Which of the following statements regarding the coefficient of determination is least accurate? A) When the coefficient of determination is high (close to 1), it proves that there is a causal relationship between the X and Y variables. B) 1 - R2 is the percent of Y’s variability that is unique to the Y variable. C) The coefficient of determination is the square of the correlation coefficient. D) A high R2 indicates that most of the dependent variable’s variability is explained by the regression equation.
this question sucks. I posted it because I really am weak at regression. The answer is A because apparently there is no causal relationship between the variables. If anybody can explain the Coefficient of Determination, I would be grateful thanks
coefficient of determination = R^2 (Correlation coefficient squared).
I guess the thing is that there is no effect cause relationship just that they tend to move toghether
Coefficient of dtermination is the amount of variability in the dependent variable that is explained by the independent variable. So if r-squared was .5, it means that the independent variable explains 50%. I saw one question that gave you the r-squared of like .35, and then asked how much unexplained variation there was. The answer would be 65%.
When you are running a regression you can use R^2 to say that XX% of the dependent varibale can be explained by the movement of the independant variable. This doesn’t not mean that the independant variable caused the dependent variable to move that way. D does a good job of explaining this… It could still be a spurios correlation.
don’t A and D look much alike then?
everything comes down to understanding that correlation doesn’ t imply causation http://en.wikipedia.org/wiki/Correlation_does_not_imply_causation