A pediatrician wants to determine the relationship that exists between a child's height (x) and head circumference (y). She randomly selects 11 children from her practice and measures their height and head circumference in inches. She finds that the correlation is 0.813, and the regression equation is y=0.273x+3.37.
What proportion of the variation in head circumference can be explained by the variation in the values of height? Round your answer to three decimal places.

Question

19-12-2022
Mathematics

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A pediatrician wants to determine the relationship that exists between a child's height (x) and head circumference (y). She randomly selects 11 children from her practice and measures their height and head circumference in inches. She finds that the correlation is 0.813, and the regression equation is y=0.273x+3.37.
What proportion of the variation in head circumference can be explained by the variation in the values of height? Round your answer to three decimal places.

Answer :

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aamirmajeed5100 aamirmajeed5100 · Answer 1 · 2022-12-24T06:25:23-05:00

The proportion of the variation in the head circumference that can be explained by the variation in the values of height is 0.813 squared, which is 0.659.

The proportion of the variation in head circumference that can be explained by the variation in the values of height is 0.659. This can be calculated using Pearson's correlation coefficient formula. The formula is r2 = r2, where r is the correlation coefficient, which in this case was 0.813.

Thus, the proportion of the variation in the head circumference that can be explained by the variation in the values of height is 0.813 squared, which is 0.659.

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