Is there a way to calculate a p-value for the hypothesis that population coefficient regression coefficient $B_1$ is larger than that of $B_2$ when doing multiple regression on a sample group?  In the test I'm trying to perform $x_1$ and $x_2$ are both binary, but I'm interested in the general case as well.
If this is a duplicate question, please point to the right way, but the similar questions I've found here haven't been sufficiently similar. Suppose I estimate the model $$Y=\alpha + \beta X + u$$  and find that $\beta&gt;0$. However, it turns out that $X=X_1+X_2$, and I suspect $\partial Y/\partial X_1 \ne \partial Y / \partial X_2$, and in particular, that $\partial Y/\partial X_1 &gt; \partial Y / \partial X_2$. So I estimate the model $$Y=\alpha + \beta_1 X_1 + \beta_2 X_2 +u$$and find significant evidence for $\beta_1,\beta_2&gt;0$. How can I then test whether $\beta_1&gt; \beta_2$? I considered running another regression $$Y=\alpha +\gamma(X_1 - X_2) + u$$ And testing whether $\gamma&gt;0$. Is this the best way?  Also, I need to generalize the answer to many variables, i.e. suppose we have $$Y=\alpha + \beta^1 X^1 + \beta ^2 X^2 + \dots + \beta^nX^n + u$$ where for each $j=1,\dots,n$, $X^j=X_1^j+X_2^j$, and I would like to test for each $j$ whether $\partial Y/\partial X_1^j \ne \partial Y / \partial X_2^j$.  By the way, I am primarily working in R.
How can I make iconv replace the input file with the converted output? I have a bash script which enumerates through every *.php file in a directory and applies iconv to it. This gets output in STDOUT.   Since adding the -o parameter ( in my experience ) actually writes a blank file probably before the conversion takes place, how can I adjust my script so it does the conversion, then overwrites the input file?  for file in *.php do     iconv -f cp1251 -t utf8 "$file" done Considering that sound can't travel through vacuum. MVC DateTime binding with incorrect date format I updated the chrome to version 61, and the auto-scroll stopped working, it is necessary to scroll down the page manually. The problem does not occur in the previous version or in firefox.  Also, the reply icon no longer working when the message replied to is not in the current chat page. (Middle click still works and opens the link in new tab.) I have just bought a new computer and I have everything migrated over except for my Steam games.  I looked in Program Files/Steam/ and I found a folder full of the games I have downloaded, but I do not know if it is safe to just copy these folders from one computer to another (seeing as a lot of other applications will not work if you do this), or is there another recommended way?  I don't really feel like re-downloading all my games. I don't have the time nor bandwidth to download 20GB over a 1.5mbps connection.  Is it possible to contact Valve and get a disk with the games on it? Do these new insights into prime numbers affect encryption security? reports:  Two mathematicians have uncovered a simple, previously unnoticed property of prime numbers [...]. Prime numbers, it seems, have decided preferences about the final digits of the primes that immediately follow them. Among the first billion prime numbers, for instance, a prime ending in 9 is almost 65 percent more likely to be followed by a prime ending in 1 than another prime ending in 9.  Do these insights make breaking keys based on primes more mathematically plausible in a shorter amount of time? Video editing software options? What video editing software would you recommend on Ubuntu (or Linux in general) and why?  It can be for either beginners or experienced users.  Please only place one piece of software per response and include details to what makes it great! So I understand that Euclidean distance is valid for all of properties for a metric. But why doesn't the square hold the same way? It is a known fact that if $R$ is a UFD, then $R[X_1,X_2,\dots]$ is also a UFD, but there is a subtlety that is making me uncomfortable.  The standard approach essentially goes something along the lines of...let $f$ be a polynomial, so it only involves finitely many variables, say up to $X_1,\dots,X_n$. Then since $R[X_1,\dots,X_n]$ is a UFD, $f$ has a factorization into irreducibles. Then $f$ cannot have a factorization involving indeterminates $X_N$ not in $R[X_1,\dots,X_n]$. If it did, then $f$ would have two factorizations in the UFD $R[X_1,\dots,X_n,\dots, X_N]$, a contradiction.  This seems to assume that the prime factorization in $R[X_1,\dots,X_n]$ is still a prime factorization in $R[X_1,\dots,X_n,\dots,X_N]$. But how can you see that irreducibles in $R[X_1,\dots,X_n]$ are still irreducibles in $R[X_1,\dots,X_m]$ for $m&gt;n$? This does not seem obvious.  