All Questions
8
questions with no upvoted or accepted answers
2
votes
0
answers
743
views
What do the eigenvalues of a correlation matrix represent?
I was wondering if there was any special meaning to the eigenvalues/eigenvectors of a correlation matrix. I get what they mean in a covariance matrix, and how that relates to PCA, though. Can you do ...
- 321
1
vote
0
answers
38
views
Transformations to solve question surrounding correlation of vectors
I am trying to solve part (b) of this question, but I am having trouble with something.
With some help, I have been able to solve the following:
$$
\begin{align*}
\max_{a \neq 0, b \neq 0}\...
1
vote
0
answers
129
views
Find correlation between A and C given correlation between A and B & B and C. Conflicting results?
Let $A, B, C$ be three random variables. Suppose their Pearson correlation coefficients are $\rho(A, B) = \frac{1}{2}$ and $\rho(B, C) = \frac{1}{2}$, what is the possible range for $\rho(A, C)$?
I ...
- 365
1
vote
0
answers
3k
views
Relation between correlation and the inner product
I saw in several places in the numerical linear algebra that the inner product is interpreted as the correlation. However, I don't see why they do it. Please, can you explain to me what is the ...
- 1,689
1
vote
0
answers
23
views
Augmenting a matrix with a highly-incorrelated column
Consider a binary matrix:
$$\begin{pmatrix} 1 & -1 & 1 \\ -1 & 1 &1 \\ \vdots & \vdots &\vdots \\ 1 & 1 & -1\end{pmatrix}$$
with a random distribution of 1 and -1 ...
1
vote
0
answers
140
views
Redundancies in covariance matrix
We know that covariance matrix is symmetrical. I have a vague intuition that there may be some other redundancies beyond that. For example, if A is correlated to B and B is correlated to C then A and ...
- 11
0
votes
0
answers
159
views
covariance matrix to correlation matrix and conversely (if we have deviation vector)
hey what's the formula for a covariance matrix if i have a given collation matrix and standard deviation vector? And in the other direction what is the formula for the correlation matrix if I have a ...
- 303
0
votes
2
answers
118
views
Correlation Coefficients in Simple Linear Regression Model
I need to compute the correlation between $y$ and $\hat y$, between $\hat y$ and $r$, and between $y$ and $r$. In this case, $\hat y$ is the estimator of $y$, and $r$ is the residual. The catch is ...
- 1