I was running a regression with 1000 observations and 7 explanatory variables (with a constant term included as a "variable").  So, the population model initially stated was:  $Y_{i} = \beta_{1} + \beta_{2}X_{2i} + ....+ \beta_{6}X_{6i} + u_{i}$  So the sample model is:   $\hat{Y_{i}} = b_{1} + b_{2}X_{2i} + ....+ b_{6}X_{6i}$  (Estimated via OLS, meaning that I used the Gauss-Markov assumptions:  )  After performing an individually significant test over $\beta_{6}$ i got the result that I can not reject the Null Hypothesis of $\beta_{6} = 0$.  But, if I make a F-test, of joint significance, I get that I can reject the Null Hypothesis of $\beta_{6} = 0$.  What's the intuition? (and maybe the mathematics behind)   How can it be that one test contradicts the other?  Thanks!
I'm fitting a multiple linear regression model between 4 categorical variables (with 4 levels each) and a numerical output. My dataset has 43 observations.  Regression gives me the following $p$-values from the $t$-test for every slope coefficient: $.15, .67, .27, .02$. Thus, the coefficient for the 4th predictor is significant at $\alpha = .05$ confidence level.  On the other hand, the regression gives me a $p$-value from an overall $F$-test of the null hypothesis that all my slope coefficients are equal to zero. For my dataset, this $p$-value is $.11$.  My question: how should I interpret these results? Which $p$-value should I use and why? Is the coefficient for the 4th variable significantly different from $0$ at the $\alpha = .05$ confidence level?  I've seen a related question, , but there was an opposite situation: high $t$-test $p$-values and low $F$-test $p$-value. Honestly, I don't quite understand why we would need an $F$-test in addition to a $t$-test to see if linear regression coefficients are significantly different from zero.
What's the best way to convert a string to an enumeration value in C#? I have an HTML select tag containing the values of an enumeration. When the page is posted, I want to pick up the value (which will be in the form of a string) and convert it to the corresponding enumeration value. In an ideal world, I could do something like this: StatusEnum MyStatus = StatusEnum.Parse(&quot;Active&quot;);  but that isn't a valid code. Website giving pronunciations of English words recorded in different dialects? I'm aware that there are certain websites around that provide recorded examples of English words pronounced in different accents/dialects.  Could anybody list some of them? We all know how to blow up the first Death Star: Fire a couple of proton torpedoes into the thermal exhaust port.  It's ray shielded, so only torpedoes will do.  To do this, the Rebel pilots had to fly down a very long trench, where they were vulnerable to fire from any TIE fighters to the rear.  In fact they were so vulnerable that most of the pilots on this run were blown up once the Imperial forces started responding to the attack. This battle is in space, so the fighters can, if necessary, come to a dead stop and hold their position while firing.  Also, when Luke fired his torpedoes, they took a 90 degree turn and went straight into the port.  So the torpedoes didn't have to be fired from in the trench. We also didn't see any gun emplacements firing at the fighters from near the exhaust port, but if there were, the Rebels could have targeted them and taken them out or run interference to make it hard for the towers to fire at a fighter targeting the exhaust port.  (They were already dodging fire in the trench as well.) A fighter could have easily flown directly at the exhaust port, firing torpedoes multiple times on approach and, if not under fire (or if protected by other fighters), could have actually stopped and taken time to target the exhaust port before firing. Is there any valid in-universe reason that the pilots had to fly down the trench before firing on the port?  And if there is, is there any reason they had to enter the trench so early? Just for reference, here is the  on YouTube.  