Meaning of principal components I have difficulty understanding the meaning of the Principal Components (PC) -    On one hand, PC are computed by finding loading vectors that maximize the variance, but on the other hand I read another interpretation that says PC are the closes to the n-observations. It seems to me like there is a contradiction, how are they closest if they have the highest variance?.. In general, when do we know to stop at the first PC and not go for the second one?    Thanks
Principal component analysis "backwards": how much variance of the data is explained by a given linear combination of the variables? I have carried out a principal components analysis of six variables $A$, $B$, $C$, $D$, $E$ and $F$. If I understand correctly, unrotated PC1 tells me what linear combination of these variables describes/explains the most variance in the data and PC2 tells me what linear combination of these variables describes the next most variance in the data and so on.   I'm just curious -- is there any way of doing this "backwards"? Let's say I choose some linear combination of these variables -- e.g. $A+2B+5C$, could I work out how much variance in the data this describes?
I'm looking for a story that was probably written somewhere from the 1940s to the 1960s. I think I read it in an anthology, possibly in the 1970s.  A group of human explorers landed on a planet with primitive aliens, living in hunter-gatherer villages. They hoped to make a profit from trading our goods for—well, I'm not clear on what they wanted from the aliens.  The native people learned the human language before the explorers could learn theirs. Then the natives suddenly started producing technological innovations far beyond what they originally used. I remember that wooden sailing ships suddenly replaced their canoes. All the natives had to do was hear a story once from the explorers before copying the technology in the story.  Finally, the explorers realized that the natives were much, much smarter than us and that Earth faced a serious problem.  I'm fairly certain that it wasn't a Heinlein story, but I remember that it had some qualities similar to his work. Linear Combination of Random Normal Variables In order to prove that the linear combination of two independent normal distributions(say Z=X+Y) is normal, i am using their MGFs to show that the linear combination also has a similar mgf. This works okay when Z = X+Y. But when Z=X-Y, i run into trouble :  E[$e^{tZ}$] = E[$e^{t(X-Y)}$] = E[$e^{tX}$]E[$e^{-tY}$]  Now i cannot put this as $M_{x}$(t) * $M_{y}$(t) because of the negative sign. How is a generator found for a group, both in case of DH & ECDH? What is a good way to catch the Mysterious Stranger? When ever I hear the music to indicate the Mysterious Stranger has arrived, I can never find him. It is almost like he is not in the vault.  What is a good way to catch the Mysterious Stranger? Where does he usually show up? JavaScript OR (||) variable assignment explanation !! Do not use the future tense after unless   [✓]  I won't go unless you go   [✘] [I won't go] unless you will go. [✘]   Why not? Even if the above is prescriptive, what may be some reasons? In my separate question , I quote: unless = if not. If not can precede future tense; so why can't unless?  Footnote:  motivated this. Multivariate multiple regression validation Why don't Death Eaters always use Avada Kedavra? When the Death Eaters attacked Hogwarts, why did the Death Eaters not just use Avada Kedavra and kill everyone? I wrote a question about blocking certain characters in passwords. It became tremendously unpopular, and it seemed like everyone wanted to rain on my parade every day.  Eventually, I "got it," agreed completely with what people were saying to me, and just wanted to withdraw my question so that my reputation didn't slide even further downhill.  Unfortunately, the system is designed such that I can't withdraw my question or redeem myself. Instead, I just get daily reputation attacks. That's a terrible system, and it needs to be changed. My keyboard is typing by itself, could there be a ghost in it? The keyboard on my laptop seems to be typing by itself:   It sometimes types characters like 134, whether by itself or when I hit certain keys. Repeating characters may appear unexpectedly. The system volume may change by itself, or windows like the Print dialog or Web browser may appear.   This can happen without any input or as I type, and may occur more often when certain keys are pressed. Sometimes, the keyboard fails to respond altogether. This is happening regardless of the software involved.  Is there a ghost in my keyboard—is my keyboard broken?  A sample of text from the keyboard might look like this (normal QWERTY...ASDF...ZXC... sequence is expected):   QWERTYUIOPASDF)(G@*HKLZXCVBN QWERTYIOPASDFGL!#ZXCVB13 QWERTYUIOPASDFGHJKLZXCVB!#N qwertyu41iopasdf19g13h28j113k4113zxcvb4n qwerty4u1iopasdf0g7h1jklzxcvb13m qwert13uuuuuuuuuuuuuuuiopasdf87091134ghhhhhhhhhhhhhhhhhhhhhhh13jk13zxcvb14      This question comes up often and the answers are usually the same. This post is meant to provide a definitive, canonical answer for this problem. Feel free to edit the answer to add additional details. Do you recommend using semicolons after every statement in JavaScript? In many situations, JavaScript parsers will insert semicolons for you if you leave them out. My question is, do you leave them out?  If you're unfamiliar with the rules, there's a description of semicolon insertion on the . Here's the key point:     If the first through the nth tokens of a JavaScript program form are grammatically valid but the first through the n+1st tokens are not and there is a line break between the nth tokens and the n+1st tokens, then the parser tries to parse the program again after inserting a virtual semicolon token between the nth and the n+1st tokens.   That description may be incomplete, because it doesn't explain @Dreas's example. Anybody have a link to the complete rules, or see why the example gets a semicolon? (I tried it in JScript.NET.)   is related, but only talks about a specific scenario. How can I get admin access to a Mac without knowing the current password? My Father died last year and I inherited his Mac Mini. My wife has retired and we are trying to set up the mini for her use but the changes we want to make require admin access and we do not have the information my father used to set up the machine.  Is it possible to reset the admin information without having the old information? If so, how would I go about it?   I am not a Mac user usually so any guidance will have to be pretty simple! Move post to different user I updated some entries in the  at C:\WINDOWS\System32\drivers\etc.  As a test, I decided to make Google point to 127.0.0.1.  # Additionally, comments (such as these) may be inserted on individual # lines or following the machine name denoted by a '#' symbol. # # For example: # #      102.54.94.97     rhino.acme.com          # source server #       38.25.63.10     x.acme.com              # x client host  127.0.0.1       localhost ::1             localhost 127.0.0.1       google.com   This works fine on Windows Vista, but not on Widows 7. When I type google.com into my browser, it goes directly to Google's website.  I am not using a proxy server, and I think there might be some temporary DNS settings that need to be flushed, but I'm not sure.  Does anyone know how to fix this? Please see the following image, where you can find the inconsistency of SO reputation score among different flair themes (one with 7165, while all other three 7265).   I always thought that these four themes are based on the same data until now. Is this a bug? Are different flair themes really updated individually?    P.S.: The inconsistency only shows on my mobile, no problem from my desktop. Uses of the 'Golden Ratio' I have heard much about the numerous appearances of the ratio found in nature: 1.6180339887.  Are there any actual mathematical uses that have been found of this number? What are its advantages? Just curiosity, really. There's someone much like Crazy Earl in Oasis behind a locked door. He tells me to leave until I've killed a seraph guardian or I get some sort of guardian crystal.  I just beat the DLC and did many of the sidequests and I'm still stumped as to how to get such a crystal. I assumed there would be Guardian foes just like in Borderlands 1, and they'd drop this item. After completing the story...there were no such enemies. So what do I do? How to encrypt folders (not in Home)? Put the book back on the table.   I'm having trouble. I think it is a preposition. I'm following the , but on launching the upgrade tool I get this response:  Checking for a new ubuntu release No new release found   Am I doing something wrong? Is there a workaround?