I know the one for the one variable version... β =∑ xiyi / ∑ x2  but nobody seems to have the one for the multiple variable version is there a way to do it by hand for something like  y = β1x1 + β2x2  (no intercept)  EDIT: this is about the MULTIPLE variable model equation (MUST go through the origin)..the answer provided is the one I tried that doesn't go through the origin
In An Introduction to Statistical Learning (James et al.), in section 3.7 exercise 5, it states that the formula for $\hat{\beta}_1$ assuming linear regression without an intercept is  $$\hat{\beta}_1 = \dfrac{\displaystyle\sum\limits_{i=1}^{n}x_iy_i}{\displaystyle \sum\limits_{i=1}^{n}x_i^2}\text{,}$$ where $\hat{\beta}_0 = \bar{y}-\hat{\beta}_1\bar{x}$ and $\hat{\beta}_1 = \dfrac{\displaystyle S_{xy}}{S_{xx}}$ are the usual estimates under OLS for simple linear regression ($S_{xy} = \displaystyle\sum\limits_{i=1}^{n}(x_i - \bar{x})(y_i - \bar{y})$).  This is not the actual exercise; I am merely wondering how to derive the equation. Without using matrix algebra, how do I derive it?   My attempt: with $\hat{\beta}_0 = 0$, we have $\hat{\beta}_1 = \dfrac{\bar{y}}{\bar{x}} = \dfrac{S_{xy}}{S_{xx}}$.  After some algebra, it can be shown that $\displaystyle S_{xy} = \sum\limits_{i=1}^{n}x_i^2 - n\bar{x}\bar{y}$ and $\displaystyle S_{xx} = \sum\limits_{i=1}^{n}x_i^2 - n\bar{x}^2$. From here, I'm stuck.
Continuous v. per-chapter/section numbering of figures, tables, and other document elements Some document elements (e.g., figures in the book class) are numbered per chapter (figure 1.1, 1.2, 2.1, ...). How can I achieve continuous numbering (figure 1, 2, 3, ...)?  And vice versa: Some document elements (e.g., figures in the article class) are numbered continuously. How can I achieve per-section numbering?  \documentclass{book}% for "vice versa" variant, replace `book` with `article`  \begin{document}  \chapter{foo}% for "vice versa" variant, replace `\chapter` with `\section`  \begin{figure} \centering \rule{1cm}{1cm}% placeholder for graphic \caption{A figure} \end{figure}  \end{document}   Bonus question: Is it possible to adjust the numbering of the sectioning headings themselves? Can I, e.g., switch from per-chapter to continuous numbering of sections in the book class? $a+b+c =0$; $a^2+b^2+c^2=1$. Prove that: $a^2 b^2 c^2 \le \frac{1}{54}$ If a,b,c are real numbers satisfying $a+b+c =0; a^2+b^2+c^2=1$.  Prove that $a^2 b^2 c^2 \le \frac{1}{54}$. The names of the derived functors $\operatorname{Tor}$ and $\operatorname{Ext}$ seem quite cryptic to me. Does anyone know what these abbreviations stand for? I would be glad if someone could tell me where these names come from. Prerequisites for classical mechanics by Susskind So I am an undergraduate in Electrical Engineering. We had a course on Physics in our freshman year which is equivalent to Classical Mechanics I as taught in MIT. I am interested in studying advanced classical mechanics (which includes Lagrangian formulation and other stuff) as equivalent to Classical Mechanics lecture by Susskind. I wanted to know are they any prerequisites which I should know about before taking this course.   In general what are the prereqs for this course? In my script, I have for loop over many cube objects (~1000) and the treatment is very slow. Looking more in details, I notice that in the same amount of loops:   if I use python operation or simple blender operation like  obj = bpy.data.objects[obj_name]   or   obj.select = True   it takes less than 0.08s (for all 1000 objects) but as soon as I start using blender operators like:  bpy.ops.object.select_pattern() # or bpy.ops.object.duplicate() # or bpy.ops.object.location_clear() # or bpy.ops.object.transform_apply() # etc.   then, the performance drops down deeply with more than 6s for the same amount of objects.   And, a last information, if I reduce the amount of objects from 1000 to 50, the same set of operations with bpy.ops is 0.03s - so extrapolating, it would be 0.6s for the 1000 objects and not 6s. It is as is with 1000 objects, we loose a factor 10 in speed in comparison than with 50 objects.  I tried reducing the complexity of my mesh changing the cubes in planes but it had no effect at whole on performance.  Is there something particular to know to improve these performance or a way to use the bpy.ops methods with better performances? Obviously, I am missing something important probably. How do I compute the normalisation of $A=k[X,Y]/(Y^3 - X^5)$? I'm trying to solve exercise 4.7 in Reid's UCA:  "Find the normalisation of $A=k[X,Y]/(Y^3 - X^5)$."  I can easily show $A$ is not normal: let $x$ and $y$ denote the images of $X$ and $Y$ in $A$. Thus $y^3 = x^5$. So there exists $t=y/x\in\operatorname{Frac} (A)$ which is a root of the monic polynomial $T^3 - x^2 \in A[T]$. But since $t\notin A$, $A$ is not normal.  However, I don't know how to compute the normalisation of $A$; I have not seen dimension theory developed, so  to a similar question doesn't really help me. Similarly I cannot try and apply something like  to a related question, because in this case the map $k[X,Y]\rightarrow k[t]$ sending $X\mapsto t^3, Y\mapsto t^5$ is injective so the image isn't isomorphic to $A$  UCA never really gives a good explanation on how to actually compute normalisations, so I'd be grateful if anyone could walk me through it. Can I nohup/screen an already-started process? How do I send SMS from PC through Android Phone or to Android Phone? I'm looking for an app that will let me type text messages on my PC and send the SMSs directly from the PC through my phone, or save the messages to the phone for later use.  I'm basically looking at something like Nokia PC Suite's equivalent.  