I understand the interpretation of what occurs when we plot residuals for a normal probability plot, but I am trying to recollect/understand what we are plotting those residuals against?  It would make sense to plot the residuals against the theoretical &quot;error&quot; values, but we don't have those. So what is it we are using per se? This is all under the assumptions of a simple linear regression where the errors are assumed to be normally distributed with constant variance. I should also add this is at the level of an introductory course on linear regressions.
I'm sorry if this is a broad question but can someone explain to me how to interpret these regression diagnostic plots? I understand the Normal Q-Q show's how normal the spread of the data is, but the other three I am confused by. For the Residuals vs Leverage, what does it mean for a point to be outside of the bounds? What does it mean if the red lines are parabolic and curved like in the first two? Why do we care about residuals, and what do they tell us? I've searched the web multiple times for some guide to interpret these and I can't get any straight forward answers. Any help is appreciated, thank you.
How to run .sh script with keybind Better yet, are there any Spacewalk-like software packages that work for both RedHat-based and Debian-based systems? "They are quite full up this year." Differences between hosting options for SharePoint apps Normal subgroup of prime index How to delete all files in a current directory starting with a dot? regexp in ksh for extensions tgz, tar.tgz I'm trying to get a regexp (in ksh) to identify files with only the following extensions: tgz, tar.gz, TGZ and TAR.GZ. I tried several but can't get them to work. I'm using this regexp to select only files files with those extensions to do some work with them:  if [ -f $myregexp ]; then    .....  fi I have two feature Datasets. Both are Polygons. Dataset A has very big Areas and Dataset B just small ones. Now, B still overlaps in 2 or 3 Zones from Dataset A.   I want to perform a spatial join and put the result comma seperated in just one row like this:  Zone_ID_A  |  Zone_ID_B     1       |   2,3    2       |   2,4    3       |   5    4       |   1,6   I know this is possible with ArcMap but i could not figure out a way to do this in QGIS, any ideas? How can we prove charge invariance under Lorentz Transformation? Firstly, I apologise that this question is specific to two polynomials. I understand that this post will not help a lot of people, and for that I am sorry. I will make it up to you all by anwsering lots more questions in the future! However, as my lecturers enjoy time off on the weekend, I am unable to ask this to anyone else who would know what the heck I'm talking about. Sorry if my notation is not widely used, I can elaborate more if required. Please excuse my poor Latex too.  Let:  $B = Y^2 - X^3 + X$, and   $F = (X^2 + Y^2)^3 - 4X^2Y^2$.  I wish to find the intersection number of $B$ and $F$ at $P = (0,0)$  i.e $I(P,F \cap B). $  However, I want to use the following proposition to do this:  If $P$ is simple on $B$ then $I(P,F \cap B) = ord_P^B(F) $.  I will omit proving that $P$ is simple on $B$ as I hope it is clear to see it is.  I know that $I(P,F \cap B) &gt; M_p(F) * M_p(B) = 1 * 4 $, where $M_P(G)$ is the multiplicity of $P$ on $G$.  Now, consider the Image of $X$ and $Y$:  $K[X,Y] \longrightarrow \frac{K[X,Y]}{Y^2 - X^3 + X} \longrightarrow O_P(Y^2 - X^3 + X)$  $X \longrightarrow x$  $Y \longrightarrow y$  Where lower case denotes the image.  Then $ord_P^{Y^2 - X^3 + X}((X^2 + Y^2)^3 - 4X^2Y^2)$  Can be found by substituting $y^2 = x^3 - x$ into $(x^2 + y^2)^3 - 4x^2y^2$  Which gives:  $ord_P^{Y^2 - X^3 + X}(x^9+3x^8 -5x^6 -4x^5 +3x^4 +3x^3)=3$  i.e $I(P,F \cap B) = 3$, a contradiction to  $I(P,F \cap B) &gt; 4$ as above.  