Trying to understand this relationship I came across this conversation in an email group:           I got a problem while analyzing my data using NN.      I got R-square with 0.45 with MSE around 5000.     SO I am wonder why? There must be a relation     between R-square and MSE?         R2 = 1 - SSE/SS0      SSE = N*MSE SS0 = (N-1)*VAR(Target)      VAR(T) = SS0/(N-1) = [SSE/(1-R2)]/(N-1)      = [N/N-1]*MSE/(1-R2)      ~ 5000/0.55 ~ 9091      If you had standardized your targets to unit variance you would have   obtained MSE ~ 0.55   Is that correct? What insights can we reach understanding this relationship?
For regression problem, I have seen people use "coefficient of determination" (a.k.a R squared)  to perform model selection, e.g., finding the appropriate penalty coefficient for regularization.   However, it is also common to use "mean squared error" or "root mean squared error" as a measure of regression accuracy.  So what is the main difference between these two? Could they be used interchangeably for "regularization" and "regression" tasks?  And what are the main usage of each in practice, such as in machine learning, data mining tasks?
How to stop people from using my domain to send spam? I receive Mailer Daemon messages saying certain emails fail. My domain is itaccess.org which is administered by Google apps. Is there any way I can identify who is sending emails from my domain, and how they are doing it without me creating an account for them?  Delivered-To: 7e949ba@itaccess.org Received: by 10.142.152.34 with SMTP id z34csp12042wfd;         Wed, 8 Aug 2012 07:12:46 -0700 (PDT) Received: by 10.152.112.34 with SMTP id in2mr18229790lab.6.1344435165782;         Wed, 08 Aug 2012 07:12:45 -0700 (PDT) Return-Path: &lt;whao@www20.aname.net&gt; Received: from smtp-gw.fsdata.se (smtp-gw.fsdata.se. [195.35.82.145])         by mx.google.com with ESMTP id b9si24888989lbg.77.2012.08.08.07.12.44;         Wed, 08 Aug 2012 07:12:45 -0700 (PDT) Received-SPF: neutral (google.com: 195.35.82.145 is neither permitted nor denied by best guess record for domain of whao@www20.aname.net) client-ip=195.35.82.145; Authentication-Results: mx.google.com; spf=neutral (google.com: 195.35.82.145 is neither permitted nor denied by best guess record for domain of whao@www20.aname.net) smtp.mail=whao@www20.aname.net Received: from www20.aname.net (www20.aname.net [89.221.250.20])     by smtp-gw.fsdata.se (8.14.3/8.13.8) with ESMTP id q78EChia020085     for &lt;7E949BA@itaccess.org&gt;; Wed, 8 Aug 2012 16:12:43 +0200 Received: from www20.aname.net (localhost [127.0.0.1])     by www20.aname.net (8.14.3/8.14.3) with ESMTP id q78ECgQ1013882     for &lt;7E949BA@itaccess.org&gt;; Wed, 8 Aug 2012 16:12:42 +0200 Received: (from whao@localhost)     by www20.aname.net (8.14.3/8.12.0/Submit) id q78ECgKn013879;     Wed, 8 Aug 2012 16:12:42 +0200 Date: Wed, 8 Aug 2012 16:12:42 +0200 Message-Id: &lt;201208081412.q78ECgKn013879@www20.aname.net&gt; To: 7E949BA@itaccess.org References: &lt;20120808171231.CAC5128A79D815BC08430@USER-PC&gt; In-Reply-To: &lt;20120808171231.CAC5128A79D815BC08430@USER-PC&gt; X-Loop: whao@whao.se From: MAILER-DAEMON@whao.se Subject: whao.se:  kontot avstängt - account closed X-FS-SpamAssassinScore: 1.8 X-FS-SpamAssassinRules: ALL_TRUSTED,DCC_CHECK,FRT_CONTACT,SUBJECT_NEEDS_ENCODING      Detta är ett automatiskt svar från F S Data - http://www.fsdata.se      Kontot för domänen whao.se är tillsvidare avstängt.     För mer information, kontakta info@fsdata.se      Mvh,     /F S Data      -----    This is an automatic reply from F S Data - http://www.fsdata.se    The domain account "whao.se" is closed.   For further information, please contact info@fsdata.se    Best regards,   /F S Data I just updated from Ubuntu 10.10 to 11.04 and have an issue regarding the screen resolution. I have Intel integrated gfx chip and my monitor supports resolutions larger than 1024x768. (in 10.10 I've been using 1280x1024) But as soon as I upgraded, I'm stuck with 1024x768 resolution and seems I can't change it.  running xrandr In terminal yields the following results,   Screen 0: minimum 320 x 200, current 1024 x 768, maximum 4096 x 4096 LVDS1 connected 1024x768+0+0 (normal left inverted right x axis y axis) 0mm x 0mm    1280x800       58.1 +    1024x768       60.0*     800x600        60.3     56.2      640x480        59.9   VGA1 connected 1024x768+0+0 (normal left inverted right x axis y axis) 344mm x 194mm    1366x768       59.9 +    1360x768       60.0      1024x768       75.1     72.0     70.1     60.0*     832x624        74.6      800x600        72.2     75.0     60.3     56.2      640x480        72.8     75.0     66.7     60.0      720x400        70.1     1280x1024_60.00 (0xce)  109.0MHz         h: width  1280 start 1368 end 1496 total 1712 skew    0 clock   63.7KHz         v: height 1024 start 1027 end 1034 total 1063           clock   59.9Hz   What maybe the problem? Is it a bug? What kind of steps I should take in order to get a higher resolution? (changing xorg.conf maybe?) Any insight is highly appreciated. Thanks in advance.   UPDATE    Screenshot after running xrandr --addmode VGA1 1360x768  As you can see, side bar is not completely visible and Ubuntu logo at the task bar is missing. Also when you open an application, the Task bar of the application (where it should go to the top panel) is missing as well.. Possessive form of coordinated noun phrases? Which of the following is accurate in British English to describe our own wedding?        Alex and Jen's Wedding   Alex's and Jen's Wedding   Alex and Jens' Wedding Static posts page with home.php For my website, I am using a static home page page Home (template front-page.php) and for posts- page News (template home.php)  I need to show all the post titles and exceprts on that page News (templ. home.php), but also show the original title and the_content from that page News itself.  