Question

A proper interpretation for r^2= .754 is:

A. 75.4% of the variation in the response variable can be explained by our knowledge of the explanatory variable.
B. 75.4% of the variation in the explanatory variable can be explained by our knowledge of the response variable
C. the amount of variation in the response variable is reduced by 24.6%
D. for each unit increase in the explanatory variable, the response variable increases 75.4%
E. None of the above

Answer 1

R squared is the percentage of the response variable variation that is explained by **the chosen regression [best fit] line**. ie you choose a line relationship to connect response variable to explanatory variable, and just measure the square of the difference between data point and corresponding point on line, for each data point.

so, strictly speaking , it's none of the above.

of the other options, and depending on how hand-wavey you are prepared to be, it is closest to:

"75.4% of the variation in the response variable can be explained by our knowledge of the explanatory variable."

but that's not even in good english.