Let us consider the simple linear model $y = \beta_0 + \beta_1 X + \epsilon$, where $y$ is real number, $X$ a matrix of reals and $\epsilon$ is the random "noise". The least-square estimate of the coefficients $\beta_0$ and $\beta_1$ does not depend on the nature of the "noise" term $\epsilon$. It is reasonable to assume that the expectation of $\epsilon$ is zero. For the regression problem really computes $E(y|X)$. It is also reasonable to require that $\epsilon$ has the same variance across the range of $X$. Why do we also require $\epsilon$ to be normally distributed? What does wrong it is not normally distributed but has a distribution symmetric around zero?
In linear regression, each predicted value is assumed to have been picked from a normal distribution of possible values. See below.  But why is each predicted value assumed to have come from a normal distribution? How does linear regression use this assumption? What if possible values are not normally distributed?
What steps does a manuscript typically go through from submission to publication (or rejection) in a typical journal? How are these steps referred to, in particular by editorial systems, and how long do they each typically take?  Note that this question is about the typical situation and hence not about:   Journals with an atypical workflow, e.g. those that allow for an instantaneous reviewer–author interaction. Exceptional steps or rare occurrences such as withdrawal or .   This is a canonical question on this topic as per . Due to its nature, it is rather broad and not exemplary for a regular question on this site. Please feel free to improve this question. Can the Room of Requirement provide anything if needed? For example:   James Potter wanted to hide from Voldemort, it would have served as a perfect hiding place. Harry Potter wanted all the Hocruxes, he should have gone straight to the room of requirement where he would have found all the Hocruxes along with the Sword. All the muggle borns of the wizarding community could have taken refuge in the room of requirement. Can someone meet a dead person in the room of Requirement if needed? Would it have been possible for Harry to go in past in order to see Dumbledore for the explanation of many things? Can the room duplicate something? For instance, Harry needed the Elder wand; with Voldemort having it, could he still get it? Someone wishes to be knowledgeable than Dumbledore, would the seeker find his desired wish by finding books and things?   Who created the room of requirement (surely not Salazar)? Was it beyond Dumbledore's magic to create such a place? What happens to folks who get question banned, by and large? There is a steady stream of duplicates of  coming in lately. It's got me wondering. Roughly speaking, out of say 100 folks who get this ban, how many    wander away and never interact with SO again?   do the sorts of things that might lift a ban, but don't get it lifted? do the sorts of things they should, and lift the ban? post a question of their own on Meta which we close as a dupe?   Among the continue-to-interact folks, is there a difference in success rate between those who post on Meta about it (motivated, but not good rules-readers, who nonetheless get customized advice) and those who do not (better rules readers, but working to some extent blind) - which do better?  Is there a reasonable chance of recovering from a ban, assuming you care enough to try? How to handle a deliberate duplicate question Kubuntu - can not enter wifi credentials after adding external wifi card My ethernet connection is quite unreliable (It uses powerline adapters) so I bought an external wifi adapter. I have plugged it in and run the command sudo ip address add 192.168.0.39/24 brd + dev enp7s0, and KDE has detected it. Unfortunately, it doesn't seem to realise it is a wireless network and therefore needs credentials. Where I could normally find a place to enter credentials (the network widget, system settings) there are none. KDE reports that the device is connected in the UI. How do I make it work out that it is wireless and therefore needs credentials? Edit: With ethernet plugged out, (USB) adapter plugged in: $ ip address show 1: lo: &lt;LOOPBACK,UP,LOWER_UP&gt; mtu 65536 qdisc noqueue state UNKNOWN group default qlen 1000     link/loopback 00:00:00:00:00:00 brd 00:00:00:00:00:00     inet 127.0.0.1/8 scope host lo        valid_lft forever preferred_lft forever     inet6 ::1/128 scope host         valid_lft forever preferred_lft forever 2: enp7s0: &lt;NO-CARRIER,BROADCAST,MULTICAST,UP&gt; mtu 1500 qdisc fq_codel state DOWN group default qlen 1000     link/ether 04:d9:f5:8a:f5:e0 brd ff:ff:ff:ff:ff:ff  With