There's no explanation given for having to fly in the trench. Inner product on $C(\mathbb R)$ With axiom of choice it is possible to construct an inner product on $C(\mathbb R)$. My question is, is it possible to explicitly construct an inner product on $C(\mathbb R)$? I.e. to give a closed formula to calculate the inner product? I know it is straight-forward to write down a scalar product using a Hamel basis. This is not the answer I am looking for. This question came to me, when a student asked me in the lecture today 'whether there are vector spaces without inner products'. So I tried to find scalar produces for function spaces. I think I managed to write one down for $L^1((0,1))$. But I failed to construct one for $C(\mathbb R)$. I've seen a contraction of two words.  I can't see why it wouldn't've been possible to have been contracted twice.  Is it possible and how should it be punctuated?  Update:  Ok, to sum up the answers so far   This appears in spoken British and American English It is from one of the lower  Even if spoken this way sometimes, it isn't really written as a double contraction, except as written speech in fiction. And from my own googling in , it appears most written forms are old British words, often nautical like fo'c'sle. When i tried to install PIP for python3 in Ubuntu 18.04.2 LTS  Command I used:   root@DESKTOP-0BEE3OD:/mnt/c# apt install python3-pip  E: Could not read response to hello message from hook [ ! -f /usr/bin/snap ] || /usr/bin/snap advise-snap --from-apt 2&gt;/dev/null || true: Success   I am not able to fix this error. Push Notification Badge Count Not Updating Formula across objects Content replacement from external website Markdown + Mathjax => PDF I've used LaTeX a lot in the past, but now, when comparing with StackExchange's great , I find it tedious, for short documents (&lt; 2 pages), to have to use pure LaTeX. For a short document, instead of having 30 lines as introduction: \begin{document} \documentclass[11pt,a4paper]{article} \usepackage[frenchb]{babel} \usepackage[latin1]{inputenc} \usepackage[T1]{fontenc} \usepackage{amsmath} \usepackage{amsfonts}  + &lt;lots of other things&gt; ...  I'd like to write my short document with MarkDown + Math, like on . Question: Is there an offline compiler such that compilemarkdown exercice.tex  would produce a PDF from this: #Title  Here is a *short document* including Markdown and Math, here is the equation:  $$f(x)=x^2$$  ___  Proof: ...   This is **bold**. How can we run a command stored in a variable? How to prefix post permalinks with /blog/ - without affecting custom post types? I have several custom post types, which are properly structured as /%post_type%/%postname%/, however I wish to have the same effect for regular blog entries: /blog/%postname%/  If I prepend the permalink structure with /blog/ it affects the custom post types as well, so currently my permalink structure is simply /%postname%/  Which is the recommended way of doing this? I had a solution involving some rewrites, but the permalink shown in the post editor area does not reflect it. Enabling tftpd  sudo launchctl load -F /System/Library/LaunchDaemons/tftp.plist   Start:  sudo launchctl start com.apple.tftpd   See logs syslog -w  com.apple.xpc.launchd[1] (com.apple.tftpd[30687]) &lt;Warning&gt;: Service exited with abnormal code: 1   Or with log stream --process tftp --level debug  Filtering the log data using "process BEGINSWITH[cd] "tftp"" Timestamp                       Thread     Type        Activity             PID    TTL 2020-01-21 12:35:44.903240+0200 0x5292a    Activity    0x6afa0              31479  0    tftpd: (libsystem_info.dylib) Retrieve User by Name 2020-01-21 12:35:44.903949+0200 0x5292a    Default     0x0                  31479  0    tftpd: recvfrom: Resource temporarily unavailable   I also tried to run tftpd directly without launchctl sudo /usr/libexec/tftpd -d -i /private/tftpboot/ with the same results.  Earlier I used this configuration and it worked fine. But after some changes (may be OS update) it became broken. Current MacOS version is 10.14.6 (18G2022)    How to fix tftpd?    Appendix. Configuration file /System/Library/LaunchDaemons/tftp.plist has default content:  &lt;?xml version="1.0" encoding="UTF-8"?