相关系数计算公式

相关系数计算公式

相关系数计算公式

Statistical correlation coefficient

Due to the statistical correlation coefficient used more frequently, so here is the use of a few articles introduce these coefficients.

The correlation coefficient: a study of two things (in the data we call the degree of correlation between the variables).

If there are two variables: X, Y, correlation coefficient obtained by the meaning can be understood as follows:

(1), when the correlation coefficient is 0, X and Y two variable relationship.

(2), when the value of X increases (decreases), Y value increases (decreases), the two variables are positive correlation, correlation coefficient between 0 and 1.

(3), when the value of X increases (decreases), the value of Y decreases (increases), two variables are negatively correlated, the correlation coefficient between -1.00 and 0.

The absolute value of the correlation coefficient is bigger, stronger correlations, the correlation coefficient is close to 1 or -1, the higher degree of correlation, the correlation coefficient is close to 0 and the correlation is weak.

The related strength normally through the following range of judgment variables:

The correlation coefficient 0.8-1.0 strong correlation

0.6-0.8 strong correlation

0.4-0.6 medium degree.

0.2-0.4 weak correlation

0.0-0.2 very weakly correlated or not correlated

Pearson (Pearson) correlation coefficient

1, introduction

Pearson is also known as the correlation (or correlation) is a kind of calculation method of the linear correlation of British statistician Pearson in twentieth Century.

Suppose there are two variables X, Y, then the Pearson correlation coefficient between the two variables can be calculated by the following formula:

A formula:

Formula two:

Formula three:

Formula four:

Four equivalent formulas listed above, where E is the mathematical expectation, cov said the covariance, N represents the number of variables.

2, scope of application

When the two variables of the standard deviation is not zero, the correlation coefficient is defined, the correlation coefficient for Pearson:

(1), is the linear relationship between the two variables, are continuous data.

(2) overall, two variables are normally distributed, or near normal unimodal distribution.

(3) and the observation values of two variables is in pairs, each pair of observations are independent of each other.

3, Matlab

Pearson correlation coefficient Matlab (according to the formula four):

[cpp] view plaincopy

Function coeff = myPearson (X, Y)

% of the function of the realization of the Pearson correlation coefficient calculating operation

%

% input:

% X: numerical sequence input

% Y: numerical sequence input

%

% output:

% coeff: two input numerical sequence X, the correlation coefficient of Y

%

If length (X) ~ = length (Y)

Error (two 'numerical sequence dimension is not equal to');

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