What is the relationship between orthogonal, correlation and ...
Sep 7, 2015 · Here is the relationship: If X and Y are uncorrelated, then X-E[X] is orthogonal to Y-E[Y]. Unlike that independent is a stronger concept of uncorrelated, i.e., independent will lead …
what does it mean for a single variable to be uncorrelated?
Oct 10, 2015 · $\begingroup$ here is an example from my textbook (p19, 5th ed, Montgomery, Peck Vining): in the derivation of Var[b], Var distributes across the summation "because the …
correlation - Uncorrelatedness + Joint Normality = Independence.
Nov 10, 2018 · However, two variables that are uncorrelated AND jointly normally distributed are guaranteed to be independent. Can someone explain intuitively why this is true? What exactly …
Why are principal component scores uncorrelated?
May 26, 2015 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for …
Simple examples of uncorrelated but not independent $X$ and $Y$
Mar 5, 2016 · The variables are uncorrelated but dependent. Alternatively, consider a discrete bivariate distribution consisting of probability at 3 points (-1,1),(0,-1),(1,1) with probability 1/4, …
Why are PCA eigenvectors orthogonal and what is the relation to …
Apr 11, 2017 · Can someone provide an example to show why orthogonal vectors ensure uncorrelated variables? What would happen in PCA if I chose vectors which are not …
In practice, how to clearly prove that variables are uncorrelated?
Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their …
Uncorrelated/orthogonal random vectors - Cross Validated
Correlation and orthogonality, although closely related concepts, are not the same things. This question is confusing because both answers are correct, depending on which version of the …
Are estimates of regression coefficients uncorrelated?
Two multiple regression coefficient estimates $\hat\beta_i$ and $\hat\beta_j$ are uncorrelated whenever either (or both) of the corresponding columns of the design matrix are orthogonal to …
Correlated Residuals - The Big Bad Wolf of Statistics?
Oct 31, 2022 · Uncorrelated or independent residuals/observations/errors* are often assumed (but not required) for statistical inference like computing confidence intervals or p-values. If that …