The meaning of covariance

Source: Internet
Author: User

The meaning of covariance

Reproduced in: http://bbs.mathchina.com/cgi-bin/topic.cgi?forum=5&topic=14444 (thanks to the original author)


In probability theory, two random variables X and Y are related to each other in roughly the following 3 cases:


When the joint distribution of x, Y is like that, we can see that there are roughly: the larger the X, the greater the X, the smaller the Y, the less the case we call " positive correlation ".


When the joint distribution of x, Y is like that, we can see that there are generally: the larger the x y instead the smaller, the smaller the x, the larger the case, and we call it " negative correlation ".

When the joint distribution of x, Y is like that, we can see: Neither x is larger, y is larger, nor is x larger y but smaller, so we call it " not relevant”。

How can these 3 related situations be expressed in a simple number?

In the plot area (1), there is X>ex, y-ey>0, SO (X-ex) (Y-ey) >0;

In the plot area (2), there is X<ex, y-ey>0, so (X-ex) (Y-ey) <0;

In the plot area (3), there is X<ex, y-ey<0, so (X-ex) (Y-ey) >0;

In the area (4) of the figure, there is X>ex, y-ey<0, so (X-ex) (Y-ey) <0.

when X with theYPositive Correlation, most of their distributions are in the region (1) and (3), a small portion of the region (2) and (4 ), so on average, there is E(x-ex) (Y-ey) >0 .

when  x &NBSP; Y 2 4 1 3 (X-ex) (Y-ey) <0 &NBSP; .

when X is not related to Y, they are distributed in regions (1) and (3), with the region ( 2) and (4) in the distribution almost as much, so on average, there (X-ex) (Y-ey) =0 .

So, we can define a digital feature that represents X, Y correlations, which is covarianceCoV (X, Y) = E (X-ex) (Y-ey).

when CoV (x, y) >0 , it indicates that x and y Positive Correlation ;

when   CoV (X, Y) <0 X and Y ;

when CoV (X, Y) =0 when it indicates X with the Y not relevant .

This is the meaning of covariance.


The meaning of covariance

Contact Us

The content source of this page is from Internet, which doesn't represent Alibaba Cloud's opinion; products and services mentioned on that page don't have any relationship with Alibaba Cloud. If the content of the page makes you feel confusing, please write us an email, we will handle the problem within 5 days after receiving your email.

If you find any instances of plagiarism from the community, please send an email to: info-contact@alibabacloud.com and provide relevant evidence. A staff member will contact you within 5 working days.

A Free Trial That Lets You Build Big!

Start building with 50+ products and up to 12 months usage for Elastic Compute Service

  • Sales Support

    1 on 1 presale consultation

  • After-Sales Support

    24/7 Technical Support 6 Free Tickets per Quarter Faster Response

  • Alibaba Cloud offers highly flexible support services tailored to meet your exact needs.