Let $R_k=R[X_1,\dots,X_k]$. The explanantion I found is this: Suppose $p\in R[X_1,\dots,X_n]$ is irreducible in $R_n$. Suppose $p=ab$ for $a,b\in R_m$. Evaluating $X_1,\dots,X_n$ at $1$, you get  $$ \bar{p}=\overline{ab}\in R[X_{n+1},\dots,X_m] $$ But $\bar{p}\in R$, which implies that $a$ and $b$ do not involve any variables $X_{n+1},\dots,X_m$. So $a,b\in R_n$, and thus one is a unit, hence a unit in $R_m$.   The part I don't follow is how evaluation at $1$, implies $a$ and $b$ do not have indeterminates other than $X_1,\dots,X_n$. Isn't it possible that some of the higher indexed indeterminates disappear when you evaluate? Suppose for instance $p\in R_1$, and $a\in R_2$ is $a=-X_1X_2+X_2$. Then evaluting at $1$ gives $\bar{a}=0$ so we may not get the desired contradiction since $\overline{ab}=0\in R$? What is the probability that all three tosses result in the same outcome? A coin is tossed three times: The probability of zero heads is 1/8 and the probability of zero tails is 1/8.  And my question is: What is the probability that all three tosses result in the same outcome?   So, if P(zero heads)= 1/8 , then that should be the same of p(all tails)?  If so, we could use the Addition Rule which is $P(A \cup B) = P(A) + P(B)$  where A and B are disjoint events, i.e. $A \cap B = \emptyset$, A is the event of tossing all heads and B is the event of tossing all tails.  I'm not sure how to continue after that... would the complement be used? $\Bbb Z^\ast$ What is this notation? What does $\Bbb Z^\ast$ mean? I would think some subset of the integers but I cannot find a definition. Thank you. Single word to denote date and time I want one word that means Date and Time. For example in "the date and time of the event will be announced later" I want to use single word instead of "date and time" Use LaTeX to simulate old typewriter written texts This question led to a new package:      I'm giving my students an old exam and barely remembered to change the date at the top. A colleague and I joked about how long we could reuse the same exam, and it made me wonder if I could use LaTeX to create an exam that looked like it was written in 1963 on a typewriter.  Here's what I'd like to see:   Typewriter font even in math mode. (Several ways to accomplish this; is there a "best" way?) Slight inconsistencies in the printing of each letter. I attempt this below adapting code taken from . Each word has a random vertical shift, though I'd like to see it reduced to each letter having its own vertical shift. Other typewriter-like irregularities would be great. It would be great if math-mode delimeters \left(, \right}, etc., can be created in a piece-meal fashion as they did in days of old. Fraction bars, tops of square-root symbols -- any horizontal line, really -- is made up of a series of en-dashes that don't quite match up.   Here is what I've come up with so far:  \documentclass[10pt]{article}% This is a document class providing more font size options \usepackage{graphicx} \usepackage{ifthen} \usepackage[textwidth=7.5in,textheight=9.5in]{geometry} \pagestyle{empty}  % thanks to Bruno Le Floch: https://tex.stackexchange.com/q/9331/4012 % and in his comments to https://tex.stackexchange.com/a/29458/4012 \usepackage[first=-1,last=1]{lcg}% you can play around with these values \makeatletter \newcommand{\globalrand}{\rand\global\cr@nd\cr@nd} \makeatother  \newcommand{\randomvshift}[1]{\globalrand\raisebox{\value{rand}pt}{#1}}  %%% thanks to Martin Scharrer: https://tex.stackexchange.com/q/11598/4012 \makeatletter \def\typewriter#1{%     \@typewriter#1 \@empty } \def\@typewriter#1 #2{%    \randomvshift{#1}\space    \ifx #2\@empty\else     \expandafter\@typewriter    \fi    #2% } \makeatother \begin{document}\tt  \typewriter{Math 101 Fall 1963}  \begin{enumerate} \item   \typewriter{$\frac{\texttt{d}}{\texttt{dx}}\texttt{(x)}^2$}  \item \typewriter{State the Fundamental Theorem of Calculus.}  \end{enumerate}  \end{document} Possessive 's for things Building a wormhole We regularly get questions about wormholes on this site. See for example  and . Various wormhole solutions are known, of which my favourite is  because it's closest to what every schoolboy (including myself many decades ago) thinks of as the archetypal wormhole.  The trouble is that Visser has pulled the same trick as  of starting with the required (local) geometry and working out what stress-energy tensor is required to create it. So Visser can tell us that if we arrange exotic string along the edges of a cube the spacetime geometry will locally look like a wormhole, but we know nothing about what two regions of spacetime are connected.  