The correlation coefficient between heart weight and body weight in a group of mice is一组小鼠心脏体重与体重的相关系数为r = 0.765. r = 0.765。 Using body weight as the Independent Variable we can conclude that:使用体重作为自变量，我们可以得出结论：

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This question involves interpreting the correlation coefficient r between heart weight and body weight.
Option a: This states that 58.5% of the variation in heart weight is explained by the variation in body weights. Since r = 0.765, the proportion of variance explained is r^2 = 0.765^2 ≈ 0.585, or 58.5%. This is the correct interpretation because R^2 (the coefficient of determination) represents the fraction of variance in the dependent variable explained by the independent variable in a simple linear relationship.
Option b: This asserts that heart weight is 76.5% of body weight. The correlation coefficient r does not imply that heart weight is a fixed percentage of body weight; it measures the strength and direction of a linear relationship, not a direct ratio or proportion between the variables. Therefore this is incorrect.
Option c: This states that heart weight is 58.5% of body weight. Similar to option b, the percentage 58.5% here would incorrectly conflate the proportion of variance explained with a direct proportion between the variables. The units and interpretation are not about a fixed percentage relationship of means or values.
Option d: This says that 76.5% of the variation in heart weight is explained by variation in body weights. While 76.5% equals the correlation coefficient r expressed as a percent, the correct statistic for explained variation is r^2, not r. Therefore this is incorrect.
In summary, the correct interpretation is that r^2 ≈ 58.5% of the variance in heart weight is explained by body weight, while the other options misinterpret either the meaning of r or the meaning of r^2.

MUF0142 Fund. Mathematics Unit 2 - Semester 2, 2025 MUF0142 基金。数学第 2 单元 - 第 2 学期，2025 6.1 Displaying/Summarising Bivariate Data Quiz (Formative) 6.1 显示/总结双变量数据测验（形成性）

The correlation coefficient between heart weight and body weight in a group of mice is一组小鼠心脏体重与体重的相关系数为r = 0.765. r = 0.765。 Using body weight as the Independent Variable we can conclude that:使用体重作为自变量，我们可以得出结论：

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