I ran a linear regression with one dependent and one explanatory variable. The data covers log returns of an index and log returns of a stock (natural logarithm).  log return of stock = Alpha + Beta + log return of index + error  The p value for the Beta estimate is &lt;2e-16. I googled the meaning of this number, which means that the p value is extremely close to zero, but it does not equal to zero.  Now I am confused, since values below 0.01 show significant results, but what if the p value is practically zero? Does it mean that the regression provides a perfect fit?
For some tests in R, there is a lower limit on the  calculations of $2.22 \cdot 10^{-16}$. I'm not sure why it's this number, if there is a good reason for it or if it's just arbitrary. A lot of other stats packages just go to 0.0001, so this is a much higher level of precision. But I haven't seen too many papers reporting $p &lt; 2.22\cdot 10^{-16}$ or $p = 2.22\cdot 10^{-16}$.   Is it a common/best practice to report this computed value or is it more typical to report something else (like p &lt; 0.000000000000001)?
What would be an informative introduction to quantum computing software? I am new to Stack Exchange and am working on a quantum learning platform for minority youth groups (LGBTQ, low-income, at risk, etc).  In the question below they are looking for courses on the subject, which I am also interested in, and do plan on checking those links out for ideas.        What I am looking for are simple videos, articles, or even games, that cover basic quantum theory at an introductory level.  There are some games I have looked into and played.  Hello Quantum! was fun and informative, though on my end there was still a lack of comprehension on how the quantum computer (or anything else "quantum") would actually function and play out.   My focus for the educational platform is more directed towards the software side of quantum computing. Is there anything  that gives a good introduction to the functions and uses a quantum computer will have? As well as what language would be best to program one? Also, would there be a way to program a quantum computer through a classical computer? And, is there a simple introduction to any of this already existing? How to use `ybar interval` without skipping the last value Java equivalent to PHP's preg_replace_callback I'm in the process of moving an application from PHP to Java and there is heavy use of regular expressions in the code.  I've run across something in PHP that doesn't seem to have a java equivalent:  preg_replace_callback()   For every match in the regex, it calls a function that is passed the match text as a parameter.  As an example usage:  $articleText = preg_replace_callback("/\[thumb(\d+)\]/",'thumbReplace', $articleText); # ... function thumbReplace($matches) {    global $photos;    return "&lt;img src=\"thumbs/" . $photos[$matches[1]] . "\"&gt;"; }   What would be the ideal way to do this in Java? You have two identical eggs. Standing in front of a 100 floor building, you wonder what is the maximum number of floors from which the egg can be dropped without breaking it. What is the minimum number of tries needed to find out the solution? How to prove that the center of the dihedral group $D_{2n}$ is $\{1,r^{n}\}$ and the center of $D_{2n-1}$ is $\{1\}$?  I don't know how to prove it in this general case. Evaluation of $\sin \frac{\pi}{7}\cdot \sin \frac{2\pi}{7}\cdot \sin \frac{3\pi}{7}$ Evaluation of $$\sin \frac{\pi}{7}\cdot \sin \frac{2\pi}{7}\cdot \sin \frac{3\pi}{7} = $$   $\bf{My\; Try::}$ I have solved Using Direct formula::  $$\sin \frac{\pi}{n}\cdot \sin \frac{2\pi}{n}\cdot......\sin \frac{(n-1)\pi}{n} = \frac{n}{2^{n-1}}$$  Now Put $n=7\;,$ We get   $$\sin \frac{\pi}{7}\cdot \sin \frac{2\pi}{7}\cdot \sin \frac{3\pi}{7}\cdot \sin \frac{4\pi}{7}\cdot \sin \frac{5\pi}{7}\cdot \sin \frac{6\pi}{7}=\frac{7}{2^{7-1}}$$  So $$\sin \frac{\pi}{7}\cdot \sin \frac{2\pi}{7}\cdot \sin \frac{3\pi}{7} =\frac{\sqrt{7}}{8}$$  Now my question is how can we solve it without using Direct Formula, Help me  Thanks Why does Sass change the format of my colors? When I wanted to download Ubuntu 12.10 from ubuntu.com, I was asked to make a donation. However, there is only a PayPal option to make the payment. But I don't use PayPal. Is there any other option to make the payment? I would like to see a full how-to guide on how to install Ubuntu. GOTO still considered harmful? Everyone is aware of Dijkstra's  (also  .html transcript and  .pdf) and there has been a formidable push since that time to eschew the goto statement whenever possible. While it's possible to use goto to produce unmaintainable, sprawling code, it nevertheless remains in . Even the advanced  control structure in Scheme can be described as a sophisticated goto.  What circumstances warrant the use of goto? When is it best to avoid?  As a followup question: C provides a pair of functions, setjmp and longjmp, that provide the ability to goto not just within the current stack frame but within any of the calling frames. Should these be considered as dangerous as goto? More dangerous?    Dijkstra himself regretted that title, for which he was not responsible. At the end of  (also  .pdf) he wrote:     Finally a short story for the record.   