My question is this: suppose I construct a Visser wormhole by starting in Minkowksi spacetime with arbitrarily low densities of exotic matter and gradually assembling them into the edges of a cube, how would the spacetime curvature evolve as I did so?  I'm guessing that I would end up with something like Wheeler's bag of gold spacetime. So even though I would locally have something that looked like a wormhole it wouldn't lead anywhere interesting - just to the inside of the bag. I'm also guessing that my question has no answer because it's too hard to do any remotely rigorous calculation. Still, if anyone does know of such calculations or can point me to references I would be most interested. Are partitions to the inner/outer edge significantly faster Some linux dual/multi-boot tutorials / general partitioning tutorials say that the inner side of a hard disk is faster than the outer side so partitions towards the outside tend to be slower while some say that the exact opposite is true.  Which side is actually faster?  Is the difference noticeable?  How are the partitions physically placed on the disk as compared to the partition listing order-for example gparted shows a logical ribbon layout of the partitions. Are the partitions shown to the left side of this ribbon near the outer or inner edge of the disk physically?  Are there software benchmarks like testing some disk intensive stuff for the first time on identical vanilla installs of the same OS but on different partitions, inner and outer?  EDIT: Links   ctrl + f for "slower" on this page   Says outer side is faster   Says inner side is faster   Says outer side is faster(not about dual-booting) 'pagesize' attribute ignored in hot network list Steps to reproduce:   Open  in Guest/Incognito mode or with cookies disabled. This will have 30 questions per page by default. Click the  link and as expected, you'll see questions 1-50 with page size of 50. Go the the  and see the bug: you're in the second page of 30 items per page, i.e. you'll see questions 31-60 instead 51-100 as expected.     It is very annoying. Please fix it.  My user-agent is: Mozilla/5.0 (Macintosh; Intel Mac OS X 10.15; rv:70.0) Gecko/20100101 Firefox/70.0  There are no plugins installed affecting the site. It happens both when logged in or not.  The mechanism used to work before, but some weeks/months ago it stopped, enough to bother me to post here :)  Here are all modified "privacy" settings from about:support page:  privacy.clearOnShutdown.offlineApps true privacy.clearOnShutdown.openWindows true privacy.clearOnShutdown.siteSettings    true privacy.cpd.offlineApps true privacy.cpd.openWindows true privacy.cpd.passwords   true privacy.cpd.siteSettings    true privacy.donottrackheader.enabled    true privacy.history.custom  true privacy.item.cookies    true privacy.sanitize.migrateClearSavedPwdsOnExit    true privacy.sanitize.migrateFx3Prefs    true privacy.sanitize.pending    [{"id":"shutdown","itemsToClear":["cache","cookies","offlineApps","history","formdata","downloads","sessions","siteSetti privacy.sanitize.sanitizeInProgress ["cache","cookies","offlineApps","history","formdata","downloads","sessions","siteSettings","openWindows"] privacy.sanitize.sanitizeOnShutdown true privacy.sanitize.timeSpan   0 privacy.trackingprotection.enabled  true privacy.trackingprotection.introCount   20 Sets with no asymptotical density over $\mathbb N$ Let's consider the  defined by:      Take $ A\subset \mathbb N$; define the sequence $x_n= \dfrac{|A\cap[1,n]|}{n}$, and then if $\lim\limits_{n\to\infty} x_n$ exists, call it $d(A)$, the density of $A$ over $\mathbb N$.   My teacher said that the collection of sets that have a natural density is not an algebra, but I don't know why. I can't even find a set that does not have a natural density.  Please help me )= Suppose $f$ and $g$ are Lebesgue measurable, we want to show $f+g$ is measurable. So, the hint is to consider the continuous functions $F : \mathbb{R}^2 \to \mathbb{R} $ given by $h(x) = F(f ,g ) $. If we can show $F$ Is measurable, then Taking $F = f +g $ would solve our problem.  In other words, I want to show that the set $R = \{ (f,g) : F(f,g) &gt; a $ } is lebesgue measurable.. But this set is just a rectangle in the plane. And since $F$ is continuous, then $R$ must be open, and hence a union of open rectangles which are measurable and hence $R$ must be measurable. Is this a correct approach to the problem? Can someone help me to make this formal? thanks What makes some laser beams visible and other laser beams invisible? What makes the beam of some lasers:    visible?  such as the ones used in clubs or such as the laser pointers sold at amazon which if pointed to the sky look like a solid visible beam of light crossing the sky (it reminds me of the lightsaber in Star Wars). invisible?  such as the ones used in pointers for presentations.