ethernet plugged in, adapter plugged in: 1: lo: &lt;LOOPBACK,UP,LOWER_UP&gt; mtu 65536 qdisc noqueue state UNKNOWN group default qlen 1000     link/loopback 00:00:00:00:00:00 brd 00:00:00:00:00:00     inet 127.0.0.1/8 scope host lo        valid_lft forever preferred_lft forever     inet6 ::1/128 scope host         valid_lft forever preferred_lft forever 2: enp7s0: &lt;BROADCAST,MULTICAST,UP,LOWER_UP&gt; mtu 1500 qdisc fq_codel state UP group default qlen 1000     link/ether 04:d9:f5:8a:f5:e0 brd ff:ff:ff:ff:ff:ff     inet 192.168.0.51/24 brd 192.168.0.255 scope global dynamic noprefixroute enp7s0        valid_lft 863988sec preferred_lft 863988sec     inet6 fe80::7eb1:eca2:96a0:fe5c/64 scope link noprefixroute         valid_lft forever preferred_lft forever  With just ethernet: 1: lo: &lt;LOOPBACK,UP,LOWER_UP&gt; mtu 65536 qdisc noqueue state UNKNOWN group default qlen 1000     link/loopback 00:00:00:00:00:00 brd 00:00:00:00:00:00     inet 127.0.0.1/8 scope host lo        valid_lft forever preferred_lft forever     inet6 ::1/128 scope host         valid_lft forever preferred_lft forever 2: enp7s0: &lt;BROADCAST,MULTICAST,UP,LOWER_UP&gt; mtu 1500 qdisc fq_codel state UP group default qlen 1000     link/ether 04:d9:f5:8a:f5:e0 brd ff:ff:ff:ff:ff:ff     inet 192.168.0.51/24 brd 192.168.0.255 scope global dynamic noprefixroute enp7s0        valid_lft 863960sec preferred_lft 863960sec     inet6 fe80::7eb1:eca2:96a0:fe5c/64 scope link noprefixroute         valid_lft forever preferred_lft forever  With nothing: 1: lo: &lt;LOOPBACK,UP,LOWER_UP&gt; mtu 65536 qdisc noqueue state UNKNOWN group default qlen 1000     link/loopback 00:00:00:00:00:00 brd 00:00:00:00:00:00     inet 127.0.0.1/8 scope host lo        valid_lft forever preferred_lft forever     inet6 ::1/128 scope host         valid_lft forever preferred_lft forever 2: enp7s0: &lt;NO-CARRIER,BROADCAST,MULTICAST,UP&gt; mtu 1500 qdisc fq_codel state DOWN group default qlen 1000     link/ether 04:d9:f5:8a:f5:e0 brd ff:ff:ff:ff:ff:ff  lsusb, adapter plugged in: Bus 004 Device 001: ID 1d6b:0003 Linux Foundation 3.0 root hub Bus 003 Device 002: ID 046d:c31c Logitech, Inc. Keyboard K120 Bus 003 Device 001: ID 1d6b:0002 Linux Foundation 2.0 root hub Bus 002 Device 001: ID 1d6b:0003 Linux Foundation 3.0 root hub Bus 001 Device 003: ID 1d57:32da Xenta 2.4GHz Receiver (Keyboard and Mouse) Bus 001 Device 004: ID 0bda:b812 Realtek Semiconductor Corp. 802.11ac NIC Bus 001 Device 001: ID 1d6b:0002 Linux Foundation 2.0 root hub  I'm not adding it with it plugged out because it's obviously the Bus 001 Device 004: ID 0bda:b812 Realtek Semiconductor Corp. 802.11ac NIC. There were no restarts between any of these changes. Best way to strike out a text What is a word for someone that only does something to benefit them? Take this paragraph for example: I am a follower, not a leader. Hell, I'm not even that good of a follower either, just someone who will do your bidding for the right price. Even then, if it doesn't benefit me -- or put you in debt to me -- I won't do it. What to write in visa application form and what documents to submit as an unregistered freelancer? There are many visa applicants who are working as an unregistered freelancer (photographer, construction contractor, fashion designer, journalist etc ). Some of these freelancers make really handsome monthly income and don't really need to work as a full time employee. Most of them receive variable amount of payments (cash, cheques, demand drafts etc) When it comes to filling a visa application form (USA, UK, Schengen etc), there is always an employment section in all visa form, eg for Schengen visa employment form :    This is a very important factor to make an application really strong.  Questions:   1 Unregistered freelancers can just simply write their profession? what documents to produce along with the application?  2 Bank statements with variable methods of payments could convince the visa officer that these are all legitimate payments? How to properly scale image in uv editor Hello to anyone who come here and help out or read. I have an issue with the uv editor, I have been trying to make an proper eye. The issue is that I can't figure out how to scale this correctly.    Is there anything I can do to make the eye colors or texture? Consider the group $\mathbb{Q}$ under addition of rational numbers. If $H$ is a subgroup of $\mathbb{Q}$ with finite index, then $H = \mathbb{Q}$.  