Question

The correlation coefficient r between the size of a lake in square miles, x, and the yearly number of registered boaters, y, is 0.743. What percent of the variation in the number of yearly boaters can be explained by differences in lake sizes?
74.3%
55.2%
44.8%
37.2%

Answer 1

Actually variation is simply equivalent to the square of the correlation coefficient r. So we can say that:

variation = r^2

 

So given an r value of 0.743, so the variation is:

variation = 0.743^2

variation = 0.552

 

Answer:

55.2%