As I was working my way through my book about statistics, I came across the topic of linear regression. During the chapter the author begins with explaining that you want to minimize the residuals in order to make your y = a + bx as good a fit as possible: I do understand this, but halfway the chapter all of a sudden the residuals change into sum squares of residuals. Why is this done? I have been googling, but couldn't find the right answer. Who would like to help me understand why the sums of squares of the residuals is used instead of just the sums of residuals?  Kind regards, Bas
Why are we using the squared residuals instead of the absolute residuals in OLS estimation?  My idea was that we use the square of the error values, so that residuals below the fitted line (which are then negative), would still have to be able to be added up to the positive errors. Otherwise, we could have an error of 0 simply because a huge positive error could cancel with a huge negative error.  So why do we square it, instead of just taking the absolute value? Is that because of the extra penalty for higher errors (instead of 2 being 2 times the error of 1, it is 4 times the error of 1 when we square it).
Minimum of the Gamma Function $\Gamma (x)$ for $x>0$. How to find $x_{\min}$? As most of you know, in the Microsoft Store, there are . This means that on Windows I can emulate Ubuntu and have the Ubuntu command line directly on Windows.  The question is very easy: what can’t I do from the Ubuntu command line emulated in Windows that I can do on a proper Linux-based Ubuntu? Is it useful to download this Ubuntu application, install it, and work just with it instead of the real OS? Is it possible to install all the development libraries? Can I write (or not) device drivers? In other words: what are the limits?  What features of Ubuntu Linux-based are missing from Ubuntu-on-Windows?  New answers are welcome: I know that every software is always changing by improving characteristics and features! Do we ever get more information about the Entwives? During my recent re-reading of The Two Towers I was struck again by a question that has bothered me since I was a youngling: What on earth is up with the Entwives?  Treebeard says they went away in the distant past and just... got lost?  Did Tolkien ever make mention of them again, or is this one of those unsolved mysteries of Middle Earth? bordermatrix with blocks I need to write a complicated matrix, that has a structure as in the attached picture. How to edit Parameters for an Object after it is created? When you first add a cylinder, you have the option to change the number of vertices, etc, but once you do anything else in blender, it seems you no longer can edit those parameters.   Is there a setting anywhere or an add-on that allows these parameters to be edited later on? If not, how easy would such an addon/feature be to create for anyone reading this? Better way of saying "those who are curious"? How to mesh codeigniter with ajax Relation Between Bayesian Estimation and Maximum a posteriori estimation Is maximum a posteriori estimation some kind of Bayesian Estimation?   If yes, can you point out other Bayesian estimators?  Edit:  So I've come to know the following (don't know if they are correct):  MAP finds the mode of the posterior, and Bayesian Estimator finds the distribution of that posterior with respect to the estimating parameters. And in order for Bayesian Estimator to find the optimal parameters, some particular risk function (like Mean Squared Error, 0/1 error etc.) must be defined.  So it seems these two estimators have nothing in common except they both incorporate prior into their estimation. Or is it possible that MAP is some special case of Bayesian Estimator with some particular risk function. How to show to the user a progression in a script? Changing data type in ArcGIS attribute table? I want to be able to pull in the error log from BIOS across a network I want to be able to pull in the error log from BIOS across a network. Looking at Win32_BIOS in MSDN I did not see anything defining the error log. Would love to do this in C# with WMI, but am open to suggestions. Is it possible?  Win32_BIOS does not have a property (don't know if that is the right term) that contains the BIOS error log. Is there a library, API, etc. that I can use to pull this information locally or from the network? I have been using LaTeX for a long time now, but still all my document files look a bit messy. Now I want to get rid of this bad habit and get some order into my code.  