Summing Up Binomial Coefficients
Evaluation of ratio of two binomial expression
Consider the general linear regression model: $$y_i = \beta_0 + \beta_1x_{i1} + \beta_2x_{i2} + \cdots + \beta_px_{ip} + \epsilon_i = \mathbf{x}_i^t \beta + \epsilon_i$$  where $\textbf{x}_i = (1,x_{i1},x_{i2},\cdots,x_{ip})^T$, $\beta=(\beta_0,\beta_1,\cdots,\beta_p)^T$ and $\epsilon_i$ are iid N(0,$\sigma^2$).  I would like to see a complete proof of the following identity from first principles: $$\sum_{i=1}^n(y_i - \bar{y})^2 = \sum_{i=1}^n(\hat{y}_i - \bar{y})^2 + \sum_{i=1}^n(y_i - \hat{y}_i)^2$$ where $\hat{y}_i= \mathbf{x}_i^t \hat{\beta} $ ($\hat{\beta}$ is the least square estimator, $\bar{y}$ ia the sample mean of $y_i$).  I know that the two terms on the right can be obtained by subtracting and adding $\hat{y}_i$ on the left side. But this introduces a "cross term": $$\sum_{i=1}^n2(\hat{y}_i - \bar{y})(y_i - \hat{y}_i)$$  Many texts claim that this is zero, but I have not seen a general proof of this statement. How can this be shown? How to scale a tikzpicture including texts? It seems that the scale option scales only the length of lines, but not the size of texts. For instance, 1 and true and not scaled in the following code.  \begin{tikzpicture}[thick, scale=0.6] \draw [dashed] (1,12) -- (11,12); \node[above] at (4,11) {1}; \node[above] at (8,11) {true}; \end{tikzpicture}   Could anyone tell me how to scale everything together within a tikzpicture? Thank you very much!  PS: It is a picture in a presentation with Beamer. Kinetic energy conservation in a collision Kinetic energy conservation in collision.  In any type of collision type of collision if we take the system to comprised of both bodies then the net external force is zero. So the work done by external force is also zero. By the relation $W=K_f-K_i$ as $W$ is zero hence kinetic energy is conserved. But this not the case.   Can you tell me what is the flaw in my argument? Some people say that the argument has neglected the fact that some kinetic energy is transformed into heat. But heat is created due to the interactions between bodies during collision which is thus an internal force and thus shouldn't affect kinetic energy. NSString tokenize in Objective-C Does the review queue page show only reviews requiring your action? Does it differ, and when does it? This confusion came up in comments .  On the site I use most actively (RPG.SE), I've noticed that the counts for each review queue appear to only indicate the reviews available to me requiring my action. Just to be clear, I'm talking about this number here:        Since I'm a 10k user, that's pretty easy to tell: even after doing all my reviews, and the review page saying there's 0 items in each queue, I might still have that 10k notice in my top bar saying there's [5] reviews pending, or some other number. So they must still be there, just waiting on other users to finish them, and it just doesn't show them to me. This is fine, I like this behaviour.  However, on Meta SE about an hour ago, there was 1 item in the close vote review queue. I reviewed that item. The count stayed at 1 on the review page. When I clicked to re-enter the queue in case there were new items, I was presented with this:        Another user in that meta question I linked claims this is normal behaviour for them on their own site (Christianity.SE I think?).  What's going on here? Are the review queues supposed to be customised just to what I personally can actually review at the time? Is there a bug, are sites customised differently, or is there just some kind of caching thing leading to a time delay on the review count getting updated? (As they say, it is always caching, but is caching really the culprit here too?) Use Listing in newenvironment I am trying to do a new environment or command (i tried both) where i can put in the name, description and code of a Method in c++ and it gives me a new section with the MethodName, the code listed and the description below. But i am not able to use the listings environment in a new command or new environment.. Consider my MWE   \documentclass[a4paper,11pt]{article} \usepackage{listings}  \newcommand{\method}[3] { \section{#1}\label{#1} \begin{lstlisting} #2 \end{lstlisting} #3 }   \begin{document}  \method{MethodName}{Method Void MethodName()}{Description of the Method blablabla}  \end{document}   How can I fix this?   I would prefer to do it using a macro since I don't need an ending. When you add a new object into the blender scene, normally on the tool shelf a window will become available where you can put in the objects size or number of vertices etc.  These options:   For what-ever reason, when I now add an object I am no longer seeing that area where I can alter the measurements. Currently I want to use the Spin function but I need to alter it but I have no way of effecting how the spin operates. Does anyone know what I have done or how to fix it? Access a glyph on fontspec using a GID (Glyph ID) I'm trying to access a glyph, but it's only mentioned in the "Basic Latin and Latin 1" set for a font. The glyph has no name or unicode ID, but it does have a glyph ID or GID. fontspec doesn't mention possibilities for using this glyph. Neither does Adobe in the adobe feature file syntax:   I'd still like to be able to access a glyph through its ID, since it's the only way I can access it (I think).  