Why is it that the below are true?  $\sum_{i=1}^n \hat{y}_ie_i= 0$  so far, I have, for the above: $\sum_{i=1}^n (\hat{y_i})(y_i-\hat{y_i})=0$ = $\sum_{i=1}^n \hat{y_i} y_i- \hat{y_i}^2$ so does the first term after the summation equal the squared $\hat{y_i}$ term? May be explained by some linear algebra, but not sure.  $\sum_{i=1}^nx_ie_i= 0$
In class we've seen that $a$ (the weights) must satisfy $$X^T (y-Xa) =0$$  Here $X$ is a $(n\times d)$ matrix (so we have $n$ samples in $\mathbb R^d$)  let's denote the residuals $r = y-Xa$. In our class notes, it is written that     The normal equations require the residuals to be orthogonal to each of the columns of $X$.   Why?     Therefore, the solution of the linear regression is a projection of $y$ onto the subspace spanned by $v_1 , \ldots , v_d$ (the columns of $X$)   Can you please explain this?
Allow us to vote to delete from the Android app Currently, the only way to vote to delete (and undelete, since you can't see deleted posts) in the Android app is to open the post in a browser, and then vote to delete from there.  Can we get delete vote functionality within the app, as well as the ability to delete our own posts?  Worth to mention: users , so it's possible in the API.  Related: Using $\epsilon-\delta$ to prove that a limit is not a specific number I want to use $\epsilon-\delta$ formulation to prove that $\lim_{x\to 1 } 2x+3 \neq 6$.  I know that I need to show that there exists an $\epsilon&gt;0$ such that for every $\delta&gt;0$ there exists $x\in \mathbb{R}$ such that $0&lt;\left| x-1 \right| &lt;\delta$ but $|2x-3|\geq \varepsilon$.  Will someone please guide me through the process?  Thanks a lot in advance Is there a way to consistently increase the vertical spacing between equation lines in a gather (or gather*) environment from amsmath?  Specifically, I want to produce something like  \begin{gather*} a = b \\[2ex] c = d \\[2ex] e = f \end{gather*}   without having to write [2ex] at the end of each equation line.  I can think of some hacks that redefine \\ to automatically add the spacing, but is there some cleaner/better way to achieve this? I want to trace a border in a box or minipage like this model. A border customizable in left angle on top and right angle in bottom. Somebody can help me? Thanks a lot JPierre Distance from the surface as an input node for use with volumetric materials How do I disable the screensaver/lock? When I'm watching a film in Mythtv the screen turns to black every 10 - 15 mins and I have to log back into Ubuntu. Very annoying!  How do I disable the black screen / screensaver / logout in Unity?  There no longer seems to be any options to turn the screen saver off as there were in Ubuntu prior to Unity. I want to use some constants, height and width, when creating an ellipse but it won't work with \newcommand. Here is a minimal example:  \documentclass[12pt, a4paper]{article}  \usepackage{amsthm, tikz} \usetikzlibrary{arrows, shapes, trees, positioning} \begin{document}  \begin{figure} \centering \begin{tikzpicture}       \newcommand*{\width}{2}%     \newcommand*{\height}{0.5*\width}%      \draw[fill=gray!40] (0, 0) ellipse (\width and \height); \node (Y) at (0,0) {\(Y\)};      \end{tikzpicture} \end{figure}  \end{document}    I get the following error:  error: line 14:  Package PGF Math Error: Unknown operator `a' or `an' (in '2and 0.5*2'). ...ay!40] (0,0) ellipse (\width and \height) I remember I saw a apt mirror somewhere containing older distributions but I cannot find it anymore. Does anybody know where to find it? Global setting of spacing between items in itemize environment for beamer I have a series of pending jobs in the queue,   $ atq 8   Mon Oct 29 13:21:00 2018 5   Mon Oct 29 10:36:00 2018 15  Mon Oct 29 13:31:00 2018 4   Mon Oct 29 10:35:00 2018 18  Mon Oct 29 15:55:00 2018 3   Mon Oct 29 10:31:00 2018 16  Mon Oct 29 15:54:00 2018 11  Mon Oct 29 13:24:00 2018 12  Mon Oct 29 13:24:00 2018 17  Mon Oct 29 15:53:00 2018 10  Mon Oct 29 13:23:00 2018 19  Tue Oct 30 15:43:00 2018 2   Mon Oct 29 07:41:00 2018 6   Mon Oct 29 10:41:00 2018 7   Mon Oct 29 13:20:00 2018 9   Mon Oct 29 13:22:00 2018   and plan to remove them job on Oct 29. Fortunately, atrm could remove multiple jobs  atrm 8 5 15 4    despite this, a iteration might be a better solution,   $ atq | grep "Oct 29" 18  Mon Oct 29 15:55:00 2018 3   Mon Oct 29 10:31:00 2018 16  Mon Oct 29 15:54:00 2018 11  Mon Oct 29 13:24:00 2018 12  Mon Oct 29 13:24:00 2018 17  Mon Oct 29 15:53:00 2018 10  Mon Oct 29 13:23:00 2018 2   Mon Oct 29 07:41:00 2018 6   Mon Oct 29 10:41:00 2018 7   Mon Oct 29 13:20:00 2018 9   Mon Oct 29 13:22:00 2018   How could I select the first field of the job number so as to iterating them? Fourier transform of the indicator of the unit ball How can I start the Blood on the Ice quest? I am currently part of the Stormcloaks and just finished Rescue from Fort Neugard. The Jarl wants to make me a thane and is telling me to buy a house, but his steward is telling me the house is unavailable due to some unpleasantness. I have already completed the 5 quests to help people of Eastmarch.  