That is why I am wondering whether there are any coding style guidelines for LaTeX. Not necessarily anything official. It could for example make recommendations on how to format your code with respect to:   Setting comments in the text/preamble Whether to highlight sections/subsections etc. by some comments How to indent environements How to organize your preamble to make it readable etc.   If nothing as such exists (yet), it would be great if you could just post how you do it if you think your code looks rather nice. How can I render bokeh circles?  Nothing I do seems to work.   I tried using an empty as the focus point for a cube, with some point lamps in the background with about 2000 strength, but it doesn't work. It just makes everything blurry.  I also raised the blades to 4/5/6/12, and it doesn't make a difference.  I'm using Blender 2.74. I recently updated my operating system from Ubuntu 13.04 to Ubuntu 13.10. Since then, I am facing difficulties compiling my TeX code in which the french babel package is called. Please note that all my sources were compiling very fine before the system upgrade. However, now, given the following header:   \usepackage[francais]{babel}  I receive the following error:  ! Package babel Error: Unknown option `francais'. Either you misspelled it   What should I do? Please note that if I remove this part of code (\usepackage[francais]{babel}), everything is compiling well. I also tried it with french, and I receive the same result. Thank you in advance for your help.  MINIMUM WORKING EXAMPLE : \documentclass[11pt,a4paper]{article} \usepackage[utf8]{inputenc} \usepackage[francais]{babel} \usepackage[T1]{fontenc} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{amssymb}  \begin{document} This is a MINIMUM WORKING EXAMPLE. \end{document}   ! Package babel Error: Unknow option `francais'. Either you misspelled it Index entries duplicated for captions I have a proof and need some feedback. It seems really obvious that the statement is true but it is always the obvious ones that are a little trickier to prove. So I would appreciate any feedback. Thank you!  Here is what I am asked to prove:     If $n$ is composite then $(n-1)! \equiv 0 \pmod n$.   Proof:  $n$ is composite $\implies n=ab$ where $a,b \in \mathbb{Z}$ and $0&lt;a,b&lt;n$.  Case 1: If $a=b$ then $n=a^{2}$. Now $n \mid (n-1)! \implies a \mid (n-1)!$, so $$\begin{aligned} (n-1)! &amp;\equiv 1\times 2\times \dotsb \times a \times\dotsb\times (n-a)\times\dotsb\times (n-1) \\ &amp;\equiv 1\times 2\times \dotsb\times a \times\dotsb\times -a\times\dotsb\times -1 \\ &amp;\equiv 0 \pmod n \end{aligned}$$  Case 2: $0&lt;a&lt;b&lt;n$.  Then, since $a \mid n$, $b \mid n$ and $n \mid (n-1)!$ we have that $a \mid (n-1)!$ and $b \mid (n-1)!$.  So this implies $(n-1)! \equiv 1\times 2\times \dotsb\times a \times\dotsb\times b\times\dotsb\times (n-1) \equiv 0 \pmod n$, Q.E.D. There's a problem statement:     For each $m \in \mathbb{N}$, we construct a sequence $m_0$, $m_1$, $m_2,\dots$ denoted $S_m$, recursively via $m_0=m$ and      $$m_{i+1} = m_i + \left\lfloor \sqrt{m_i} \right\rfloor$$      for all $i \ge 0$.   Here, $\lfloor x \rfloor$ is the floor of $x$, the greatest integer less than or equal to $x$.   Hence, we have $\left\lfloor \sqrt{10} \right\rfloor=3$ and $\left\lfloor \sqrt{29} \right\rfloor=5$.      Show that for each positive integer $m$, the sequence $S_m$ contains the square of some integer.   I'm pretty certain that this can be proved with induction. I am just not quite sure what to induct on. Examining examples shows that $S_m$ always results in a perfect square eventually, though I'm not sure how to prove it. How do I fix 'Invalid JSON' errors? I've been at this for almost two hours and no one seems to have the same problem as I and I doubt this will be solved but I'll try anyway.  this is the code  /tellraw @p ["Would you like to teleport?",{"text":"Yes","color":"green","bold":"true","clickEvent":{"action":"run_command","value":"/tp @p ~ ~4 ~ "},"hoverEvent":{"action":"show_text","value":{"text":"Confirm"}},{"text":"No","color":"red","bold":"true","clickEvent":{"action":"run_command","value":"/tellraw @p{"text":"Come back when you want to teleport"}"}}}]   this part is fine  /tellraw @p ["Would you like to teleport?",{"text":"Yes","color":"green","bold":"true","clickEvent":{"action":"run_command","value":"/tp @p ~ ~4 ~ "},"hoverEvent":{"action":"show_text","value":{"text":"Confirm"}}   it's just when I add this  ,{"text":"No","color":"red","bold":"true","clickEvent":{"action":"run_command","value":"/tellraw @p{"text":"Come back when you want to teleport"}"}}}]   Minecraft gives me the error:     Invalid JSON at line 1 column 203   I've tried to space it out and figure out what column 203 is but I can't, I don't know what I did. Anyone got any ideas? unbalaced data set in classification tasks How to exclude some files from filename expansion mechanism in bash?