`Correlation measures the degree to which two phenomena are related to one another.相关性体现的是两个现象之间相互关联的程度。Two variable are positively correlated if a change in one is associated with a change in the other in the same direction. A correlation is negative if a positive change in one variable is associated with a negative change in the other.如果其中的一个变量的改变引发另一个变量朝着相同的方向变化，那么我们说这两个变量存在正相关性。如果一个变量的改变引发另一个变量朝着相反的方向变化，那么这两个变量存在负相关性。The power of correlation as a statistical tool is that we can encapsulate an association between two varibles in a single descriptive statstic: the correlation coefficient.相关性作为一个统计工具的魅力就在于将两个变量的关联精练成一个描述性数据：相关系数。The correlation coefficient has two fabulously attactive characteristics.相关系数拥有两个无与伦比的优势。 First, for math reasons that it is a single number ranging from -1 to 1. A correlation of 1, often described as perfect correlation, means that every change in one variable is associated with an equivalent change in the other vaiable in the same direction. A correlation of -1, or perfect negative correlation, means that every change in one variable is associated with an equivalent change in the other variable in the opposite direction. The closer the correlation is to 1 or -5, the stronger the association. A correlation of 0 (or close to it) means that the variables have no meaningful association with one another. 第一个优势体现在数学表达上，相关系数是一个区间为-1到1的常数。如果相关系数为1，即完全相关，表示一个变量的任何改变都会导致另一个变量朝着相同的方向发生等量的改变。如果相关系数为-1，即完全负相关，代表一个蛮珠任何变化都将会引发另一个变量朝着相反的方向发生等量的改变。相关系数越接近1或-1，变量间的关联性就越强。如果相关系数为0（或接近0），则意味着变量之间不存在有意义的联系。The second attractive feature of the correlation coefficient is that it has no units attached to it. The correlation coefficient does a seemingly miraculous thing: It collapses a complex mess of data measure in different units into a single, elegant descriptive statistic.第二个吸引人的优势在于，相关系数不受变量单位的限制。这就是相关系数能够为我们完成一件非常神奇的事情：将大量芜杂无序、单位不统一的复杂数据加工成一个简洁、优雅的描述性数据。One crucial point in this general disccussion is that correlation does not imply causation; a positive or negative association between two varialbes does not necessarily mean that a change in one of the variables is causing the change in the other.我们必须牢记一点，那就是相关关系并不等于因果关系。两个变量存在正相关或负相关的关系，这并不代表其中一个变量的改变是由另一个变量的变化引起的。`
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《赤裸裸的统计学》的全部笔记 52篇