The Product Moment Correlation Coefficient | 乘积矩相关系数

📚 The Product Moment Correlation Coefficient | 乘积矩相关系数

In A-Level Mathematics, the product moment correlation coefficient (PMCC) is one of the most important tools for measuring the strength and direction of a linear relationship between two variables. In the Edexcel specification, you need to be able to calculate the PMCC, interpret its value, and carry out a hypothesis test for correlation using critical values from statistical tables.

在 A-Level 数学中，乘积矩相关系数（PMCC）是衡量两个变量之间线性关系强度和方向的最重要工具之一。在 Edexcel 考试大纲中，你需要能够计算 PMCC、解释其取值，并利用统计表中的临界值对相关关系进行假设检验。

1. What Is the Product Moment Correlation Coefficient? | 什么是乘积矩相关系数？

The product moment correlation coefficient, usually denoted by r, was developed by Karl Pearson. It measures how close the data points lie to a straight line. If one variable tends to increase as the other increases, r is positive; if one increases while the other decreases, r is negative.

乘积矩相关系数通常记作 r，由卡尔·皮尔逊提出。它衡量数据点与一条直线的接近程度。如果一个变量随另一个变量增加而增加，则 r 为正；如果一个变量增加而另一个变量减少，则 r 为负。

The value of r always lies between −1

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