I have a binary dependent variable (infection + or -) and both continuous and categorical independent variables.  One continuous independent variable (BMI) seems to be nonlinear in that the lowest and highest BMI are more likely to be + and the BMI values in the middle are less likely to be +.  So when I plot BMI against the proportion that are +, I get U shaped line.  How do I incorporate that into the logistic regression?
Let's say I am building a logistic regression model where the dependent variable is binary and can take the values $0$ or $1$. Let the independent variables be $x_1, x_2, ..., x_m$ - there are $m$ independent variables. Let's say for the $k$th independent variable, the bivariate analysis shows a U-shaped trend - i.e., if I group $x_k$ into $20$ bins each containing roughly equal number of observations and calculate the 'bad rate' for each bin - # observations where y = 0 / total observations in each bin - then I get a U shaped curve.  My questions are:   Can I directly use $x_k$ as input while estimating the beta parameters? Are any statistical assumptions violated which might cause significant error in estimating the parameters? Is it necessary to 'linearize' this variable through a transformation (log, square, product with itself, etc.)?
How to debug JavaScript / jQuery event bindings with Firebug or similar tools? Show that $\gcd\left(\frac{a^n-b^n}{a-b},a-b\right)=\gcd(n d^{n-1},a-b)$ How to show that     $$ \gcd\bigg( {a^n-b^n \over a-b} ,a-b\bigg )=\gcd(n d^{n-1},a-b ) $$    $a,b\in \mathbb Z$   where $d=\gcd(a,b)$?    Note $\ $ Some of the answers below were merged from . The answers (and their comments) may depend on context provided in that question. How can I contribute to Ubuntu? I would like to know what kinds of contributions someone can make to Ubuntu. Such as Programmer, User, Proofreader, etc. What is the symbol on the supply voltage that looks like a shaded-in capacitor? I am looking at  (dual low-voltage power amplifier). On the fourth page, there is a sample circuit; right at the V+ input there is a symbol that looks like a capacitor. However, it looks like it is shaded in. What is that? Use a execute command once I am running a web site design service for local small business owner. I want avoid legal issues on the images I use. Usually, the images found on Flickr are forbidden for commercial use. Where would be a normal channel to get pictures for commercial use with minimal cost? How can I validate that the picture I used has no legal risk? Change date format [YYYYMMDD] to [MM/DD/YYYY] I generated a report that formats date as 20160509 and my Google Sheets locale is already set to United States. I've played around with various options within Format > Number > Date Format but I can't change the dates to MM/DD/YYYY format without doing a simple find and replace. How do I accomplish this? Need a proofreading why all the units are satisfied $a^2-2b^2 =\pm1$ for $\mathbf{Z}[\sqrt{2}]$ All the units are satisfied Pell's equation $a^2-2b^2=\pm1$  for $\mathbf{Z}[\sqrt{2}]$, $a,b\in\mathbf{Z}$.  Here is my proof:  Let $a+b\sqrt{2}$ be a unit $\in\mathbf{Z}[\sqrt{2}]$. This implies $$(a+b\sqrt{2})(c+d\sqrt{2})=1, c+d\sqrt{2}\in\mathbf{Z}\sqrt{2}$$ $$\implies \mathrm{norm}((a+b\sqrt{2})(c+d\sqrt{2}))=1$$ $$\implies \mathrm{norm}(a+b\sqrt{2})\cdot \mathrm{norm}(c+d\sqrt{2})=1$$ $$\implies (a+b\sqrt{2})(a-b\sqrt{2})(c+d\sqrt{2})(c-d\sqrt{2})=1$$ $$\implies (a^2-2b^2)(c^2-2d^2)=1$$ $$\implies \left[ a^2-2b^2=1\text{ and } {c}^2-2{d}^2=1\right]\text{ or } \left[ a^2-2{b}^2=-1\text{ and }{c}^2-2{d}^2=-1\right]$$ $$\implies {a}^2-2{b}^2=\pm1$$ Why didn't mastery of the Elder Wand move on from Harry? There's a lot of emphasis on Harry becoming the master of the Elder Wand after he defeats Draco. But what constitutes a “defeat”?  It seems that Harry wins a wrestling match with Draco, so now he’s the master of the Elder Wand.  But lots of other stuff happens to Harry: Nagini almost kills him, and he escapes just in time, but his wand breaks. The Snatchers chase him through the forest. He and his friends practically surrender (and Hermione even tries to disguise Harry). Voldemort almost kills Harry in the Forbidden Forest (or actually does, depending on how you look at it).  Why are none of these considered to be “defeats”? I am making an Android game that is only in portrait screen orientation.  It works great when I run it on my phone, but when I run it on a tablet, even though the screen size is bigger, all of the bitmaps are the same size. Is there any way to make the bitmaps stay the same proportion even on different size screens? Is there a simple reason why the expected number of coin flips till getting $m$ more heads than tails or $n$ more tails than heads should be $mn$? I flip a coin until I get $m$ more heads than tails, or $n$ more tails than heads. Let the expected number of flips of the coin before stopping be $f(m,n)$.  I obtained $f(m,n)=mn$ from the recursion $f(m,n)=1+\frac{f(m-1,n+1)+f(m+1,n-1)}2$ with $f(k,0)=f(0,k)=0$ for all $k$.   Other than going through this recursion (and either solving by inspection or by writing as linear recurrence in single variable and solving brute force), is there an intuitive reason you should expect this process to take $mn$ flips? I was thinking about the more general problem with probability $p$ of getting heads and was struck by how simple the formula became when handling, what turned out to be a special case (general formula broke down) of $p=\frac12$. Update Manager doesn't ask for a password Oneiric update manager no longer asks for a password to update already installed software.  This is a change in behavior from previous versions.  Is there a way to revert this behavior and get the Update Manager in Oneiric to ask for a password again?  Thanks! When do I use "I" instead of "me?" From some comments in the answers for  (now deleted, 10k only), there's confusion around the usage of I vs. me:  While the sentence, "the other attendees are myself and Steve," is agreed to be incorrect, there's confusion about whether the correct form is "the other attendees are me and Steve" or "the other attendees are Steve and I."  (I've always used the heuristic of removing the other people from the sentence, so I always thought "the other attendee is me" would be correct, instead of "the other attendee is I." Is this true, or am I using a flawed heuristic?) How is hotness score calculated at larger sites? To start with, I am aware that hot questions from larger sites are somehow "penalized" and :     This is designed to ensure that a single site doesn't dominate the list, and that users see a good sampling of questions that are likely to interest them throughout the network...   I would like to understand how is hotness score really calculated at these sites. The reason why I ask is that per my observations, this seems to be quite different than is documented in the . Specifically, I would like to understand the difference in the impact of answer(s) score and aging factor.  Regarding impact of answers score, my observations of hot questions from smaller sites appear to be in agreement with known formula: (MIN(AnswerCount, 10) * QScore) / 5 + AnswerScore. For example, a question with low score (+1, +2) can get into hot list if it has got answer(s) with sufficiently high score.  At larger sites, this doesn't seem to be the case. Say, it looks like Stack Overflow questions just don't enter hot list until they reach certain score (+6,+7), no matter how many answers are there and how high is their score.  Does system simply totally ignore answers until question reaches certain score?  Another thing I noticed is that questions seem to age away from the hot list 2-3 times faster than ones from smaller sites (having comparable question and answers scores). Granted, this is harder to track and I am not yet sure if I figured that correctly. Do larger sites questions age away faster than those from smaller sites?    For those interested, here is a (partial) list of example questions I studied before asking this: , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , .  Although above examples are only from Stack Overflow, my question isn't (I only used it as an example of a large site in my studies). I would like to understand if hot questions from other larger sites are handled in a similar way. Aligning table within latex editor How can I install Broadcom Wireless Adapter BCM4352 802.11ac PCID [14e4:43b1] (rev 03) on fresh install of Ubuntu 14.10 (Utopic Unicorn)? I have a brand new Dell XPS 15. I   dual boot it with Windows 8.1 and  Ubuntu 14.10  The Wireless Network Adapter is Broadcom BCM4352 802.11ac with PCID [14e4:43b1] (rev 03).  The 4352 is not included in the list for installation via bcmwl-kernal-source file. I tried this anyway, but the Terminal command led to the file starting to install, but then stopping. Sometimes I get a permission denied error message.  As a result of reading and trying all advice from forums I have decided to completely reinstall Ubuntu 14.10. I doubt my particular Broadcom Wireless Card has no support on Ubuntu 14.10?    Edit:  The advice of Chili555 worked. I now have working wifi using Broadcom Wireless Adapter BCM4352 802.11ac PCID [14e4:43b1] (rev 03) I am creating table in LaTeX and I need to get the text to perform line break automaticaly when it's too long. And if possible, I'd like to get the text alignment to the left. Is it possible to handle this situation? This post is an expansion of  For many graduated sites (eg Physics), moderators do not want to apply the unilateral close vote in all cases--it is better to let some community votes pile on first.  We only use the unilateral in obvious cases then. This renders the CV queue useless to us. If we &quot;skip&quot; something, we can't get back to it. If we say &quot;do not close&quot;, it's removed from the queue and our community can't see it. If we use &quot;close&quot;, we are using a unilateral mod vote--we don't want to do that. What I propose is a set of &quot;next/previous&quot; buttons, that let us navigate the queues, looking for closeable questions, and coming back to the others later. Thoughts? Update and bounty reason Due to the recent Great Flag Overhaul, mods no longer see close flags in the flag queue. Which means that the only way to get to them is via the review queue 1 Shog's solution is ideal in this case; let mods view the close queue as a list. (In fact, a list similar to the old flag queue -- which shows a list of mods who have seen the post and what mod actions have already been taken -- would be great) On Physics, the majority of the flags that we get are VTC flags. And the community isn't always able to close things on their own, so we have to step in. However, powering through the close queue isn't an option; because &quot;skip&quot;ing a post2 leads to it being dumped into the void (I can't get back to it unless I have a link). Extremely inconvenient. Could the workflow here be improved? 1. The /tools listing for posts with outstanding close votes doesn't work because it doesn't list posts which have been flagged but not VTCd 2. which I may want to take a closer look at later; gotta be careful with the binding votes. Is there a tag in HTML that will only display its content if JavaScript is enabled? I know &lt;noscript&gt; works the opposite way around, displaying its HTML content when JavaScript is turned off. But I would like to only display a form on a site if JavaScript is available, telling them why they can't use the form if they don't have it.  The only way I know how to do this is with the document.write(); method in a script tag, and it seems a bit messy for large amounts of HTML. I'm considering the ring $\mathbb{Z}[\sqrt{-n}]$, where $n\ge 3$ and square free. I want to see why it's not a UFD.   I defined a norm for the ring by $|a+b\sqrt{-n}|=a^2+nb^2$. Using this I was able to show that $2$, $\sqrt{-n}$ and $1+\sqrt{-n}$ are all irreducible. Is there someway to conclude that $\mathbb{Z}[\sqrt{-n}]$ is not a UFD based on this? Thanks.