How to calculate the correlation coefficient and correlation degree in grey correlation analysis?

One 、 application

The grey correlation analysis method studies the data relevance （ The degree of association between the parent sequence and the characteristic sequence ）, Through correlation degree （ That is, the relevance size ） Measure the degree of association between data , So as to assist decision-making .

Two 、 operation

SPSSAU operation

（1） Click on SPSSAU Comprehensive evaluation ‘ Grey correlation analysis ’ Button . Here's the picture

（2） Drag the data, select the standardization method, and then click start analysis

PS： If you need to drag and drop data , Don't forget the reference values below .

3、 ... and 、SPSSAU Analysis steps

Four 、 Case study

background

At present, the company studies GDP and primary industry respectively , The grey correlation between the secondary industry or the tertiary industry , So as to find out which industry has a greater impact on GDP . A total of 2000~2005 common 6 Years of data , The gross domestic product is ‘ The mother sequence ’, primary industry , The secondary or tertiary industry is ‘ Characteristic sequence ’, In this example, the parent sequence and characteristic sequence have been confirmed , And get the data ready , The standardization method is ‘ initialization ’. Some data are shown in the figure ：

5、 ... and 、 analysis

Put data into analysis box ,SPSSAU The system automatically generates analysis results , as follows ：

Calculation formula

1. Correlation coefficient

（1） The initial value result is shown in the figure below ：

Simply put, each data in a set of data should be divided by the first one . example ：2061/1988=1.037; And so on .

（2） Difference sequence

give the result as follows ：

（PS： Simply put, for the first column of the table after initialization minus the number corresponding to the second column , The first column minus the number corresponding to the third column , And so on , Pay attention to the absolute value ）

（3） Find the two extreme differences

（4） Find the correlation coefficient

Generally, the resolution coefficient is taken   , Put in the calculation , Finally, the result of correlation coefficient is obtained .

2. Degree of relevance

example ： 

6、 ... and 、 summary

  Combine the above correlation coefficient results for weighting , Finally, we get the correlation value , Use the correlation value for 6 Evaluate and sort the evaluation objects ;
  The correlation value is between 0~1 Between , A higher value means that it is related to “ reference value ”（ The mother sequence ） The stronger the correlation between , That means the higher their evaluation . As can be seen from the table above ： For this time 3 Evaluation items , The comprehensive evaluation of the tertiary industry is the highest （ The correlation degree is ：0.830）, The second is the secondary industry （ The correlation degree is ：0.731）.