I've read through  regarding calculating the variance explained from PCA output. I think I got it right but might be off in my interpretation of R output.  In the example below, I would like to calculate the percentage of variance explained by the first principal component of the USArrests dataset.  pca &lt;- prcomp(USArrests, scale = TRUE) eigs &lt;- pca$sdev^2 eigs[1] / sum(eigs) [1] 0.6200604   I assumed that R uses sdev as the square root of the eigen values. So I square it and divide the first value by the total. Is this correct?
In general, what is meant by saying that the fraction $x$ of the variance in an analysis like PCA is explained by the first principal component? Can someone explain this intuitively but also give a precise mathematical definition of what "variance explained" means in terms of principal component analysis (PCA)?  For simple linear regression, the r-squared of best fit line is always described as the proportion of the variance explained, but I am not sure what to make of that either. Is proportion of variance here just the extend of deviation of points from the best fit line?
Are the memories still there? How Can I prove (a+b) mod m = (a mod m) + (b mod m)) mod m? modular arithmetic  How Can I prove (a+b) mod m = (a mod m) + (b mod m)) mod m ? Execution of a command locally after ssh tunneling I have a script file ./run_app.sh which contains of the following:  ssh -L 8888:localhost:8888 ubuntu@address ./run_website.sh   # it should be executed locally   but it tries to run the second line on the remote machine. Actually, I want to run it on my pc. Any idea? How to interpret the coefficients from a beta regression? I have some data that is bounded between 0 and 1. I have used the betareg package in R to fit a regression model with the bounded data as the dependent variable. My question is: how do I interpret the coefficients from the regression? EncFs insecure, what to use now I love encfs as it provides file-based encrypting which is quite useful when it comes to cloud storage. But it looks like that especially for this use case, . I'm aware that  but how to deal with it in the meantime? Are there any alternatives that integrate well in ubuntu?  Edit: The security issue I mostly refer to is . It is still present in version 1.8 and makes your files vulnerable if someone get's multiple versions of your encrypted files. If one is worried about services like Dropbox are not that thrustworthy and encrypts folders uploaded into the cloud because of that, the opportunity that the attacker (the service) gets more than one copy of the cyphertext is absolutely given. "This one is" OR "This is" I have seen people using "This one is Daddy's" with the word "one" before a form of the verb be. I am confused about which is more accurate, to use:     This is Daddy's.   or     This one is Daddy's.   Hope you can address my concerns, thank you. Brace expansion not working in a script for i in {1..40} do     echo $i done   I got  {1..40}   and I would like to have something like  1 2 3 and so on   so I can use the variable i inside a command's parameter. Is it possible to detect a player consuming food items? How can I create and extract zip archives from the command line? Are counters (noun) physical things? When you respond to someone in a comment you use @PersonsName. Is there anyway it could be linked like this @ Use Yaml for MongoMapper Config How to make Gmail automatically label incoming emails I would like to set it up so that Gmail labels incoming mail based on which business email of mine the emails are sent to. I have two business emails that come to my Gmail account.  For instance, if someone emails me at example@firstbusiness.com, I would like the email to be automatically labeled first business. If someone emails me at my other email address (which also is forwarded to Gmail), example@secondbusiness.com, I would like that email to be automatically labeled second business.   Is there any way to do this? Have Peter Capaldi's previous acting roles in the Doctor Who universe ever been addressed? Similar to this question posted in August 2014:       Has the fact that  (as  in The Fires of Pompeii, and  in Torchwood’s Children of Earth season) yet been addressed/explained either in, or out of universe? Is it just that nvarchar supports multibyte characters? If that is the case, is there really any point, other than storage concerns, to using varchars? Writing string at the same position using Console.Write in C# 2.0 I have a console application project in C# 2.0 that needs to write something to the screen in a while loop. I do not want the screen to scroll because using Console.Write or Console.Writeline method will keep displaying text on console screen incremently and thus it starts scrolling.  I want to have the string written at the same position. How can i do this?  Thanks Generally accepted root mean square (RMS) error for rectifying topographic maps This is a generic inquiry on the common practice/standard for determining the acceptable values of RMS when georeferencing topographic maps.  Is there an absolute value?  Some literature suggests that it should be "less than or equal to 1/2 of the side of a cell which make up the total resolution of the image." Difference between “with”, “at” and “for” with a business title and a company name I've only just begun studying group theory (up to Lagrange) following on from vector spaces and I am still finding them almost frustratingly  arbitrary. I'm not sure what exactly it is about the axioms that motivated them defining groups.  My textbook asks you to list 'common features' of vector spaces and then later defines a set of axioms for vector spaces under addition, scalar multiplication and both, noting that the axioms under addition form an Abelian group. So are groups just a generalisation of vector spaces under any binary operation?  My main problem is that the book notes that 'the axioms may seem rather arbitrary' and links groups with vector spaces but doesn't elaborate.   When introducing groups, you are tasked to complete Cayley tables for the symmetries of an equilateral triangle and square.  Then, similarly to the delivery of vector spaces, notes that the tables have common properties (Closure, Identity, inverse and association) and defines a group as a set of elements under a binary operation that has these features.  So what's so important about these 4 properties? For example, if 1 or 2 the properties were excluded form the  axioms, or we added an extra few properties as axioms how would that cripple the effectiveness of groups?  Are the group axioms ever difficult to work with or do they always work, forgive the crude Littlewood analogy, like a mathematical skeleton key?  What is it about these 4 properties that make groups such a powerful tool in mathematics and physics?  My best guess is that a group is the best way to express our sense of  symmetry and what is symmetric mathematically, but I would prefer some elaboration. This is probably easier to show than tell...   On the recent question , I see the following:    As you can see, the first five links render properly, but after that, they stop converting.  Unfortunately, this isn't obvious to the person writing the post, which I discovered when I went to edit the post to fix the "broken" links. In the edit window, it renders all of the links just fine:    I understand that this behavior is expected based on balpha's answer :        Links to questions on the same site are unlimited.   Links to other sites are limited to             a) 5 linked-to sites and     b) N questions per target site, where N is 200 on meta sites and 10 on non-metas (this is about the site that the post containing the link is posted on, not the site that is being linked to)         So if this rule is still going to stay in effect, please fix the edit view to also not automatically convert more than five linked-to sites to help people writing posts know that they need to manually title the links to the other questions.  That said, I'd prefer that (at least on MSE) this limitation be removed or raised. Even in the answer, balpha says:     The restrictions are currently as follows, but note that they do look a bit contrived, resulting from the fact that they have grown over time (from single site to cross-site, from "there are no subsites" to "facebook.SO", etc.), so it's not unlikely that we'll revisit them.   So, if it's not hurting performance, can we please increase the limit or remove it?