A perfect positive or negative correlation means that


A) the explanatory causes the y-variable.
B) 100% of the variation is explained.
C) we get the same regression equation if we switch the x and y variables.
D) the slope of the regression equation is 1.0

I chose B

Correlation does not necessarily mean causation. I would choose c.

To determine which option is the correct answer, let's analyze each option and explain its meaning in the context of a perfect positive or negative correlation:

A) "the explanatory causes the y-variable" - This statement suggests a causal relationship between the explanatory variable (x-variable) and the response variable (y-variable), which is not necessarily true for a correlation. A correlation only measures the strength and direction of the relationship between the variables.

B) "100% of the variation is explained" - This statement is not accurate because a perfect correlation does not imply that all variation in the data is explained. It only indicates that there is a strong and consistent relationship between the variables.

C) "we get the same regression equation if we switch the x and y variables" - This statement is correct for a perfect correlation. In a perfect correlation, the regression equation will be the same regardless of which variable is considered the independent (x) or dependent (y) variable.

D) "the slope of the regression equation is 1.0" - This statement is not true for all cases. A perfect correlation indicates that the variables move perfectly together (positive correlation) or completely opposite (negative correlation), but the slope value can vary based on the specific data.

After analyzing these options, we can conclude that the correct answer is C) "we get the same regression equation if we switch the x and y variables."