What are the methods of correlation analysis?

<> simple correlation analysis, SPSSAU provides a total of three correlation coefficients, one is Pearson correlation analysis, one is Spearman correlation analysis, and the last one is Kendall correlation coefficient. Pearson correlation analysis.

Pearson's rule is a classical correlation coefficient calculation method, which is mainly used to characterize linear correlation, assuming that 2 variables are normally distributed and the standard deviation is not 0, and his value is between -1 and 1, the closer the absolute value of the Pearson correlation coefficient is to 1, the higher the correlation between the two variables, that is, the more similar the two variables. Its correlation coefficient is calculated as follows:

Spearman correlation analysis.

Let the two random samples of the independent variables x and y be ( x1 ,y1 ),xn ,yn ), and x1 , xn and y1 , yn are arranged in ascending order, then the spearman rank correlation coefficient of x and y is:

<> kendall correlation coefficients.

It is a measure of the degree of relationship between two ordinal variables or between two rank variables, so it is also a non-parametric measure. The analysis takes into account the influence of nodes (of the same rank). It is calculated as follows:

Partial correlation analysis is the study of the linear correlation between two variables to control the variables that may affect them. For example, to study the correlation between wages and purchase intentions, it is necessary to control the impact of brand effect in the correlation analysis. The analysis locations in SPSSAU are as follows:

A typical correlation analysis is the study of the correlation between a set of x and a set of y.

Why do correlation analysis Reasons for doing correlation analysis.

The so-called correlation refers to the law that exists between the values of two or more variables in a certain sense, and the purpose of holding rock is to explore the hidden correlation network in the data set.

SPSSAU correlation analysis.

Operation Path: [General Method Related (Pearson Related)] Drag and drop the data into the analysis box on the right. Click [Start Segmented Grinding];

Result: <>

As can be seen from the above table, the correlation coefficient between the two is about and the p-value is less, so it shows that there is a correlation between salary and purchase intention.

At the same time, it was found that the results were exactly the same as those of SPSS, but SPSSAU was more convenient to operate and the results were more rich and easy to understand.

1. Correlation analysis is equivalent to testing whether there is a correlation between many independent variables and dependent variables, of course, the correlation coefficient obtained through correlation analysis is not as accurate as regression analysis.

If there is no correlation between the respective variables and the dependent variables during correlation analysis, there is no need for regression analysis; If there is a certain correlation, then the exact relationship between them is further verified by regression analysis.

At the same time, the purpose of correlation analysis is to see how collinearity there is between independent variables, and if the correlation between independent variables is very large, it may indicate that there is collinearity.

2. Correlation analysis is only to understand the covariant trend between variables, we can only determine the correlation between variables through correlation analysis, this association is not directional, it may be A affects B, it may be B affects A, and it may be that A and B affect each other, and correlation analysis cannot determine which kind of correlation between variables is. Imitation.

And this is the problem that we need to solve with regression analysis, we make assumptions about the independent variable and the dependent variable through regression analysis, and then Sakura can verify the specific relationship between the variables, and then the variable relationship has a specific directionality.

Therefore, correlation analysis is usually used as a descriptive analysis, and the results obtained by regression analysis are more important and precise.

Correlation analysis refers to the analysis of two or more variable elements with correlation, so as to measure the degree of correlation between the two factors, and there needs to be a certain connection or probability between the relevant elements before the correlation analysis can be carried out.

1. How to use the correlation coefficient to judge the relationship between data.

1) Draw a scatter plot.

The most intuitive way to determine whether the data is correlated is to draw a scatter plot.

How to judge the relationship between multiple data, the drawing of scatter plots will be more cumbersome, and it is necessary to choose to draw scatter matrices.

2) The number of silver servants is related to the relationship.

The correlation coefficient measures the degree of uniformity of the two variables, with a range of -1 1, with '1' being a perfect positive correlation and '-1' being a completely negative correlation.

The most commonly used ones are Pearson' correlation coefficient and Spearman's 'Spearman' correlation coefficient.

