在统计学中为什么要对变量取对数？ - 知乎
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因为我们度量相关性时使用的Pearson相关系数检验的是变量间的线性关系，只有两变量服从不相关的二元正态分布时，Pearson相关系数才会服从标准的t-分布，但如果变量间的关系是非线性的，则两个不独立的变量之间的Pearson相关系数也可以为0.
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