14
votes
Is it possible to have a multivariate random distribution with all its random variables (pair-wise) reverse correlated?
If $X \mathrel{:=} \left(X_1, \ldots, X_k\right)^\top \sim \mathop{\mathrm{Multinomial}}\left(n, \left(p_1, \ldots, p_k\right)^\top\right)$ with $n \in \mathbb N_{\geq 1}, k \in \mathbb N_{\geq 2},$ ...
- 4,995
13
votes
Accepted
Is it possible to have a multivariate random distribution with all its random variables (pair-wise) reverse correlated?
Mathematically, as I commented, you can use the equi-correlation matrix
\begin{align*}
\Sigma =
\begin{bmatrix}
1 & \rho & \cdots & \rho \\
\rho & 1 & \cdots & \rho \\
\vdots ...
- 16.6k
8
votes
Accepted
What does reported "r" mean in the context of a t-test?
The reported $r$ is usually referring to an effect size. It is calculated from the t-statistic and the degrees of freedom
$$
r = \sqrt{\frac{t^2}{t^2 + df}}
$$
where $t$ is the t-statistic and $df$ is ...
- 56.7k
8
votes
What does reported "r" mean in the context of a t-test?
Without any other information, I would say $r$ is correlation. And that is an effect size.
- 109k
7
votes
Is this a correlation request?
First, I would expand it to 13 columns.
Then, while you could do some measure of association for each combination of products, that would give you $12\times 11/2 = 66$ measures. Hard to interpret, ...
- 109k
6
votes
Is it possible to have a multivariate random distribution with all its random variables (pair-wise) reverse correlated?
Let X,Y have a negative covariance/correlation, and define a third variable as a linear sum of those two plus independent noise $\epsilon$
$$Z = -X -aY + \epsilon$$
Now, this will be inverse ...
- 71.7k
3
votes
Is this a correlation request?
Instead, consider employing association rule mining techniques, such as Apriori or FP-growth algorithms. These methods, commonly used in market basket analysis, can reveal meaningful associations ...
- 31
3
votes
Regarding Least Angle Regression
$\newcommand{\aset}{\mathcal{A}_k}$
What you need to show is that $|\operatorname{Corr}(x_j, r_k(\alpha) - \alpha u_k)| = \frac{|\langle x_j, r_k - \alpha u_k\rangle|}{\|r_k - \alpha u_k\|}$ are ...
- 16.6k
3
votes
Homoskedasticity and Collinearity
There really isn't anything saying that these two things are explicitly related. You can have two predictors that are:
Almost perfectly collinear with heterogenous variance
Almost perfectly collinear ...
- 8,485
3
votes
Is it possible to have a multivariate random distribution with all its random variables (pair-wise) reverse correlated?
YES
(I find this fact surprising, too.)
...
- 58.2k
2
votes
Accepted
Could multicollinearity be messing up my logistic regression? Can I overcome it?
Multicollinearity might mess things up and might not. It really depends on what you're trying to do and what do you consider as risks...
If you want to use Logistic Regression for prediction (...
- 189
2
votes
How to quantify the similarity between three sets of complex numbers?
"Three sets of complex numbers" very much sounds like you have a predefined clustering of 2-dimensional points into three clusters. Which in turn suggests the silhouette score, which is a ...
- 117k
2
votes
Do I always need to adjust the p value when using cor.test function in R?
There is a major difference between "I saw many p-values" and "I let this p-value determine how I should report my results". In fact, this has nothing to do with multiple testing.
...
- 60.5k
2
votes
Accepted
Why do my residual plot and scatterplot look the same and what does this mean?
Your scatterplot and residual plot do not need to look like each other, though often they will display similar patterns based on how the regression is fit. A good example is a well-fit nonlinear ...
- 8,485
2
votes
Is this a correlation request?
Mostly out of curiosity, I would explore a random network approach.
Suppose a random graph $G$ with a fixed vertex set $v(G) = \{ \text{products} \}$ representing your set of products and a random ...
- 7,118
1
vote
Accepted
Generate multivariate distributions of lognormal and normal distribution in python
Strategy:
Calculate the normal mean and variance for the lognormal variables, then simulate the normal variables and calculate $e^\cdot$.
An AR-process with diagonal $\phi$ and noise cov $C_a$ will ...
- 1,756
1
vote
Generate multivariate distributions of lognormal and normal distribution in python
To generate random numbers from correlated distributions where two are lognormal and one is normal, and then extend it to an AR(1) process, you can follow these steps:
Step 1: Define Parameters and ...
- 248
1
vote
Sign of correlation between $y$ and $\hat{y}$ with and without intercept
For simple linear regression (with an intercept) you have $\hat \beta_1=\frac{\sum (x_i-\bar x)(y_i-\bar y)}{\sum (x_i-\bar x)^2}=\frac{s_y}{s_x}r_{x,y}$ and, since $s_x >0$ and $s_y > 0$, this ...
- 37.2k
1
vote
Models for fully correlated data
Your question includes aspects of basic longitudinal data analysis, time-series analysis, and multi-state time-to-event analysis. Each of those is complicated enough; combining them can be even ...
- 86.6k
1
vote
Spearman vs. Pearson for an evenly distributed variable. Can I just choose the coefficent with the stronger correlation?
Have you read about Anscombe's quartet? Get that data and compute the Spearman's r and also Kendall's tau; the results are interesting. Bivariate correlation analysis is quite limited and can be ...
- 418
1
vote
Calculate Correlation/Distance Between Two Sets of Binary Vectors
This problem is not exactly a binary comparison problem. The binary comparison problem would be the comparison of two vectors of binary values. In term of machine learning, what you call a binary ...
- 111
1
vote
What is the difference between an association rule and Pearson's correlation?
Example
As @Arun Jose mentioned, correlation is a pairwise measure between two variables. In your case, the dataset would have to contain a variable (column) for each of the items you have to make it ...
- 11
1
vote
Sources of within-cluster correlation other than "random shocks"
The "random shocks" you are describing is just a random intercepts model. Theoretically, random intercepts are one of the simplest and yet most useful models. In application it may be yet ...
- 60.5k
1
vote
Dataset with two unique trends?
I also see two trend lines in your data, but they go in the opposite direction of yours!
The human brain has an awesome power to find patterns in random data. Without a prior hypothesis (or a ...
- 19.6k
1
vote
Accepted
Should I orthogonalize variables before regression?
Orthogonalization of predictor variables can be used to handle multicollinearity in linear regression models, but it should be done with an understanding of its implications on interpretation. ...
- 56.7k
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