EDIT:  Google Voice is only for US, doesn't work in India at least, and also defeats the purpose (it will go through the internet, why, when it's possible through the usb cable/modem/wifi). DesktopSMS is a good program, but kept crashing, for some reason. PDANet worked for me. But I liked the tiny . It's weird, and I had to change the bluecove library jar file for Windows 7 x64, but it's compact (a concern for me). Does a creature with Lifelink provide lifegain equal to its power, or the defender's toughness? I have recently began playing a deck that has a number of creatures with lifelink in it.  I want to be certain I understand the mechanic and the following question occurred to me.  Which damage total do you use to determine the life gain from lifelink?  I had assumed that if  a 3/3 creature with lifelink was blocked by a 2/2 creature that the life gain total would be 2, the maximum that the blocker can absorb before dying.  This seems to be incorrect, as when I read the example attached to CR 119.4c      [...] attacks with a 3/3 creature with wither and lifelink. It’s blocked by a 2/2 creature, [...]. The damage event starts out as [3 damage is dealt to the 2/2 creature, 2 damage is dealt to the 3/3 creature]   Have I been short changing myself? If matrix $A$ is unitary and $B^2=A$, is $B$ necessarily unitary? Why did I just get the Announcer Badge and the Booster badge? Today I got both the Announcer badge and the Booster badge for  that I asked last year.   I don't remember ever sharing a link to it, and it seems odd to me that I would get both badges in one day, implying that there were at least 276 people who viewed it today from a link I don't remember ever sharing.  What's going on? I am a novice user and I am trying to install Oracle Java. The process calls for me to access /usr/local/java, but here is the problem. I get as far as /usr/local, then this is the message I get:  leonard@leonard-MT6452:/usr/local$ dir bin  etc  games  include  java  lib  man  sbin  share  src  leonard@leonard-MT6452:/usr/local$ cd /java/ bash: cd: /java/: No such file or directory  leonard@leonard-MT6452:/usr/local$ rm -r ~/java rm: cannot remove ‘/home/leonard/java’: No such file or directory   Help? Solve the functional equation $f(xy) = f(x)f(y) - f(x + y) + 1$ and $f(1) = 2$ I'm working on this problem already, the domain and co-domain are the set of Rational Numbers. we see that setting $x = 1$ and $y = n$, we obtain $f(n + 1) = f(n) + 1$  But I'm trying to prove that $f(n) = n + 1$ for all $n$, the case when $n = 1, 2$ is obviously true, how do I approach this via induction? Passport validity for Canada I am traveling from Boston to Canada by cruise ship. The first port of arrival is on July 30 and the last port in Canada is on August 4. Then I'm flying on August 5 from Montreal to California. My passport is valid until August 20th. Will I have a problem? Proper capitalization of commonly used acronyms and initialisms I was always under impression, that acronyms ought to be written all caps. However reading  site very often I see some of the common acronyms written as proper names (first cap). For example "Nato" instead of "NATO".   I know that BBC is quite strict in proper English usage, so what would be the reason behind this? Why am I still getting a password prompt with ssh with public key authentication? I'm working from the URL I found here:    My ssh client is Ubuntu 64 bit 11.10 desktop and my server is Centos 6.2 64 bit. I have followed the directions. I still get a password prompt on ssh.  I'm not sure what to do next. I was wondering if there is any way to escape a CDATA end token (]]&gt;) within a CDATA section in an xml document. Or, more generally, if there is some escape sequence for using within a CDATA (but if it exists, I guess it'd probably only make sense to escape begin or end tokens, anyway).   Basically, can you have a begin or end token embedded in a CDATA and tell the parser not to interpret it but to treat it as just another character sequence.  Probably, you should just refactor your xml structure or your code if you find yourself trying to do that, but even though I've been working with xml on a daily basis for the last 3 years or so and I have never had this problem, I was wondering if it was possible. Just out of curiosity.  Edit:  Other than using html encoding... On Irix's  4Dwm, there was an ability to minimise windows into a box (contrary to the task bar used by modern window managers). I have seen this also on an old HPUX.  See the "console" square in the linked image:    Is it possible to accomplish on Ubuntu, either with a plugin or maybe some  window manager other than Unity? I can't play Pokemon GO! What's wrong? Pokemon GO isn't working at all for me right now. I'm in one of the following circumstances and can't do anything:   My game is displaying a "Try Again" message I'm stuck on the Loading Screen When I sign in I get a message that the servers are experiencing problems. I see the map but nothing is loaded, and my team color is wrong The "loading" Pokeball just ends up spinning and I can't catch or interact with things When I try to catch a Pokemon, the Pokeball just sits on my screen doing nothing Gym opponents will drop to 1 HP and won't take any more damage or attack When I open a pokestop, the pokestop image and the name of the pokestop does not load.   What's causing this? Is there a way to fix it? Some fields like Economics and Maths have their work in progress published as "working papers" with notes like "work in progress, do not cite or quote without the author's permission."Sometimes they upload these to their own websites or to their universities websites. I don't see much of this going on in my own field (sociology). I have heard from people that are afraid of having their work scooped or that fear that work published in this way will not be considered as "unpublished" by journals and conferences.  What are the advantages of making work in progress available in this way?