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Date: 19-2-2021
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Date: 6-2-2021
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Date: 8-4-2021
1225
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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) |
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(15) |
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(16) |
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(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 .
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تفوقت في الاختبار على الجميع.. فاكهة "خارقة" في عالم التغذية
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أمين عام أوبك: النفط الخام والغاز الطبيعي "هبة من الله"
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قسم شؤون المعارف ينظم دورة عن آليات عمل الفهارس الفنية للموسوعات والكتب لملاكاته
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