When using logistic regression how critical is to have balanced treatment groups. I have a binary response variable (pregnant and non-pregnant) from two treatments at n=40 and n=14? How does the need for balance compares to OLS analysis? Is there any published information on the subject?
I'm working on a project using logistic regression to predict student retention. The data were collected through three self-report instruments. We are trying to find out which predictors are powerful enough to predict the at-risk students. I came across some articles saying a balanced sample (50% stay, 50% dropouts) is desirable for such study, e.g. Glynn, J.G., Sauer, P.L., &amp; Miller, T.E. (2003). , NASPA Journal, 41 (1), 41-67:     A problem however, is that the distribution of the dependent variable is likely to be highly skewed toward persistence. For example, if 85% of the analysis sample were persistors, a classification model that classified every student as a persistor would have a success rate of 85%, or would classify 85% of student correctly. To resolve this issue, the maintenance of relative balance between the number of dropouts and the number of persistors (about 50% each) in the analysis sample was desirable.   Is this true? Our sample only has about 25%-30% dropout students. Will this affect the results?
Windows 10 Search not loading, showing blank window I can't seem to figure out how to get past this step. Any suggestions? Is "from where" grammatically equivalent to "from which"? shortcut for commands I have just updated (through Software Update) to Ubuntu 16.04 LTS from 15.10. There are random instances of screen flickering throughout usage. After noticing this issue, I installed Compiz Config Settings Manager, selecting Force fulls screen redraws (buffer swap) on repaint, which did nothing.   Is there any way this could be related to compiz settings or is this another issue?    EDIT: not fixed after clean install, upgrade to kernel 4.5.2, however screen flickering is reduced, it is every now and then (10 minutes apart). I will see if upgrading to kernel 4.6.0-994-generic will fix this.     EDIT: fixed as of kernel 4.6.2 generic,  currently running 4.7.2 without any issues. How to evaluate the integral $\int_0^{\pi}\frac{a^n\sin^2x+b^n\cos^2x}{a^{2n}\sin^2x+b^{2n}\cos^2x}dx$? Evaluate the integral $$\int_0^{\pi}\frac{a^n\sin^2x+b^n\cos^2x}{a^{2n}\sin^2x+b^{2n}\cos^2x}dx.$$   I have no idea.   $$\int_0^{\pi}\dfrac{a^n\sin^2x+b^n\cos^2x}{a^{2n}\sin^2x+b^{2n}\cos^2x}dx=\int_0^{\pi/2}\dfrac{a^n\sin^2x+b^n\cos^2x}{a^{2n}\sin^2x+b^{2n}\cos^2x}dx=\int_0^{\pi/2}\dfrac{a^n\tan^2x+b^n}{a^{2n}\tan^2x+b^{2n}}dx$$  I try the substitution $\tan{x}=t$, but it doesn’t work. Understanding the impact/risk of turning off "verify backup integrity" on SQL backup Currently we use standard maintenance plans for backups on the SQL Server 2005/2008/2008R2/2012 servers in our environment, and the "Verify backup integrity" box has always been checked.  Some of the backups run very long, so I've recommended turning off that option, but management needs me to document the impact and risks of this change.  I understand the use and history of this option, it just seems unnecessary to me to double the time for the backup job when (in my opinion), any error that is likely to occur would occur during the backup step, not during the verify.  Am I wrong? Is it minimal risk to turn this off, if I am backing up to disk and not to streaming tape or something? (We back up over the network to an EMC DD-800 backup appliance, if that is relevant.)  Is there any official MS recommendations for when it is safe to turn this off?   Do you run "verify" on every backup in your environment? Do you spot-check them?  EDIT: To clarify, when you check "verify backup integrity" in the maintenance plan, SQL will do a full RESTORE VERIFYONLY on each database immediately after each backup. This is just as data/IO intensive as the original backup, and (basically) doubles the overall time of the backup job. This is not the same as enabling the "checksum" option on backup (which can't be done in the wizard, as far as I know). Show that $e^3 > 20$ I read this sentence on an educational website:     Now times have changed and you are ready for situations involving forces in two dimensions.   Shouldn't there be a comma before and, since the subject of the sentence has changed (things vs. you)?      Now times have changed, and you are ready for situations involving forces in two dimensions.   