All Questions
17
questions
0
votes
1
answer
65
views
Using transformations to solve question surrounding correlation of vectors
While studying statistical inference and data-analysis, I came across this question. I have been able to show part (a) of this question already myself, but I don't know how to solve part (b). Can ...
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:
$$
\begin{align*}
\max_{a \neq 0, b \neq 0}\...
1
vote
0
answers
129
views
Find correlation between A and C given correlation between A and B & B and C. Conflicting results?
Let $A, B, C$ be three random variables. Suppose their Pearson correlation coefficients are $\rho(A, B) = \frac{1}{2}$ and $\rho(B, C) = \frac{1}{2}$, what is the possible range for $\rho(A, C)$?
I ...
- 365
2
votes
1
answer
554
views
Coefficient of Determination and Correlation between observed and fitted value in Multiple Linear Regression.
Consider Multiple Linear Model
$$y= X\beta + \epsilon$$
Then using Ordinary Least Square, we get estimate of $\beta$ as
$$\hat{\beta} = (X'X)^{-1}X'y$$
And $$\hat{y} = X\hat{\beta}$$
$$SS_{\rm Res}= (...
- 4,011
0
votes
1
answer
31
views
If a correlation matrix is a band matrix with value 1 on the band, is this equivalent to correlation matrix with all 1?
Say I have a stationary sequence ${x_1,x_2,\cdots,x_n}$ and if two elements of the sequence are less than or $m$ apart from each other, we say they are correlated. This is called an m-dependent ...
CommunityBot
- 1
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
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
2
votes
1
answer
716
views
Cholesky Decomposition - Correlation
I understand, How Cholesky decomposition can be used to generate correlated random numbers. But unable to understand, why and how does it allow for correlation?
8
votes
2
answers
2k
views
Eigenvalue decomposition of block covariance matrix for Canonical Correlation Analysis (CCA)
Edited:
My question is related to a tutorial I was reading.
The covariance matrix is a block matrix where $C_{xx}$ and $C_{yy}$ are within-set covariance matrices and $C_{xy} = C_{yx}^T$ are between-...
- 26.1k
3
votes
1
answer
3k
views
How is the auto-correlation of vectors defined?
Suppose $v$ is an $n$-ary vector with entries from the set $\{0,1\}$ (i.e. a vector of ones and zeros).
A paper I am reading defines the "auto-correlation sequences" $$v*v$$ where $*$ denotes the ...
- 51.7k
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 ...
- 16.5k
1
vote
2
answers
5k
views
What is the rank of correlation matrix and its estimate?
For a n-dimensional vector $\mathbf{x}$, a $n\times n$ correlation matrix $\mathbf{R}$ is https://en.wikipedia.org/wiki/Covariance_matrix#Correlation_matrix
\begin{equation}
\mathbf{R} = {E}\big[(\...
CommunityBot
- 1
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
1
answer
97
views
Which type of correlation should I use?
I am beginner in statistics. I have excel table with few columns. I would like to find correlation between the variables. I have to make an essay to my boss and he wants concrete answers. I searchin ...
- 51.7k
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 ...
