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? A. 74.3% B. 55.2% C. 44.8% D. 37.2% Algebra

Question

Mathematics

Terry Benton

29 August, 04:56

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? A. 74.3% B. 55.2% C. 44.8% D. 37.2% Algebra

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Answers (1)

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Randall Wong · Answer 1

The variation in any sample group is simply the square of the correlation coefficient, that is:

variation = r^2

Therefore given an r value, we can simply directly calculate for variation percentage.

variation = (0.743) ^2

variation = 0.552 or 55.2%

Answer:

B. 55.2%