I recently began learning about OLS estimation of multiple regression models and came across the following formulas explaining the calculations:   What would the formulas be for an OLS regression model with more than two independent variables?  I'm asking this because I'm trying to make an application in JavaScript that will perform the calculations. Alternatively, I would be amazing if anyone knew of a free API that could be called from JavaScript to calculate OLS multiple regressions.
In the simple linear regression case $y=\beta_0+\beta_1x$, you can derive the least square estimator $\hat\beta_1=\frac{\sum(x_i-\bar x)(y_i-\bar y)}{\sum(x_i-\bar x)^2}$ such that you don't have to know $\hat\beta_0$ to estimate $\hat\beta_1$  Suppose I have $y=\beta_1x_1+\beta_2x_2$, how do I derive $\hat\beta_1$ without estimating $\hat\beta_2$? or is this not possible?
Can't get armature to move mesh! I am trying to get an armature to move one limb on a deer I have made. Here is my design process!   I made the body and limbs as separate meshes. I wasn't sure how to create limbs out of the body of the mesh and make them look good. I tried joining  the meshes, creating the armature and setting automatic weights and then moving the armature in pose mode. The mesh would not move with the armature I thought maybe it was because many vertices between the mesh and the limb were crossing so I thought maybe that was why the armature was not moving the limbs I used the cut tool to remove the intersecting mesh on the limb and the body so that there were no intersecting vertices.  I then joined this set of meshes and created a new armature, set the weights to automatic and tried to move the mesh in pose mode and it still won't work.    What should I do? I don't know what else to try. I have been following any other online instructions exactly.  File Link: Discoveryd Alternative to Replace mDNSResponder Argument? This is a direct follow-on to . , I'd add the "-AlwaysAppendSearchDomains" argument to the mDNSResponder plist file so that all local resolver lookups added the search domains, regardless of whether there was a period in the label to be looked up. For example, whether I try to ssh to hostname foo.bar or foo, the search domain of baz.com should be tried, not only for the latter case, as was (and is) the default behavior.   Now, it looks like the mDNSResponder is gone, replaced with discoveryd. I cannot find a similar option to get it to always appending the search domain. Suggestions? I'd rather not go the route of using a non-default local resolver, but I'd consider it as an option. For now, I'll just type in the long FQDNs, but I'd really rather not.  Thanks, Pete Confused about AMD/Intel When I go to the downloads page to get Ubuntu, it automatically downloads the AMD version, but my computer has no hardware with AMD on it. I only have Intel and Nvidia. Also, when I install this AMD version on my computer, it works (other than the constant random freezing of the computer when I use Ubuntu). I don't really understand why the amd version works on a computer with an intel processor. Base64 Encode String in VBScript I have a web service load driver that's a Windows Script File (WSF), that includes some VBScript and JavaScript files. My web service requires that the incoming message is base64 encoded. I currently have a VBScript function that does this, but it's very inefficient (memory intensive, mostly due to VBScripts awful string concatenation)  [Aside; Yes, I've seen . The concatenation is happening in a loop across messages that are 1,000's to 10,000's bytes in size.]  I've tried using some custom string concatenation routines; one using an array and one using ADODB.Stream. These help, a little, but I think it would help more if I had some other way of encoding the message rather than via my own VBS function.  Is there some other way of encoding my message, preferebly using native Windows methods? Is it correct to use Bernoulli's theorem to explain that a disk floats in the air? Should the correct explanation be based on Boyle's law? In this video, a device is introduced from 1 minute to 18 seconds. After entering the air, the disc at the bottom of the device will be suspended in the air. The video explains that this is because of the Bernoulli effect, but I think this explanation is incorrect, because the disc gap, the radial volume is increasing. Therefore, the reason why the disk is suspended is that the air volume becomes larger, so the pressure decreases (according to Boyle's law). If the air moves along the radial direction at a constant speed, the volume of the air must be constantly increasing, right? So the pressure is decreasing, right? A required field that isn't really required? ...the email field in my clients data entry system is required but users of the system are allowed to enter na@na.com if the customer refuses or doesn't have an email address. Is this best practice? Have any suggestions or workarounds for their solution? I would like to convert a large LaTeX project (i.e. spanning multiple files) into plain text. The purpose is generation of statistics, so representing mathematics is not an issue. In fact, all mathematics is ideally ignored.  