&gt; &lt;!DOCTYPE plist PUBLIC "-//Apple Computer//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd"&gt; &lt;plist version="1.0"&gt; &lt;dict&gt;     &lt;key&gt;Disabled&lt;/key&gt;     &lt;true/&gt;     &lt;key&gt;Label&lt;/key&gt;     &lt;string&gt;com.apple.tftpd&lt;/string&gt;     &lt;key&gt;ProgramArguments&lt;/key&gt;     &lt;array&gt;         &lt;string&gt;/usr/libexec/tftpd&lt;/string&gt;         &lt;string&gt;-i&lt;/string&gt;         &lt;string&gt;/private/tftpboot&lt;/string&gt;     &lt;/array&gt;     &lt;key&gt;inetdCompatibility&lt;/key&gt;     &lt;dict&gt;         &lt;key&gt;Wait&lt;/key&gt;         &lt;true/&gt;     &lt;/dict&gt;     &lt;key&gt;InitGroups&lt;/key&gt;     &lt;true/&gt;     &lt;key&gt;Sockets&lt;/key&gt;     &lt;dict&gt;         &lt;key&gt;Listeners&lt;/key&gt;         &lt;dict&gt;             &lt;key&gt;SockServiceName&lt;/key&gt;             &lt;string&gt;tftp&lt;/string&gt;             &lt;key&gt;SockType&lt;/key&gt;             &lt;string&gt;dgram&lt;/string&gt;         &lt;/dict&gt;     &lt;/dict&gt; &lt;/dict&gt; &lt;/plist&gt;   Update1 It seems port is in use. Why? Who?  $ sudo lsof -i:69 COMMAND PID USER   FD   TYPE             DEVICE SIZE/OFF NODE NAME launchd   1 root   23u  IPv6 0x55f5dbd8d897c847      0t0  UDP *:tftp launchd   1 root   57u  IPv4 0x55f5dbd8d897e687      0t0  UDP *:tftp launchd   1 root   59u  IPv6 0x55f5dbd8d897c847      0t0  UDP *:tftp launchd   1 root   60u  IPv4 0x55f5dbd8d897e687      0t0  UDP *:tftp   launchd uses UDP port 69. Why?  $ ps -ef | grep tftp 501 94727 48073   0  4:16PM ttys007    0:00.00 grep --color=auto tftp In the season 8 episode finale of Game of Thrones the highest important lords met with Grey Worm to free      Tyrion and Jon. While it was pretty clear why they wanted to free Jon it was unclear to me why they also asked for Tyrion.   To make things even more strange, they asked about his opinion of a potential solution which becomes the actual final one in the end      (choose king and nominate someone).   I thought they (besides Sansa and Bran) don't like him and wanted to judge him? Or am I missing something? How to find roots of $X^5 - 1$? How to find roots of $X^5 - 1$? (Or any polynomial of that form where $X$ has an odd power.) Will yearly moderation statistics be published on all sites this year, and future years? How secure is Activation Lock on iOS 7 (and later)? Apple showed this new feature in iOS 7 called Activation Lock, that if you enable "Find My iPhone" on a device that is lost or stolen, a person that finds/gets the iPhone will not be able to wipe it or reset it. I'm curious whether the lock is designed to prevent these avenues to defeat the lock:   Can they completely drain the battery and leave the phone in that state for a couple of months and then try it? Or, can they use any third-party software that can access iPhone from outside the iTunes and wipe it that way? Or, can they simply "jailbreak" it and forget about this Activation Lock?   By what methods can this lock be defeated or bypassed? Multiplication in Permutation Groups Written in Cyclic Notation I didn't find any good explanation how to perform multiplication on permutation group written in cyclic notation. For example, if $$   a=(1\,3\,5\,2),\quad b=(2\,5\,6),\quad c=(1\,6\,3\,4), $$  then why does $ab=(1\,3\,5\,6)$ and $ac=(1\,6\,5\,2)(3\,4)$? Enumerated list with square brackets I want to make an enumerated list in the following format:  [1] foo foo [2] foo foo ...    How I can do that using enumerated lists? I have tried the following:  \begin{enumerate}[\left[ 1 \right]]   but it does not work. Let $f$ be a real, continuous function defined on $[0,\infty)$ such that $xf(x)$ is increasing for all sufficiently large values of $x$. Show that if   $$\int_0^x f(y)\,dy \sim Ax^\alpha \quad \left(\,x\to \infty\right)$$  for some positive constants $A$ and $\alpha$, then  $$f(x)\sim \alpha Ax^{\alpha -1} \quad \left(\,x\to \infty\right).$$  Clearly, I have to use differentiation somewhere, but I don't know how to manipulate $\lim_{x\to \infty}\frac{\int_0^x f(y)\,dy}{Ax^\alpha}=1$ to get the desired result.  From suggestions given, I know that by L'hospital's rule, it's enough to show that the limit $\lim \frac{f(x)}{\alpha Ax^{\alpha -1}}$ exists, and this limit equals $ \lim \frac{xf(x)}{\alpha Ax^{\alpha}}$. From here, I'll need to use the given assumption that $xf(x)$ is eventually increasing. But how can I show the existence of the limit based on these facts?  I would greatly appreciate any solutions, hints or suggestions.