My specific case requires to access the glyph ID 554 from Stevens Titling Pro Sable Brush. I will only post this font if it's strictly necessary, since I don't like to distribute these fonts to the wide world.  I posted an MWE containing another (free) font. This is not the font I intend to use, but perhaps a starting point to try and access glyphs manually.   \documentclass{article}  \usepackage{fontspec} \setmainfont{EB Garamond}  \parindent=0pt \begin{document}  Some text int EB Garamond. How can I access glyph 123 now?  \end{document} Checking if file is checked out through CSOM Is there a way to check if a file is checked out by another user? I am going trhough a list file by file and would like to avoid the "file is opened by another user" error. Something like this would be nice:  Guid id = new Guid(slideLibrary); // ID of Slide-Library. List list = ctx.Web.Lists.GetById(id); ListItemCollection items = list.GetItems(CamlQuery.CreateAllItemsQuery()); ctx.Load(items); // Loading all the fields System.Security.SecureString pwd = new System.Security.SecureString(); foreach (char c in "pwd".ToCharArray()) pwd.AppendChar(c);  ctx.Credentials = new SharePointOnlineCredentials(login, pwd); ctx.ExecuteQuery();  // Iterating through all the entries. foreach (var item in items) {     String currentID = item["ID"].ToString(); // Getting the ID of the current item.      if (!item.IsCheckedOut()) // This is the part I am looking for.     {        // Do stuff     }     else     {        Console.WriteLine("Item is blocked, skipping it.")     } }   I have yet not been able to find something fitting. How do I configure Apache 2 to run Perl CGI scripts? I would like to configure Apache 2 running on Kubuntu to execute Perl CGI scripts. I've tried some steps that I came across by googling, but nothing seems to work.  What is the right way of achieving this? The age of the universe Filter a Python list by predicate I would want to do something like:  &gt;&gt;&gt; lst = [1, 2, 3, 4, 5] &gt;&gt;&gt; lst.find(lambda x: x % 2 == 0) 2 &gt;&gt;&gt; lst.findall(lambda x: x % 2 == 0) [2, 4]   Is there anything nearing such behavior in Python's standard libraries?  I know it's very easy to roll-your-own here, but I'm looking for a more standard way. Lost access to sudo sudo: unable to resolve host   I think I need to edit the /etc/hosts file to make an entry for 127.0.1.1 PC name.  But how can I do that if I can't access sudo? It seems to have gone since I updated to 13.10.  I have tried nano, which still doesn't work. Similar matrices and field extensions Given a field $F$ and a subfield $K$ of $F$. Let $A$, $B$ be $n\times n$ matrices such that all the entries of $A$ and $B$ are in $K$. Is it true that if $A$ is similar to $B$ in $F^{n\times n}$ then they are similar in $K^{n\times n}$?   Any help ... thanks! Colors in Photoshop CS6/CC look different than in browser? The code for reference is this  @article{matcontcl,  title= {MATCONT and CL MATCONT},  author = {A. Dhooge, W. Govaerts, Yu.A. Kuznetsov, W. Mestrom, A.M. Riet and  B.Sautois},  year = {2006},  journal = {Continuation toolboxes in matlab}, }   This is the error that follows  This is BibTeX, Version 0.99d (TeX Live 2015/W32TeX) The top-level auxiliary file: PropuestaInvestigacion.aux The style file: abbrv.bst Database file #1: biblio.bib Too many commas in name 1 of "A. Dhooge, W. Govaerts, Yu.A. Kuznetsov, W. Mestrom, A.M. Riet and B.Sautois" for entry matcontcl while executing---line 1049 of file abbrv.bst Too many commas in name 1 of "A. Dhooge, W. Govaerts, Yu.A. Kuznetsov, W. Mestrom, A.M. Riet and B.Sautois" for entry matcontcl while executing---line 1049 of file abbrv.bst Too many commas in name 1 of "A. Dhooge, W. Govaerts, Yu.A. Kuznetsov, W. Mestrom, A.M. Riet and B.Sautois" for entry matcontcl while executing---line 1090 of file abbrv.bst Too many commas in name 1 of "A. Dhooge, W. Govaerts, Yu.A. Kuznetsov, W. Mestrom, A.M. Riet and B.Sautois" for entry matcontcl while executing---line 1090 of file abbrv.bst (There were 4 error messages)   How could I fix it? Why Java needs Serializable interface? We work heavily with serialization and having to specify Serializable tag on every object we use is kind of a burden. Especially when it's a 3rd-party class that we can't really change.  The question is: since Serializable is an empty interface and Java provides robust serialization once you add  implements Serializable - why didn't they make everything serializable and that's it?    What am I missing? My internet connection is very slow. I suspect someone in the network is using a BitTorrent client which takes huge amount of bandwidth.  Is there a way to detect who is using my bandwidth (network sniffing tools etc)?  I should have pointed out that I have no access to the router, what I am looking for is a way of detecting someone's MAC/IP if she uses Bittorrent. What figure of speech is this? Why cannot fermions have non-zero vacuum expectation value?