What is the exact comma rule for joining two clauses with and? How to look up a symbol or identify a letter from a math alphabet or other character? How is voltage always able to increase, if electrons move at the speed of light? Why should I put a ~ before \ref or \cite? My question is in the title of this post, but extends to other referencing commands like \eqref, \citep, \citet (and the like) as well. I'm very new to Blender and I'm trying to make a water vortex like this.(may be not the easyest first project for a newbie)     I watched several tutorial on liquids particle etc but I'm not sure what is the best aproach. What I tried  until now:   I made a particle system with a vortex force field. It looks good, but I'm not able to add the right material.      I played around with the fluid physics, the water looks good but if I add a vortex force field it does nothing.   I would be very grateful if somebody could point me in the right direction because I'm definitely stocked. JSON and escaped double quote I'm currently making a callout to a 3rd party vendor and I'm getting a huge response. What is currently messing me up is this section:   "MessageSeq":13,"Description":"config file: config-qa1.txt\"","MessageTS":"2014-02-17T14:46:58","MessageLevel":4,"IsSystemMessage":false   As you can see here, the portion at the end of the Description value is ended with backslash double quote. If I attempt to parse this via the JSONParser I get an exception. Does anyone have an recommendations on how to resolve this?  Exception Message:  System.JSONException: Unexpected character ('"' (code 34)): was expecting comma to separate OBJECT entries at [line:1, column:3699]  Updated with sample Code   public class ResponseWrapper{     // fields from JSON to auto map     public Integer messageSeq;     public String Description;     public String messageTS;     public Integer messageLevel;     public Boolean isSystemMessage;     // parsing fields     private ResponseWrapper theResponse;     private JSONParser parser;      public void parse(String jsonString){         parser = JSON.createParser(jsonString);         parseJSON();     }      private void parseJSON(){            while (parser.nextToken() != null) {             if (parser.getCurrentToken() == JSONToken.START_OBJECT) {                 theResponse = (ResponseWrapper)parser.readValueAs(ResponseWrapper.class);                            }         }     } }  String responseString = '{"MessageSeq":13,"Description":"config file: config-qa1.txt\"","MessageTS":"2014-02-17T14:46:58","MessageLevel":4,"IsSystemMessage":false}'; system.debug('\n\nBEFORE\n' + responseString); ****Place code in here to test such as ReplaceALL*** ResponseWrapper parser = new ResponseWrapper(); parser.parse(responseString); Images for Area51 proposal community promotion on imgur.com? For each proposal on Area51, a promotional image is automatically generated and it shows the current state, e.g. number of followers/supporters or comitted. Example:    They’re obviously useful for  on existing sites. Alas, the current requirements for those say that the image needs to be hosted on imgur.com. I can easily provide the URL https://area51.stackexchange.com/ads/proposal/{proposal-number}.png in the image upload dialog, to get a cryptic imgur address back, but I’m afraid that it won’t update dynamically.  Please note that I was able to use the area51 URL on some sites until right now, when the poster generator seems to be broken or off-line, but on other sites the software stopped me from posting any image not hosted on imgur. Can we please have the dynamic posters working everywhere (and in “HiDPI”) or be assured that the external service will update them regularly? Book series about aliens who put "caps" on people to control them “Unable to Connect to World” Minecraft PE 1.16.201 So my brother and I have been playing Minecraft together on our iPads for years now, but in September I got a new iPad Pro 3rd Generation and I’ve been having issues with Minecraft ever since. Every time we have tried to join each other’s worlds we get the message “Unable to connect to world”. Recently after the update on December 16th, it worked for about a week without having any issues, but now it has gone back to not letting us connect to the worlds. Both of us are able to connect to other people’s worlds, but not each other’s, we’ve tried many things to fix this but so far nothing has worked. If you have any ideas for what we should do please let me know, thank you so much! Proving that $\lim_{x \to 0} \frac{f(x)}{|x|}=1$ implies $f$ is not differentiable at $0$. $$\lim_{x \to 0} \frac{f(x)}{|x|}=1$$ Then prove that $f$ is not differentiable at $0$. I was given this assignment and I'm not sure about my proof.. it feels like I'm assuming too much and not explaining with enough detail. Is there anything I need to add to make it