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Is there a way to use the covariance matrix to find coefficients for multiple regression? For simple linear regression, the regression coefficient is calculable directly from the variance-covariance matrix $C$, by  $$ C_{d, e}\over C_{e,e} $$ where $d$ is the dependent variable's index, and $e$ is the explanatory variable's index.  If one only has the covariance matrix, is it possible to calculate the coefficients for a model with multiple explanatory variables?   ETA: For two explanatory variables, it appears that $$\beta_1 = \frac{Cov(y,x_1)var(x_2) - Cov(y,x_2)Cov(x_1,x_2)}{var(x_1)var(x_2) - Cov(x_1,x_2)^2} $$ and analogously for $\beta_2$. I'm not immediately seeing how to extend this to three or more variables. Prove $f $ is identically zero if $f(0)=0$ and $|f'(x)|\le|f(x)|$ How to reconcile the cashless human/Federation society with human traders and merchants From a variety of sources, including , we know that the Federation (or at least the humans) don't use money. This raises the problem that humans frequently visit worlds where there is currency, and, in the case of DS9, operate a station that has currency frequently in use (for example, Federation personnel frequently attend Quark's bar). Additionally, we see human traders.   My question is, how do humans get "money" (credits, latinum, etc.)? How would a human even get the resources to purchase their own merchant ship or the resources to fill its cargo holds with merchandise? If Federation personnel can simply be given money for the asking, why haven't they poured so much money down Quark's throat that he chokes on it? Should “two weeks vacation” be written “two weeks’ vacation” with a possessive apostrophe? I’ve always understood that the phrase two weeks usually turns into two weeks’ when used as a modifier as in   I’m giving my two weeks’ notice.  I get two weeks’ vacation. (“two weeks’ holiday” for Brits)   with an apostrophe on the word weeks’, indicating that the vacation “belongs” to the weeks.   One way to explain this is the phrase “two weeks of vacation” being contracted to “two weeks’ vacation” – the vacation is “of” the weeks; that is, it is possessed by them.  But I’ve seen a lot of people omit the apostrophe in casual writing, and thinking about it, it seems plausible that the noun vacation would be plainly modified by the adjectival phrase two weeks.  But on the other hand, shouldn’t adjectival phrases be hypenated, namely two-weeks vacation?  Yet that seems wrong, too: the hyphenate should be singular, two-week vacation (like two-tone shoes) because .   touches on this (and references a good ) but doesn’t explain why the plural must be possessive in this case.   suggests that two weeks might be adverbial rather than adjectival, and thus resists being used attributively. But that still doesn’t quite explain this particular muddle of pluralization, possession, and attribution.  Given all this, why should “two weeks vacation” be written “two weeks’ vacation” with a possessive apostrophe? How do you prove that $e=\sum_{n=0}^{\infty}\frac{1}{n!}$? Here I am assuming $e:=\lim_{n\to\infty}(1+\frac{1}{n})^n$. Do you have any good PDF file or booklet available online on this? I do not like how my analysis text handles this... limit of integral $n\int_{0}^{1} x^n f(x) \text{d}x$ as $n\rightarrow \infty$ How do I boot my PC from GRUB? My current idea is to use the dual graph, and prove that that is a bipartite graph, and so proving the statement. But I can't seem to figure out how even degree for all verticies means that it is bipartite.  Any help is appreciated. Thanks! Find all $n \in \mathbb{N}$ such that $\phi(n) = 4294967296=2^{32}$.  I managed to find that $16106127360$, $8589934592$, $10737418240$ and $12884901888$ are solutions for the equation, but I do not know how to find all of them. Run apt-get without sudo barchart with pgfplot - missing bar I am using PGFplot to make a barchart. There are 4 entries in my csv file and unfortunately I have only 3 bars in my figure.   my LaTeX code:  \begin{figure}     \centering     \begin{tikzpicture}          \begin{axis}[             x tick label style={/pgf/number format/1000 sep=},                 xlabel=Sequence,             ylabel=Heigth,                 ymin=0.7,             enlargelimits=0.05,             legend style={at={(0.5,-0.15)},                 anchor=north,legend columns=-1},             ybar interval=0.7,             width=\textwidth,             ]             \addplot table [col sep=comma,trim cells=true,y=height] {numericaltests/data/test.csv};              \addplot[red,sharp plot,update limits=false]                 coordinates {(-1,1.00) (34,1.00)}                 node[above] at (axis cs:15,1.00) {};             \legend{Ca2Fe2As2}         \end{axis}     \end{tikzpicture}     \caption{Sequence}     \label{fig:sequenceHeight} \end{figure}   my test.csv file:  sequence,height 1,2.0 2,1.5 3,1.8 4,2.4   Barchart: What EXACTLY cause Voldemort's soul piece to split off when he killed Lily and tried to kill Harry? What metadata does a LibreOffice file contain and how to remove it? I am using LibreOffice on Linux. One way I know of viewing and removing metadata from a LibreOffice file is going to File -&gt; Properties -&gt; General, unchecking  “apply user data” and click reset. Then go to “Description” and “Custom” Properties and remove information from there, if exists.   Does it truly remove all the metadata or something is left and what is it and what other methods can I use to remove it?   Also, if I unzip a LibreOffice file, is contents.xml the only place where metadata may be found?  If I forgot to remove any metadata, is it possible that the username is transmitted? Graphics horribly corrupted on Ubuntu 16.04 in VirtualBox, showing random strips of pixelated colors Prove that for all $n&gt;2$ there exists at least one prime $p$ such that $\sqrt{n}&lt;p&lt;n$ using elementary methods.  My try: If not, $\sum_{p&lt;\sqrt{n}} (\lfloor n/p \rfloor-\lfloor \sqrt{n}/p \rfloor) \geq n-\sqrt{n}$  then...? How to horizontally center an element Add a duplicate:0|1 search operator I often search for closed questions and sift through the ones that are not duplicates to see if any of them need to be killed. Technically, closure is the first step towards deletion and the only closed posts that are actually useful are duplicates (unless it's a crappy one).  For the rest, if the community hasn't bothered to reopen it after a while or if the OP has made no effort to edit their question, I delete it if it has no redeeming content. For example, the only closed posts seen on  are exact dupes.  But this does become tedious when there are several results for various close reasons with duplicates interspersed between them. I'd like to be able to search as:  closed:1 duplicate:0   so that it gives a list of questions closed as OT/NaRQ/NC/TL. This will be similar in behaviour to migrated:0|1.   This will also be useful for 10k+ users on all sites (2k+ in beta) in the network, especially SO, so that they can search for questions to spend their delete votes on— especially closed, non-dupe questions in the tag they specialize in. More often than not, I hesitate to vote on questions that are outside my area of interest (unless it is crappy). Can I prevent/restrict standard users from installing/uninstalling software? Can i prevent/restrict standard user from installing/uninstalling software in Ubuntu 12.04 desktop? How do you add tags to blocks so they can only be placed on 1 type of block? Wouldn't it be a good idea to be able to vote for questions to be moved to any Stack Exchange site? For example, I just voted  as off topic, but that was all I could do. I wish I could've voted it be moved to .  It's OK to have the predefined list of sites that is now when voting to move, but it would be nice to have a more link, where we could pick any Stack Exchange site.  Here's a quick mockup of how I see this implemented:    When the more link is clicked, a list of all the Stack Exchange sites should appear.