Can someone explain how to mathematically perform linear regression on some data while constraining the fit line to pass through the $(0,0)$ point?
We have the following points: $$ (0,0)(1,51.8)(1.9,101.3)(2.8,148.4)(3.7,201.5)(4.7,251.1)  \\ (5.6,302.3)(6.6,350.9)(7.5,397.1)(8.5,452.5)(9.3,496.3) $$ How can we find the best fitting line $y=ax$ through the points? My calculator has the option to find the best fitting line $y=ax+b$ through these points, which is:  $$y = 53.28x + 0.37$$  How can I find the best fitting $y=ax$? It seems to me we can't just remove the $0.37$ without compensating in the $a$?
Javascript remoting: to invokeAction or not to invokeAction Digging in deeper to Javascript Remoting and I'm a bit confused.  The  starts off by showing how to set up everything and uses code like the following:  function getRemoteAccount() {     var accountName = document.getElementById('acctSearch').value;      // This remoting call will use the page's timeout value     Visualforce.remoting.Manager.invokeAction(         '{!$RemoteAction.AccountRemoter.getAccount}',         accountName,          handleResult     ); }   However, I've also seen examples where Visualforce.remoting.Manager.invokeAction is never called.  They end up looking something like the following:  function getText() {   var text = "";   JSRemotingBasicsController.doGetText(     function(result, event) {       // do something here     }   ); }   I'm wondering what is the point to using Visualforce.remoting.Manager.invokeAction when you can just reference the RemoteAction directly like the second example?  Is there something I'm missing?  Is there a time where the second example doesn't work? What's the reason I can't create generic array types in Java? Calculating the limit $\lim((n!)^{1/n})$ Find $\lim_{n\to\infty} ((n!)^{1/n})$. The question seemed rather simple at first, and then I realized I was not sure how to properly deal with this at all. My attempt: take the logarithm,  $$\lim_{n\to\infty} \ln((n!)^{1/n}) =  \lim_{n\to\infty} (1/n)\ln(n!) =  \lim_{n\to\infty} (\ln(n!)/n)$$ Applying L'hopital's rule:  $$\lim_{n\to\infty} [n! (-\gamma + \sum(1/k))]/n! = \lim_{n\to\infty} (-\gamma + \sum(1/k))=  \lim_{n\to\infty} (-(\lim(\sum(1/k) - \ln(n)) + \sum(1/k))  = \lim_{n\to\infty} (\ln(n) + \sum(1/k)-\sum(1/k)  = \lim_{n\to\infty} (\ln(n))$$ I proceeded to expand the $\ln(n)$ out into Maclaurin form $$\lim_{n\to\infty} (n + (n^2/2)+...) = \infty$$ Since I $\ln$'ed in the beginning, I proceeded to e the infinity  $$= e^\infty  = \infty$$  So am I write in how I approached this or am I just not on the right track? I know it diverges, I was just wanted to try my best to explicitly show it. Problem with gummy-bears being too much like jelly I've been trying a simple recipe I found on the internet, which is a simple recipe consisting mostly of gelatin.  The problem is that the end result is basically just a fruit-flavoured jelly (Jell-O?), rather than the more chewy gummy-bears (Haribo) style of jelly confectionery.  Can anyone suggest what I need to do to make them less springy and more chewy.  It's all difficult to articulate!  Here's what I used for the first test-batch:   12 tbsp sugar 12/3 cup fruit juice 8 tbsp Golden Syrup 8 tbsp gelatin   soften the gelatin in 1/2 cup of cold water. place sugar, syrup and the juice in a pan and gently heat until sugar dissolves. Stir in the gelatin and stir until dissolved. Pour into moulds and wait until set.    Thanks What are the eigenvalues of matrix that have all elements equal 1? As in subject: given a matrix $A$ of size $n$ with all elements equal exactly 1.   What are the eigenvalues of that matrix ? The distance between touching objects What is the distance between, say, a cup of coffee and the table it rests on? What is the distance between two touching hands? Add an application to the command search path in csh Recently, I have installed an application (gnuplot) under user directory (/home/usr/bin). I want to run the application whenever I type 'gnuplot' in any directory. What could I do?  I tried to set the path in ~/.cshrc by  setenv gnuplot /home/usr/bin/gnuplot   but it doesn't work. It reports "command not found" as I type gnuplot in the terminal. Schengen Visa Expiration I have a multiple entry 90 days Schengen visa (category C) from 15 March 2014 till 21 Dec 2014.    With this visa I entered The Netherlands on 4 April 2014 and left there on 13 April 2014.    I am planning to re-enter The Netherlands on 19 Dec 2014 and leave there for London (I have a valid UK visa as well) on 21 Dec 2014, at 7 am from Amsterdam.    