sufficient? Assume toward contradiction that $f$ is differentiable at $0$. Then by definition we know that $f$ is continuous at $0$. Therefore $\lim _{x\to 0}f\left(x\right)=f\left(0\right)$ We know that $\lim _{x\to 0}\frac{\left(f\left(x\right)\right)}{\left|x\right|}=1$ Therefore we can conclude $\lim _{x\to 0}\frac{\left(f\left(x\right)\right)}{\left|x\right|}\cdot \left|x\right|=1\cdot 0=0$ But we can also rewrite this as $\lim _{x\to 0}\left(f\left(x\right)\right)\cdot \frac{\left|x\right|}{\left|x\right|}=f\left(0\right)\cdot 1=0$ Therefore $f(0) = 0$. Since $f$ is differentiable at $0$ we have $\lim _{x\to 0}\frac{\left(f\left(x\right)-f\left(0\right)\right)}{x-0}=\lim _{x\to 0}\frac{\left(f\left(x\right)-0\right)}{x}=\lim \:_{x\to \:0}\frac{\left(f\left(x\right)\right)}{x}\cdot \frac{\left|x\right|}{\left|x\right|}=\lim \:\:_{x\to 0}\frac{\left(f\left(x\right)\right)}{\left|x\right|}\cdot \:\frac{\left|x\right|}{x}$ Since the one sided limits of $\frac{f\left(x\right)}{\left|x\right|}$ exist, and are both equal to 1, we have $\lim \:_{x\to 0^+}\frac{\left(f\left(x\right)\right)}{\left|x\right|}\cdot \:\:\frac{\left|x\right|}{x}=\lim \:_{x\to \:0^+}\frac{\left(f\left(x\right)\right)}{x}\cdot \:\:\:\frac{x}{x}=1\cdot 1=1$ $\lim \:_{x\to 0^-}\frac{\left(f\left(x\right)\right)}{\left|x\right|}\cdot \:\:\frac{\left|x\right|}{x}=\lim \:_{x\to \:0^-}\frac{\left(f\left(x\right)\right)}{-x}\cdot \:\:\:\frac{-x}{x}=1\cdot -1=-1$ Since the limit doesn't exist, we have a contradiction to the fact $f$ is differentiable at $0$. Therefore $f$ is not differentiable at 0. $\displaystyle \int\nolimits_0^8 \sqrt{x^4+4x^2}\,dx$.   Alright, so I thought I had this figured out. Here's what I did:   I factor out an $x^2$ to get $\sqrt{x^2(x^2+4)}$. I let $x = 2\tan(\theta)$, therefore the integrand is $\sqrt{4\tan^2(\theta)  (4\tan^2(\theta) + 4)}$. Factor out a 4 and it becomes $\sqrt{(16\tan^2(\theta)  (\tan^2(\theta) + 1))}$ Which equals $\sqrt{16\tan^2(\theta) \sec^2(\theta)}$ This is easy to take the sqrt of. The integrand becomes $4\tan(\theta)\sec(\theta)$. Now, the integral of this is $4\sec(\theta)$ And it's evaluated from $0$ to $\arctan(4)$ right? Because as $x$ goes to $0$, so does $\theta$, and as $x$ goes to $8$, $\theta$ goes to $\arctan(4)$... But the end result $(4 (\sec(\arctan(4)) - 1) )$ isn't the correct answer   I put it into WolframAlpha and I get $(8/3) (17\sqrt{17} - 1)$, which is the right answer. How did they get that? (there's no "show steps" option)  Any help is greatly appreciated!  PS, what's the syntax for doing sqrts and exponentials? (I'm going to link to this Stackexchange post concerning Nullary Operations: )  In general an  is a function $f:S^n \to S$, where $n$ denotes the arity of the operation, and a  is a function $f:S^0 \to S$.  It is clear that $S^n=S \times S \times \cdots \times S$ denotes the Cartesian product of a set with itself ($n$ times), however $S^0$ makes little sense to me.  One might define $S^0=\emptyset$. At first glance, that seems like a good choice. However then a nullary operation makes no sense, since it must be a function $f: A \to B$ where $A$ and $B$ are two sets representing the domain and codomain of the function. And note a function is defined in terms of relation, where a relation is a subset of the Cartesian product $A \times B$. So when we think of $A=S^0=\emptyset$ and $B=S$, so that we have a nullary operation $f:\emptyset \to S$, what is a a subset of $\emptyset \times S$? What even is $\emptyset \times S$? By definition of the Cartesian product, \begin{equation} \emptyset \times S = \{(a,b):a \in \emptyset\textrm{ and }b \in S\}. \end{equation} But there exists no $a \in \emptyset$! Therefore there exist no ordered pairs in our Cartesian product! Therefore $\emptyset \times S = \emptyset !$. Remember a function is a relation which is a subset of the Cartesian product. Therefore our relation is the empty set, and therefore also $f=\emptyset$.    Edit: We got the definition sorted out in the comments. Thanks especially to Hayden and Christoff for their great help. In summary, we figured out that $S^0=\{()\}$, the set containing only one element, the "empty $n$-tuple". Then if taking $S=\{1,2,...,k\}$, then a nullary operation $f:S^0 \to S$ is a function, i.e. some subset of $S^0 \times S = \{()\} \times S$. Looking at $\{()\} \times S$, this equals $\{((),1),((),2),...,((),k)\}$. Then a function is a special subset of this, so that each element of the domain (and there is only one element, namely $()$) is paired with exactly one element of the codomain. Therefore a function would have the form $f=\{((),a)\}$ where $a$ is one of $1,2,...,k$. Thank you for your help.