I have found  but could not get it to run. It seems unfinished, but is exactly what I am looking for otherwise. I am using texlive 2013, and just ran the following command to update the packages.  sudo ./tlmgr update  -all   After it finished, I tried to compile tex documents that uses tikz package as the following MWE shows:   \documentclass{article}  \usepackage{tikz}  \begin{document}       aaaa  \end{document}   Then pdflatex complains; it said:   (/usr/local/texlive/2013/texmf-dist/tex/latex/pgf/utilities/pgfrcs.sty  (/usr/local/texlive/2013/texmf-dist/tex/generic/pgf/utilities/pgfutil-common.tex  ! I can't find file `pgfutil-common-lists.tex'.  l.556 \input pgfutil-common-lists.tex   The problem is that, pgfutil-common-lists.tex is indeed in the directory:   /usr/local/texlive/2013/texmf-dist/tex/generic/pgf/utilities/   Why is that? pdflatex should be able to find it, right? I even download the  again, and replace the pgf directory in   /usr/local/texlive/2013/texmf-dist/tex/generic/   Nothing changed at all........... Any idea? Thank you for your critics.  %=====================================================================  Then followed the comments, I type the following command in the terminal:    sudo mktexlsr gives me command not found;  mktexlsr gives me:  mktexlsr: /usr/local/texlive/2013/../texmf-local: directory not writable.     Skipping...  mktexlsr: /usr/local/texlive/2013/texmf-config: directory not writable. Skipping...  mktexlsr: /usr/local/texlive/2013/texmf-dist: directory not writable. Skipping...  mktexlsr: /usr/local/texlive/2013/texmf-var: directory not writable. Skipping... mktexlsr: Done; Forkpsewhich pgfutil-common-lists.tex, nothing pops up. What is the pronunciation of the possessive words that already end in s? Possible Duplicate:           My name is Greg — this is Greg 's post.  If my name ended with an 's', I am aware of the proper apostrophe usage (James&nbsp;→ James'), but how should this be pronounced?  Phonetically, am I Jameses best friend or James best friend? In Peter Jackson's film The Fellowship of the Ring, when the Council of Elrond takes place it shows a total of 22 members:    We all know the names of the ones who were part of the Fellowship, but I want to know who are the rest of the people in the council. Who are the elves that came with Legolas? The men next to the dwarves? The three old men sitting next to Boromir? Or the two elves next to Aragorn?  Starting from left to right:   Frodo Gandalf Elf Elf Legolas Elf Old Man Old Man Dwalin Gloin Gimli Nori Old Man Boromir Old Man Old Man Elf Elf Aragorn Elladan Elrond Elrohir How do I get the local machine name? Let $X$ be a space that satisfies the hypotheses used to construct a universal cover $\overline{X}$. Let $\pi = \pi_1(X)$ and consider the action of the group $\pi$ on the space $\overline{X}$ given by the isomorphism of $\pi$ with $\text{Aut}(\overline{X})$. Let $A$ be an abelian group and let $\mathbb{Z}[\pi]$ act trivially on $A$, $a \cdot \sigma = a$ for $\sigma \in \pi$ and $a \in A$.  Now, assume that $X$ is a CW complex. How do I see that $\overline{X}$ is a CW complex such that the action of $\pi$ on $\overline{X}$ induces an action of the group ring $\mathbb{Z}[\pi]$ on the cellular chain complex $C_*(\overline{X})$ such that each $C_q(\overline{X})$ is a free $\mathbb{Z}[\pi]$-module and$$C_*(X; A) \cong A \otimes_{\mathbb{Z}[\pi]} C_*(\overline{X})?$$ Resize image in Python without losing EXIF data I need to resize jpg images with Python without losing the original image's EXIF data (metadata about date taken, camera model etc.). All google searches about python and images point to the PIL library which I'm currently using, but doesn't seem to be able to retain the metadata. The code I have so far (using PIL) is this:  img = Image.open('foo.jpg') width,height = 800,600 if img.size[0] &lt; img.size[1]:     width,height = height,width  resized_img = img.resize((width, height), Image.ANTIALIAS) # best down-sizing filter resized_img.save('foo-resized.jpg')   Any ideas? Or other libraries that I could be using? Do USA States have reciprocal agreements for learner drivers' permits? I have installed Ubuntu 13.04 on my desktop (runs like a charm). Then I used Crouton to install Ubuntu 12. 04 on my chromebook samsung (ARM). It also works quite well.  Here comes my question. Can we have a true Ubuntu (preferably 13.04) on my ARM chromebook?  It seems that the Crouton/Ubuntu is not 100% the real thing.  