Read More
Date: 20-4-2021
2863
Date: 6-4-2021
1517
Date: 15-2-2021
1234
|
For two random variates and , the correlation is defined bY
(1) |
where denotes standard deviation and is the covariance of these two variables. For the general case of variables and , where , 2, ..., ,
(2) |
where are elements of the covariance matrix. In general, a correlation gives the strength of the relationship between variables. For ,
(3) |
The variance of any quantity is always nonnegative by definition, so
(4) |
From a property of variances, the sum can be expanded
(5) |
(6) |
(7) |
Therefore,
(8) |
Similarly,
(9) |
(10) |
(11) |
(12) |
Therefore,
(13) |
so .
For a linear combination of two variables,
(14) |
|||
(15) |
|||
(16) |
|||
(17) |
Examine the cases where ,
(18) |
(19) |
The variance will be zero if , which requires that the argument of the variance is a constant. Therefore, , so . If , is either perfectly correlated () or perfectly anticorrelated () with .
|
|
علامات بسيطة في جسدك قد تنذر بمرض "قاتل"
|
|
|
|
|
أول صور ثلاثية الأبعاد للغدة الزعترية البشرية
|
|
|
|
|
قسم الشؤون الفكرية والثقافية يجري اختبارات مسابقة حفظ دعاء أهل الثغور
|
|
|