This code below while statement shows all the posts, which is good, but the top the_title also shows the title from the first post, not from the News page itself.  How to achieve what I need?  &lt;?php get_header(); ?&gt;      &lt;?php     the_title();           the_content();     ?&gt;  &lt;?php if(have_posts()) while(have_posts()) : the_post(); ?&gt;          &lt;?php         the_title();         ?&gt;          &lt;?php         the_content();         ?&gt;      &lt;?php     endwhile;     ?&gt;    &lt;?php get_footer(); ?&gt; Proving $A+A'B=A+B$ without truth tables How can I prove the Boolean algebraic rule $$A+A'B=A+B$$ without using a truth table?  With the truth table, it is easy to see that the two are equal, but how can I prove it using lesser Boolean identities? How to force a table into page width? I see this often in the build scripts of projects that use autotools (autoconf, automake).  When somebody wants to check the value of a shell variable, they frequently use this idiom:  if test "x$SHELL_VAR" = "xyes"; then ...   What is the advantage to this over simply checking the value like this:  if test $SHELL_VAR = "yes"; then ...   I figure there must be some reason that I see this so often, but I can't figure out what it is. Looking to achieve frame effect with shadows at corners What makes scaling pixel art different than other images? Recently I was coaching a developer who's new to making pixel art games, and realized there's some "conventional wisdom" around scaling pixel art that's not obvious to a newcomer, and might not be well documented. So, here's an attempt to fix that....     I've heard I should only scale pixel art by 200%, 300% etc. not in-between sizes like 120%   Why is that? Shouldn't scaling "just work" the way it does with other images? What if I really need to make my character just a fraction larger or smaller to get the right gameplay or look? How do I fix this?  I'm told it's "bad" to use pixel art at different scales in one game - why?    For example, if I scaled up my character so each sprite texel is 4x4 screen pixels, while my background art is scaled up so each sprite texel is 6x6 screen pixels. Isn't a pixel a pixel at the end of the day? How can I add "Show desktop" to the GNOME dash or Ubuntu Dock? Why does volatile exist? What does the volatile keyword do? In C++ what problem does it solve?  In my case, I have never knowingly needed it. Does "no larger than" imply shapability? What is the difference between "why are you worried" and "why you are worried"? What is the difference between these two sentences?     Why are you worried?   Why you are worried?   Which one is correct? Is it proper to use "the" before the name of a government organization? Script-r Symbol The near-ubiquitous undergraduate reference on electrodynamics, "Introduction to Electrodynamics" by David Griffiths make extensive use of a script-r symbol, defined to be \vector{\scriptr} \equiv \vector{r} - \vector{r}^{\prime} and looks like:    Although the question of how to produce such a symbol in LaTeX is quite a common one I am yet to find a satisfactory solution.  The closest I've found is from the physymb package and uses the Calligra fonts:    Sadly, there is not a bold variant of this character and it is far more cursive than I would like.  I am hence wondering if there are any better facsimiles. How do I print all lines of a file with duplicate values in a certain column Performing reverse clip in ArcMap? Is there a way to perform a 'reverse' of the clip function in ArcMap?  I am not exactly sure how to explain this so here is a diagram: Why do the big nuts always remain at top? The Brazil-nut Effect Most of the time when I mixed different nuts in a bowl, I observed that the big Brazil nuts were always on top while the small peanuts settled near the base. No matter how you take it, if the big nuts are put at the bottom and then the small nuts are poured, then also after some time the big ones will come to the top. Will not the gravity attract those big nuts more and eventually will they not remain at the base? But it doesn't happen!   I googled it and found the term Brazil-nut Effect but couldn't find any proper explanation. What is the physical explanation for this effect? Possible Duplicate:             When I listen to major news programs, often I notice that they seem to intentionally omit "the" before the name of the government organizations. For example:     We contacted E.P.A. for comment but they refused our requests.   or     Others consider the actions of treasury to be detrimental to the economy.   These just sound wrong to me. I think it should be "the E.P.A" or "the treasury". However I most often hear this on very credible news programs (The PBS News Hour and Frontline come to mind) so I am sure they know what they're doing...  Is it proper to use "the" before the name of a government organization, or is it optional? From what I understood, cardinal numbers are defined as:  $\aleph_0$ = the cardinality of $\mathbb{N}$ $\aleph_{n+1}$ = is the least cardinal number greater than $\aleph_n$  The continuum hypothesis states that the cardinality of $\mathbb{R}$ is  $\aleph_1$. I more or less understand this cannot be proven (does not follow from ZFC).  However, can it be proven dat there in fact is a 'least cardinal number' greater than $\aleph_0$?  Is it possible that there are sets with cardinality $\aleph_{1/2}$, $\aleph_{1/3}$, et cetera, so to speak?  Or expressed differently: is it possible that for every set A with cardinality CA > $\aleph_0$, there exists another set B with cardinality CB where CA > CB > $\aleph_0$?