Statistics 简明教程

Statistics - Correlation Co-efficient

Correlation Co-efficient

相关系数是对一个变量的值的变化预测另一个变量的值的变化的程度的统计度量。在正相关变量中，该值同步增加或减少。在负相关变量中，当一个变量的值增加时，另一个变量的值减少。

A correlation coefficient is a statistical measure of the degree to which changes to the value of one variable predict change to the value of another. In positively correlated variables, the value increases or decreases in tandem. In negatively correlated variables, the value of one increases as the value of the other decreases.

相关系数表示为 +1 和 -1 之间的值。

Correlation coefficients are expressed as values between +1 and -1.

+1 的系数表示完美的正相关：一个变量的值变化将预测第二个变量中同一方向的变化。

A coefficient of +1 indicates a perfect positive correlation: A change in the value of one variable will predict a change in the same direction in the second variable.

-1 的系数表示完美的负相关：一个变量的值变化预测第二个变量中相反方向的变化。相关性的较小程度表示为非零小数。零的系数表示变量的波动之间没有可辨别的关系。

A coefficient of -1 indicates a perfect negative: A change in the value of one variable predicts a change in the opposite direction in the second variable. Lesser degrees of correlation are expressed as non-zero decimals. A coefficient of zero indicates there is no discernable relationship between fluctuations of the variables.

Formula

其中——

Where −

  1. ${N}$ = Number of pairs of scores

  2. ${\sum xy}$ = Sum of products of paired scores.

  3. ${\sum x}$ = Sum of x scores.

  4. ${\sum y}$ = Sum of y scores.

  5. ${\sum x^2}$ = Sum of squared x scores.

  6. ${\sum y^2}$ = Sum of squared y scores.

Example

Problem Statement:

Problem Statement:

计算以下内容的相关系数：

Calculate the correlation co-efficient of the following:

X

Y

1

2

3

5

4

5

4

8

Solution:

Solution: