It quantifies the proportion of the total variation explained, rather than the magnitude or strength of the relationship between the variables. Therefore, this answer is not correct.
E. None of these answers is correct: This answer is incorrect because answer choice B is correct.
In summary, the correct answer is B. When the coefficient of determination is 0.94, it means that approximately 94% of the total variation in the dependent variable can be explained by the independent variable.