Pearson correlation coefficient.

Also known as the Pearson product moment correlation coefficient, it is generally used to analyze the relationship between two continuous variables, which is a linear correlation coefficient.

|r|<= Low degree of linearity.

|r|<= Significant linear relationship.

r|> highly linear relationship.

1. Chart correlation analysis (line chart and scatter chart).

The first method of correlation analysis is to visualize the data, which is simply to draw charts. It's hard to spot trends and connections from a purely data perspective, but when you plot data points into graphs, trends and connections become clearer. For data with a clear time dimension, we choose to use a line chart.

2.Monary regression and multiple regression.

The second type of correlation analysis is regression analysis. Regression analysis is a statistical method for determining the relationship between two or more groups of variables. Regression analysis is divided into univariate regression and multiple regression according to the number of variables.

Univariate regression was used for two variables, and multiple regression was used for more than two variables. There are two preparations before performing a regression analysis, the first is to determine the number of variables. Second, determine the self-variable modulus and the variable of the cause and elimination wheel.

The so-called correlation refers to the law that exists between the values of two or more variables in a certain sense, and its purpose is to explore the correlation network hidden in the data set.

SPSSAU correlation analysis.

Operation Path [General Method Correlation (Pearson Related)] Drag and drop the data ridge infiltration tan into the analysis box on the right. Click Start Analysis;

Result: <>

As can be seen from the above table, the correlation coefficient between the two is about and the p-value is less than that, so it shows that there is a correlation between salary and purchase intention.

At the same time, it was found that it was exactly the same as that of SPSS, but SPSSAU was more convenient to operate, and the results were richer and easier to understand.

Significance testing is performed to eliminate errors.

Typically, levels fall into the first category of errors. The first type of error is the probability that a null hypothesis is true but is rejected incorrectly. The second type of error (is the probability that a null hypothesis is false but is accepted incorrectly, or the probability that a research hypothesis is true but is rejected.)

If the p-value is less than a predetermined level, the null hypothesis is theoretically rejected, and conversely, if the p-value is greater than a predetermined level, the null hypothesis is theoretically not rejected.

The significance of the correlation depends on the size of the sample size and the correlation coefficient, the larger the sample size, the greater the correlation defense coefficient, the higher the significance, i.e., the less likely it is to happen by chance. For example, if a person is stolen twice from a place, the presence of a person does not mean that the person is a thief.

However, this person appeared in twelve of the twenty thefts, indicating that this person is a thief.

It happens that the chance of this person appearing at a dozen or so thefts is only about a few hundredths. It can be seen that in order to prove a certain theoretical speculation when doing scientific research, it is necessary to repeat the experiment many times to verify it before it can be used as a conclusion, that is, to make the sample size reach a certain number to make the conclusion more reliable.

The distribution of the data has the assumption that the two sets of data follow a joint normal distribution.

The first step is to test the correlation between the two sets of variables (construct the likelihood ratio statistic).

Determine the number of typical correlation variables (just look at the p-value corresponding to the typical correlation coefficient) <>

Analyze the problem using normalized typical correlation variables.

Perform a typical load analysis.

To study two sets of variables x= (x1, .).xn) and y= (y1, ..)YM), a method similar to principal component analysis is adopted, in which a number of representative variables are selected to form representative composite indicators in the two groups of variables, and the correlation between these two sets of comprehensive indicators is studied to replace the correlation between these two sets of variables, which are called typical variables.

Canonical correlation analysis was first introduced by Harold Hötling. His proposed method was published in the journal Biostatistics in 1936 in an article entitled "The Relationship between Two Sets of Variants", which was gradually perfected after years of application and development, and matured in the 70s.

Due to the large number of matrix calculations involved in typical correlation analysis, the application of the method was quite limited in the early days. However, with the rapid development of contemporary computer technology and its software, it has made up for the difficulties in the analysis of typical correlations, so its application has begun to become popular. Canonical correlation analysis is a statistical analysis method to study the correlation between two sets of variables.