From what I can see online, I need to begin the Blood on the Ice quest. It is supposed to begin by walking in the windhelm graveyard at night, however every time I go there I don't see anyone.  Someone online said it's possible to miss the scene that triggers the quest if you go into Windhelm and leave without triggering it, but I am hoping this isn't the case. I am in Windhelm a lot because the Enchanting table, Blacksmith, and Fence are all in one location, so find it very convenient. The lady who is supposed to be murdered in the Graveyard (Susanna) is still alive in Candlehearth Hall, so I think I'm not bugged.  The wiki suggests that you have to "The quest will initiate after you entered Windhelm four times from another hold", however I have entered and left quite a few times during the course of my game and know I've been here way over 4 times.  I tried pickpocketing the key, however I don't automatically get the quest on entering the house, and there are a bunch of "Investigate InvestigationTarget" spots in the house. Also, I was reading the Butcher's journal and he was saying he almost caught Susanna when she left Candlehearth, however I have never seen her leave Candlehearth. Perhaps my glitch is she never leaves? I'll have to head to Windhelm on another character and check it out.  Also, I saw something online saying this quest won't trigger if you go past 245 in-game days. Would someone be able to confirm this for me? (Have the XBox version, so waiting 245 days is annoying)  Can someone tell me the exact steps to begin this quest? revtex4-1 and colortbl doesn't fill cells The MWE below shows that the \cellcolor command doesn't properly fill a table cell in revtex4-1 where it would do so in a simple article. Can anyone help me get fills that extend to the boundaries of my cells in revtex4-1?    \documentclass{revtex4-1} \usepackage{colortbl} \begin{document} \begin{tabular}{ |c|l|l| } \hline \rowcolor{red} A    &amp; B     &amp; C     \\ \hline Hello World         &amp; other     &amp; \cellcolor{blue}stuff\\ \hline \end{tabular} \end{document} Reducibility of polynomials modulo p Custom sorting (non-alphabetical) How to show loading spinner in jQuery? In Prototype I can show a "loading..." image with this code:  var myAjax = new Ajax.Request( url, {method: 'get', parameters: pars,  onLoading: showLoad, onComplete: showResponse} );  function showLoad () {     ... }   In jQuery, I can load a server page into an element with this:  $('#message').load('index.php?pg=ajaxFlashcard');   but how do I attach a loading spinner to this command as I did in Prototype? Install 18.04 server without network connection The latest version of Ubuntu server (18.04) seems to demand network configuration and refuse to boot without it. I have no desire to connect the server in question to the internet for anything, and have installed previous versions of Ubuntu server without network no questions asked.  Is a network connection an absolute requirement for the latest version of Ubuntu server? Or is there something I'm missing?  The installation cannot proceed past the network configuration page unless an ethernet connection is active, by my current estimates. I have no ethernet network within range of the machine so can't test it on an internet-less network. I only have WiFi within immediate range (which does have internet access) but it won't recognise the device and it should be simpler to get the installation to happen without any updates than to go to the effort of finding the drivers to support the WiFi adapter.  Note that this is NOT a duplicate of  since the new installer seems to be the real problem here. I have two tables, both with start time and end time fields. I need to find, for each row in the first table, all of the rows in the second table where the time intervals intersect.  For example:             &lt;-----row 1 interval-------&gt; &lt;---find this--&gt; &lt;--and this--&gt; &lt;--and this--&gt;   Please phrase your answer in the form of a SQL WHERE-clause, AND consider the case where the end time in the second table may be NULL.  Target platform is SQL Server 2005, but solutions from other platforms may be of interest also. Install Linux from Linux Decode Base64 data in Java