b*****n
发帖数: 143 | 1 A, B and C are three variables. Suppose we know the correlation coefficient
between A and B is x, and correlation coefficient between B and C is y. I
remember that the correlation coefficient between A and C must be in a
certain range. But I can not find the formula. Can anybody tell me? Thanks. |
g*****1
发帖数: 18 | 2 Triangle rule.
A-B with an angle of alpha, correlation = cos(alpha)
B-C with an angle of beta, correlation = cos(beta)
A-C with an angle of 180-alpha-beta, correlation = cos(180-alpha-beta)
Correlation between A and C can be explicitly expressed in terms of other
two correlations. |
b*****n
发帖数: 143 | 3
Thank you very much for your reply. Do you happen to know where I can find a
mathematical proof of this rule?
【在 g*****1 的大作中提到】
: Triangle rule.
: A-B with an angle of alpha, correlation = cos(alpha)
: B-C with an angle of beta, correlation = cos(beta)
: A-C with an angle of 180-alpha-beta, correlation = cos(180-alpha-beta)
: Correlation between A and C can be explicitly expressed in terms of other
: two correlations.
|
b*****n
发帖数: 143 | 4 I have an impression that the correlation coefficient of (X,Z) is in a
certain range. But according to the triangle rule, it will be a fixed value?
Correct me if I am wrong. Thanks. |
g*****1
发帖数: 18 | 5 Yes, a fixed value.
If you have two angles fixed, the third is also known.
You can test with some examples. |
p********6
发帖数: 1802 | 6 correlation matrix is positive define?
coefficient
【在 b*****n 的大作中提到】
: A, B and C are three variables. Suppose we know the correlation coefficient
: between A and B is x, and correlation coefficient between B and C is y. I
: remember that the correlation coefficient between A and C must be in a
: certain range. But I can not find the formula. Can anybody tell me? Thanks.
|
x******a
发帖数: 6336 | 7 A-B=1 alpha=0
B-C=1 beta=0
then A-C=-1 since 180-0-0=180
anything wrong?
【在 g*****1 的大作中提到】
: Triangle rule.
: A-B with an angle of alpha, correlation = cos(alpha)
: B-C with an angle of beta, correlation = cos(beta)
: A-C with an angle of 180-alpha-beta, correlation = cos(180-alpha-beta)
: Correlation between A and C can be explicitly expressed in terms of other
: two correlations.
|
L**********u
发帖数: 194 | 8 这种题目还有什么讨论的意义？
不就是求个行列式的问题吗。 |
L**********u
发帖数: 194 | 9 semi-positive
【在 p********6 的大作中提到】
: correlation matrix is positive define?
:
: coefficient
|
