How can 2 variables each be strongly correlated with a 3rd variable, but uncorrelated with each other?
If A and B are correlated with C, why are A and B not necessarily correlated?
$\newcommand{\Var}{\operatorname{Var}}$In this  is claimed that if the equation of errors in OLS is given by: $$u=y - X\beta$$ Then in the presence of heteroscedasticity the variance of $u$, will not be constant, $\sigma^2 \times I$, where $I$ is an identity matrix, but: $$\Var(u\mid X)=\sigma^2\Omega$$ In order to account for the heteroskedasticity, we can estimate the transform system, such that $P$ is a transformation matrix. $$Py=PX\beta-Pu$$ Where "the variance of a constant matrix $P$ times a random vector $u$" is: $$\Var(Pu\mid X)=P\Var(u\mid X)P'=P(\sigma^2\Omega)P'$$ Can somebody explain me the proof for that? In Python, you can do this:  import webbrowser webbrowser.open_new("http://example.com/")   It will open the passed in url in the default browser  Is there a ruby equivalent? Ways to put numbered balls in boxes no box being empty I know the formula for putting $n$ identical balls in $r$ different boxes such that each box has at least 1 ball, but what is the formula for putting $n$ different balls in $r$ different boxes, no box being empty?  Thanks! How to install a dictionary (danish) in Texmaker Why isn't there a centre of charge? When determining the gravitational attraction between 2 solid bodies, we can simplify computations by taking their masses to be concentrated at their respective centres of mass. However, had they been electrically charged bodies and we needed to compute electrostatic attraction, there is no "centre of charge" notion available to us. ( We would evaluate a 2-dimensional integral, or equivalently, apply Gauss's law. )  Is there any simple reason for the absence of such a centre of charge? Frequently, I've got the answer: "charge just doesn't work that way". I'm wondering if there's any log which stores information about a particular program such as when the program has started and closed manually on Windows such as MS Word, or Chrome. Any ideas? What are the consequences of "copying" a data set for OLS? How to generate a random snowflake NSString tokenize in Objective-C Push Faces Like Sketchup Is there a way in Blender to push faces like Sketchup does?     The best I can get is doing a regular extrude and a lot of work to clean the "mess" up...    Thank you for your time! I just got off a very long and very frustrating phone call with Apple support.  I purchased a used Apple computer which came installed with Mountain Lion. Meaning that the computer was shipped by Apple with Mountain Lion installed, and received by me with that same installation.  As a precaution, I tried to reinstall Mountain Lion via Recovery mode. This failed because my Apple ID hasn't purchased Mountain Lion.  Apple insisted that because I didn't purchase the computer new, I don't have a license for OS X. I don't believe this is correct, or even legal. This means that anyone using a used computer is doing so illegally, unless they've purchased a separate OS license.  Am I way off-base here? I'm pretty sure I now "own" a copy of Mountain Lion, and Apple is in the wrong. If this is correct, what are my options? Is there a way to exclude other particle systems from the effects of a Wind effect? I have a scene with a number of particle systems. I'd like to have a separate wind effect for my main scene and another for an extra: an emitter + wind-effect to blow leaves into my scene. I can't find any way to exclude, so here I am. At the very worst, I can just render the main scene and then render the wind effect and composite it, but I figured I'd check first. Why does my Mac OS X 10.6 kernel run in 32-bit mode? I have a MacBook Pro (5,1) with 4GB of memory running 10A432 - but it's running the 32-bit kernel.  Any ideas why it wouldn't be running in 64-bit mode, and how I can get it to do so? Expected Value Of Number of Removals From Urn Here's the question: "An urn contains b blue balls and r red balls. You repeatedly and independently remove balls from urn (without returning them) until the first blue ball is drawn. All balls currently in the urn have an equal probability of being selected each time a ball is removed. Define the random variable X as the number of balls that are drawn (number of red balls that are removed plus the first blue ball that is removed). Find E[X], the expected value of random variable X."  I'm having trouble finding a closed form expression for the expected value. Here's the work I've done: Is it possible to restore a MySql database only using files from Data directory? How to make an embedded question from "What time is it?" If the original question is "What time is it?" and I want to communicate it to another person, are these Embedded Questions OK?        I don't know what time is it.       or        I didn't know what time was it. (if communicated later) Why don't C++ compilers define operator== and operator!=? Why can only some child meta sites host chat rooms? Is there any way to bypass this restriction? When I try to create a new  room from , and type "meta" in the "select a site" box, I see only 8 child meta sites. Any specific reason for this?  Update:  I just noted  (pointed out by ). The conclusion of the experiment there was:        This experiment suggests that only the meta sites, for which at least   one room already exists, are offered.   ...the distinction between beta sites and graduated sites is not sufficient to explain this.      So, if I'm reading it correctly, it is currently impossible to create a room hosted on those child metas which do not already have an existing meta room (smells like a bug!)? Or is there a way to bypass this restriction somehow?  I can think of several legitimate reasons as to why a site may choose to keep their main chat rooms and meta chat rooms separate. Killing off that freedom of choice, and that too non-uniformly, isn't a good idea. If this really is a  rather than  (for a good cause), then it should be fixed! What can I do on a Visualforce page that is a renderAs="pdf" that will result in the name of the file that shows up when the user clicks Save As... to not be the name of the Visualforce page.  The page is generated via a GET request coming from clicking a custom button.  Below is some code that is representative of the PDF.   &lt;apex:page standardController="Account" extensions="AccountPdf"           showHeader="false"           sidebar="false"           renderAs="PDF"          title="AccountReport.pdf"          contentType="application/pdf#AccountReport.pdf"          &lt;head&gt;              &lt;title&gt;AccountReport.pdf&lt;/title&gt;          &lt;/head&gt;          &lt;apex:outputText value="Hello World"/&gt;  &lt;/apex:page&gt;   The browser bar does not have the title value in it and when the user clicks Save As... the name of the file is the name of the Visualforce page (e.g., myPageName).  If I remove the renderAs="pdf" the file downloads automatically with the correct file name due to the contentType, but the actual content type doesn't appear to be a PDF. What is a NullReferenceException, and how do I fix it?