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? 44.8% 37.2% 74.3% 55.2%

Explanation:

Step1: Recall the formula for the coefficient of determination

The coefficient of determination \( R^{2}\) is used to find the percentage of variation explained. \(R^{2}=r^{2}\), where \(r\) is the correlation coefficient.

Step2: Calculate \(R^{2}\)

Given \(r = 0.743\), then \(R^{2}=(0.743)^{2}\).

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Step3: Convert \(R^{2}\) to a percentage

To convert a decimal to a percentage, multiply by \(100\). So \(0.552049\times100 = 55.2049\%\approx55.2\%\)

Answer:

55.2%