In 1968, the Communications of the ACM   published a text of mine under the   title "The goto statement considered   harmful", which in later years would   be most frequently referenced,   regrettably, however, often by authors   who had seen no more of it than its   title, which became a cornerstone of   my fame by becoming a template: we   would see all sorts of articles under   the title "X considered harmful" for   almost any X, including one titled   "Dijkstra considered harmful". But   what had happened? I had submitted a   paper under the title "A case against   the goto statement", which, in order   to speed up its publication, the   editor had changed into a "letter to   the Editor", and in the process he had   given it a new title of his own   invention! The editor was Niklaus   Wirth.   A well thought out classic paper about this topic, to be matched to that of Dijkstra, is , by Donald E. Knuth. Reading both helps to reestablish context and a non-dogmatic understanding of the subject. In this paper, Dijkstra's opinion on this case is reported and is even more strong:     Donald E. Knuth: I believe that by presenting such a   view I am not in fact disagreeing   sharply with Dijkstra's ideas, since   he recently wrote the following:   "Please don't fall into the trap of   believing that I am terribly   dogmatical about [the go to   statement]. I have the uncomfortable   feeling that others are making a   religion out of it, as if the   conceptual problems of programming   could be solved by a single trick, by   a simple form of coding discipline!" Convert all text from uppercase to lowercase and vice versa? My question is how can I convert all text from uppercase to lowercase and vice versa? That is to change the cases of all the letters. It has to be done with a sed replacement somehow. I'm trying to understand Python's approach to variable scope. In this example, why is f() able to alter the value of x, as perceived within main(), but not the value of n?  def f(n, x):     n = 2     x.append(4)     print('In f():', n, x)  def main():     n = 1     x = [0,1,2,3]     print('Before:', n, x)     f(n, x)     print('After: ', n, x)  main()   Output:  Before: 1 [0, 1, 2, 3] In f(): 2 [0, 1, 2, 3, 4] After:  1 [0, 1, 2, 3, 4] How does the Ranger's Extra Attack feature work with Two-Weapon Fighting? I think I know the answer to this one but I'm double checking.  At the 5th level the Ranger gets Extra Attack, which lets them attack a second time during the Attack action. If they are fighting with 2 weapons, the second weapon normally uses their bonus action.  Does this mean when using the Extra Attack and using two weapons, a ranger can attack twice during the Attack action, and still make 1 extra attack as a bonus action, for a total of 3 attacks? In sketchup you can move an object based on two points. This makes it very easy to align a vertex in one object to vertex in another object. Here is an example:    I want to know how to do this in Blender. It seems that Translate can't align vertexs The 'ok' on the 'Your Answer' dialog on unregistered sites is a bit too high The 'ok' on the 'Your Answer' dialog on unregistered sites is a bit too high:     You can see the top of the k is outside the actual box, increasing the margin-top by 10px in the containing div fixes it. Consider a set $A$ of $10$ integers, $A = \{a_1,a_2, \ldots ,a_{10}\}$. Prove that there is at least one subset of $A$ whose sum is divisible by $10$. What is the chance that at least two people were born on the same day   of the week if there are 3 people in the room?   I'm wondering if my solution is accurate, as my answer was different than the solution I found:  Probability that there are at least 2 people in the room born on the same day = 1 - (No one was born on the same day) - (Exactly one person was born on the same day)  There are (3 choose 2) different pairs of couples. Each couple has the same birthday as another couple with the chances of 1/7 and different with chances 6/7. Thus:  $$1 – (6/7)^3 – 3(1/7)(6/7)^2 = 0.0553$$  Thanks for any help! A guy scammed me, but he gave me a bank account number & routing number. Can I use that to take out what he owes me? I've been Googling around with no luck.  I'm looking for a way to do getc() or gets() or whatever that does not echo to the terminal.  I saw kbhit() but this doesn't appear to be part of ANSI.  Ideally, I'd like code that looks like  char s[100]; no_echo_gets(s); /* Won't echo to screen while being typed */ printf("%s\n", s);   Does anybody know a good ANSI compliant way to do this? I am having the same trouble as others getting my Atheros AR8131 Ethernet card recognised by Ubuntu 12.10 on my new HP Pavillion P7-1449 PC. I found the same question where the answer suggested the following:   Download Tarball compact-wireless-3.6.8-1-snpc Run  ./scripts/driver-select alx make sudo make install    The problem is when I run the make command I get the following:  make -C /lib/modules/3.5.0-21-generic/build M=/home/chris/Downloads/compat-wireless-3.6.8-1-snpc modules make: *** /lib/modules/3.5.0-21-generic/build: No such file or directory.  Stop. make: *** [modules] Error 2   Found a link to an alternative patch file (compat-wireless-2012-09-25-pc) but then I get the similar error:  make -C /lib/modules/3.5.0-21-generic/build M=/home/chris/Desktop/compat-wireless-2012-09-25-pc modules make: *** /lib/modules/3.5.0-21-generic/build: No such file or directory.  Stop. make: *** [modules] Error 2   Any help you could provide would be greatly appreciated.