I just saw this on our exam earlier and was stumped on how to show this. Any ideas? Why isn't the eigenclass equivalent to self.class, when it looks so similar? I am stuck in a question where energy conservation is failing and momentum conservation is correct. I think I might be doing something wrong, that's why I'm asking this question. The problem is as follows:     A bullet of mass $25\,g$ is fired horizontally into a ballistic pendulum of mass $5.0\,kg$ and gets embedded in it. If the centre of pendulum rises by a distance of $10\,cm$, find the speed of the bullet.   (H.C. Verma, Centre of Mass, Q47)     Let the mass of the bullet be $m=25\,g$. Let the mass of the pendulum be $M=5\,kg$. Let the peak height be $h=0.1\,m$. Let the initial and final velocities be $u$ and $v$ respectively.  Method 1: (Momentum Conservation)  $$mu=(M+m)v \implies v=\frac{mu}{M+m}\\ \text{Also, }\frac{1}{2}(M+m)v^2=(M+m)gh\\ \implies u^2=2\biggl(\frac{M+m}{m}\biggr)^2gh\\ \implies u=201\sqrt2 \text{ m/s}$$  Method 2: (Energy Conservation)  Since both the masses move together after the collision, and because the velocity at highest point is null, therefore: $$\frac{1}{2}mu^2=\frac{1}{2}(M+m)v^2=(M+m)gh\\ \implies u^2=2gh\biggl(\frac{M+m}{m}\biggr) \implies u=\sqrt{402}$$    To summarize myself, I am curious about the following: Why do the results differ? Shouldn't the energy be conserved as well as the momentum? Since it should be, then what is the flaw in my calculations? Webforms and jQuery, how to match the ID's? I want to use jQuery with asp.net webfoms.  Do I need to get a special toolkit so the .net controls spit out friendly Control ID's?  Reason being, I don't want to write javascript referencing my html ID's like control_123_asdfcontrol_234.  Has this been addressed in version 3.5?  (I remember reading you have to get some special dll that makes ID's friendly). Repeating the consonant in many words in a sentence or phrase In the movie 'V for Vendetta' you have for example (bold part):     Evey: Who are you?        V. : Who? Who is but the form following the function of what and what I am is a man in a mask.      Evey: Well I can see that.        V. : Of course you can, I’m not questioning your powers of observation, I’m merely remarking upon the paradox of asking a masked man who he is.      Evey: Oh, right.      V. : But on this most auspicious of nights, permit me then, in lieu of the more commonplace soubriquet, to suggest the character of this dramatis persona.      V. : Voila!   In view humble vaudevillian veteran, cast vicariously as both victim and villain by the vicissitudes of fate. This visage, no mere veneer of vanity, is a vestige of   the “vox populi” now vacant, vanished. However, this valorous visitation of a bygone vexation stands vivified, and has vowed to vanquish these venal and virulent vermin, van guarding vice and vouchsafing the violently vicious and voracious violation of volition. The only verdict is vengeance; a vendetta, held as a votive not in vain, for the value and veracity of such shall one day vindicate the vigilant and the virtuous. Verily this vichyssoise of verbiage veers most verbose, so let me simply add that it’s my very good   honour to meet you and you may call me V.       Evey: Are you like a crazy person?      V. : I’m quite sure they will say so.   What do you call sentences like these? And do you know some other ones? How to get the pid of the last executed command in shell script? I want to have a shell script like this:  my-app &amp; echo $my-app-pid   But I do not know how the get the pid of the just executed command.  I know I can just use the jobs -p my-app command to grep the pid. But if I want to execute the shell multiple times, this method will not work. Because the jobspec is ambiguous. I can't get into my field research prize Cleaning PCBs... using water? I found  where a technician with a lot of experience seems to clean his PCBs using water, and then he just puts it in the sun so it can dry. I was just amazed to see the circuit keeps working as intended, he says he keeps doing this all the time and several times, however I doubt this is normal.  Which leave me some questions:   What are the recommended methods to clean huge PCBs like the one in the video? What happens to charged capacitors when water shorts them out? Solder joints do not get any kind of corrosion? Is the antisolder mask waterproof? Extracting phone number from string Every time I click to open a link, other windows start opening. They all want to sell me Detox your Mac or have warnings about how my Mac is at risk or infected.  How can I check for malware? Adding boolean yes/no field in ArcGIS Desktop? How does one add a field to an ArcGIS feature class with a boolean data type? That is an attribute where the allowed value is only one of a pair such as 1/0, Yes/No, On/Off, Present/Not-present, etc.   A boolean data type is not available in the Data Type pick-list.