The best option would be to have the full Ubuntu 13.04 and remove the Chrome OS. Is it worth it to upgrade a Toshiba Satellite C55-A5300 laptop given the latest productivity software requirements? I would like to upgrade a Toshiba Satellite C55-A5300 laptop so it can be as useful as it can be nowadays. I haven’t needed to use much software for a few years now, and I’m not able to gauge whether a maxed out upgrade of this laptop would be up to running the latest versions of MS Office and Acrobat smoothly. Maybe even run some Photoshop and Lightroom? I want to install the best CPU that will work optimally within the parameters of this laptop, including the laptop’s cooling capabilities. I ultimately want improved performance, but I want the performance to be as smooth as possible. From what I gather the Pentium 2030M is the best processor this motherboard will accept. Am I on the right track? I also plan to fully upgrade the memory and the hard disk speed with respective upgrades. What is the max memory per RAM slot (2 total)? What is the fastest speed of RAM I can use?  Copied from the Toshiba spec sheet:  Processor and Graphics Intel® Celeron® Processor 1037U o (2M Cache, 1.80GHz) Mobile Intel® NM70 Express Chipset Mobile Intel® HD graphics with shared graphics memory Memory Memory Configured with 4GB DDR3 1333MHz (max 16GB) 2 main memory slots. One slot is occupied Storage Drive 500GB (5400 RPM) Serial ATA hard disk drive Power 45W (19V 2.37A) 100-240V/50-60Hz AC Adapter How to find the running network services and the port and user I want to find a list of all network services running on my system, including details of the port and services and the users. I know that I need to use netstat, ps and fuser. but I don't know how to write the command. Do I need to write a shell script to find all of them? or I can use in a line of commands? Thanks for your help. How to draw a Sankey Diagram using TikZ "It is they who lied" or "it is them who lied?" Which is the correct usage of the third person, plural pronoun?     It is they who lied.   It is them who lied. If there was a black hole on earth, what would it look like? If an answer does exist, I'd love to hear it. I'm trying to incorporate a doomed earth story in something I'm writing, and the end of the world I'm going for is a black hole.  Let's say the black hole was created in the Philippines (I chose it because it's on the equator). Here's  for reference.  If I was standing 90 degrees of that, in Kenya, or if I was standing 180 degrees of that, in Mexico; what would I see in those two separate instances? What if I was standing in Japan above it, or in Australia below it?  Let's also say I was riding a boat towards the source of the black hole. Unlike most imagined scenarios where I am orbiting the black hole and slowly falling into it, this time I'm no longer orbiting it - I'm getting sucked into it instead. I'm imagining that the black hole will "half" be inside Earth and "half" will be in the atmosphere. But as it pulls me in, what will it look like to me (if I was massless, so no tidal forces)? It's probably not going to be a black hemisphere sticking out of the ground. Light will be lensed around it in some way so as to appear like a hole in the air.  Also, if the black hole was very small, it probably won't have a strong gravitational pull, and assuming it doesn't disappear, you'd be able to look at it (or at least, its effect on the light in its surroundings). Of course, as you approach it, it would still have an event horizon, so spacetime would still be warped if you're near enough and the surroundings will still experience tidal forces.  As the black hole gains mass, it will get larger, and so its event horizon will increase. If I was standing in Kenya and the event horizon "washes over me," (as in a water wave) what will I see?  I've so far imagined that, at least when seen from outer space, there will be a hole on the ground and light will be lensed around it. When you are on the ground, though, it becomes a bit harder to imagine.  I do hope someone can lend me a hand!  Edit: Someone had previously answered this question, but I'm not sure why it's been deleted. It was pointed out to me, though, that a black hole cannot stay in place. So an additional question for me is, does that mean it is impossible to be standing still, and the event horizon "washes over you"?  Edit2: Here's a guiding thought experiment that could answer the question. Imagine that you are in outer space directly above the black hole, looking at the black hole that is on the earth's surface. Can you imagine what it would look like? It would simply be a hole with the surrounding light gravitationally lensed around it (possibly lensing the entire earth if it's big enough - but let's say it's not).  Now imagine that you are on the direct opposite of where you were above - you're right behind the black hole this time, looking directly at the black hole but unable to see it because the earth is blocking your view.  Now try to imagine, from the second image, rotate the earth into the first image. I find it a bit hard to do. Just as the black hole is appearing as you rotate the earth, how would the light be lensed?