The correct answer I know is 6, so where have I gone wrong? Real analysis derivate problem. How can I prove this? Let $f$ be differentiable in $[a,b]$ and $f(a)=0$. If $\exists M \in R$ such that $\vert f'(x) \vert \leq M \vert f(x)\vert \ $,  $\forall x \in [a,b]$, then $f(x)=0, \ \forall x \in [a,b]$.  $\\$ I have an idea, but I can´t see it clear. I have arrived to the inequality $\vert f(x)\vert \leq  K\vert f(y)\vert $ for $y \in (a,x)$, supposing $k&gt;0$ and repeating the process $\vert f(x)\vert \leq  K^n\vert f(z)\vert$ for $a&lt;z&lt;y&lt;x$. If $K&lt;1$, then if $n \rightarrow \infty \ $, $f(x)=0$. That´s a sort of intuitive idea. I saw that it has been already reported that also they have earned courious badge but the badge has not been given. but their answers say that they must wait a day and the badge will be awarded.  In my case its 8/5 and it was 5/5 long time ago and I have never received a message telling that I have earned it. its just telling me that the next badge to be awarded is Curious badge.  this is my profile: Let ${\rm f}:\left[a, b\right]\to\mathbb{R}$ be twice differentiable, and suppose   $$\lim_{x\to a^{+}} \frac{{\rm f}\left(x\right) - {\rm f}\left(a\right)}{x - a} = \lim_{x\to b^{-}}\frac{{\rm f}\left(x\right) - {\rm f}\left(b\right)}{x - b} =0 $$  Show that there exists $\xi \in \left(a, b\right)$ such that $\displaystyle{% \left\vert\vphantom{\Large A}\,{\rm f}''\left(\xi\right)\right\vert \geq \frac{4\left\vert\vphantom{\Large A}% \,{\rm f}\left(a\right) - {\rm f}\left(b\right)\right\vert} {\left(b - a\right)^{2}}}$.  I don't know how to start. Any hints ?. Today in the feed on the Android Stack Exchange app there is a Stack Overflow blog post. This post had the site icon next to it for  rather than the proper site logo (Meta).        Stack Exchange Android App Version 1.0.73 and 1.0.74 Android 5.1 on a Moto X (2013) running stock firmware.  Same behavior on a Nexus 7 (flo) running Android 6.0 (stock).  This issue also happens on the iOS app.    The most recent featured SO blog post (as of 17 Nov) is showing up with the "edX" site logo.  The logo is seemingly randomly incorrect. Commutator of two normal subgroups with trivial intersections So I tried looking everywhere but I'm really lost with this proof. I need to to show that:  Let $H$, $K$ be normal subgroups of a group $G$, satisfying $H\cap K = \{e\}$. Let $h\in H$, $k \in K$. (a) Prove that the commutator $w = hkh^{-1}k^{−1}$ satisfies $w \in H$ and $w \in K$. Then conclude that $w = e$ (b) Prove that $hk = kh$, for all $h \in H$, $k \in K$. Beamer: How to Disable `\pause` Temporarily How can magnets be used to pick up pieces of metal when the force from a magnetic field does no work? I learned that the force from a magnetic field does no work. However I was wondering how magnets can be used to pick up pieces of metal like small paperclips and stuff. I also was wondering how magnets can stick to pieces of metal like a refrigerator? meaning of the word "in" in context It is from . It is at around 8 minute and 39 second. Here it goes:     Culinary cultural fusion is all the rage; more novels translated from languages then ever before, although few are read, and in the surest sign of cultural globalization, football, the world's game, finally has reached America.   I guess the sentence would make sense if the preposition in were dropped out. Could you please tell me what did the host use it for? Movie with killer androids (glowing eyes, screaming) When a PHP application makes a database connection it of course generally needs to pass a login and password. If I'm using a single, minimum-permission login for my application, then the PHP needs to know that login and password somewhere. What is the best way to secure that password? It seems like just writing it in the PHP code isn't a good idea.