Am I permitted to stay in The Netherlands on 21 Dec 2014 or should I leave the country on 20 Dec evening itself? Do Arcane Ward's starting hit points include the INT modifier once or twice? An abjuration wizard's Arcane Ward states:     [...] The ward has hit points equal to twice your wizard level + your Intelligence modifier.   So how many hit points is this supposed to be?  \$ (2 \times WizardLevel) + INT_{mod}\$  or  \$2 \times (WizardLevel + INT_{mod})\$ ?  I feel like the phrasing hints toward the first calculation, but it's still somewhat ambiguous. How can I upload files asynchronously with jQuery? I have a consideration about new off-topic close reason:     Questions asking us to recommend a tool, library or favorite off-site   resource are off-topic for Stack Overflow as they tend to attract   opinionated answers and spam. Instead, describe the problem and what   has been done so far to solve it.   For example take that question:   It has a close vote with the reason above. But if it would be formed     How to zoom image in an absolute position div to the side?   The answer would be probably also a jQuery plugin or javascript library, but it would follow the patter of most questions about jQuery.  Take that question:   This is the good question about real-life problem. The answer is to use a maven plugin. It is correct, there's no need to reinvent the wheel or rediscover the America.   But  I'm afraid the off-topic text could be misleading and could be misused to close such a questions as that about maven simply because a tool, library or plugin is the answer.   Is it a new guideline that the questions such as cited above should be banned, no matter how they are formed (this would make most how-to-do-in-maven/jquery) questions illegal? Or the close reason should be changed to make more clear what the guidelines are (it's not clear to me now)? Proof: How many digits does a number have? $\lfloor \log_{10} n \rfloor +1$ I read recently that you can find the number of digits in a number through the formula $\lfloor \log_{10} n \rfloor +1$ What's the logic behind this rather what's the proof? No indent in the first paragraph in a section? Word for lights on police cars, etc Biblatex: submitting to a journal Suppose that I moved from BibTeX to biblatex. With BibTeX I just copied the content of .bbl file into final version of my paper before submitting it to a journal. What should I do at same stage having .bbl file produced by biblatex? It is of quite different format. Bottom to top explanation of the Mahalanobis distance? I'm studying pattern recognition and statistics and almost every book I open on the subject I bump into the concept of Mahalanobis distance. The books give sort of intuitive explanations, but still not good enough ones for me to actually really understand what is going on. If someone would ask me "What is the Mahalanobis distance?" I could only answer: "It's this nice thing, which measures distance of some kind" :)   The definitions usually also contain eigenvectors and eigenvalues, which I have a little trouble connecting to the Mahalanobis distance. I understand the definition of eigenvectors and eigenvalues, but how are they related to the Mahalanobis distance? Does it have something to do with changing the base in Linear Algebra etc.?  I have also read these former questions on the subject:       I have also read .  The answers are good and pictures nice, but still I don't really get it...I have an idea but it's still in the dark. Can someone give a "How would you explain it to your grandma"-explanation so that I could finally wrap this up and never again wonder what the heck is a Mahalanobis distance? :) Where does it come from, what, why?   UPDATE:   Here is something which helps understanding the Mahalanobis formula: This is Exercise 26 from Chapter V Algebraic Extensions in Lang's Algebra.  $F$ is finite normal extension over $k$ and $f(x)$ is irreducible in $k[x]$. If $f(x)=g(x)h(x)k(x) \in F[x]$ where $g(x),h(x)$ are monic irreducible factors in $F[x]$, I need to show that there exists an automorphism of $F$ which takes $g(x)$ to $h(x)$.  Any hints would be appreciated.  Sending one root to another is okay but how to do that for a collection of roots? How do I make all the theorem-alike environments have an ending symbol? What part of speech is handsome in the sentence:     The bridegroom looked so handsome. What is the difference between <%# and <%= in ASP.NET MVC?