I have a simple question about regression. The situation:  I have three variables $X_1,X_2,X_3$ and a variable I try to estimate $Y$. (In practice I have a list of participants for which the values of all of these variables are known) Using regression I obtain $$Y= a_0 + a_1X_1 +a_2 X_2 +a_3 X_3 +a_{1,2}X_1\cdot X_2 + a_{1,3} X_1\cdot X_3 + a_{2,3} X_2\cdot X_3 + a_{1,2,3}X_1\cdot X_2\cdot X_3$$ and I get $p$-values for each of these coefficients. I made these changes:  I decreased all the values of $Y$ by $10$ (because I wanted the values to start at zero). Then I replaced $X_1$ with $X_1-1$ ($X_1$ was the gender, and instead of $1,2$ I wanted it to be $0,1$). Finally I divided $X_2,X_3$ by $40$ to get values between $0$ to $1$. All these changes also changed the coefficieints $a_0,a_1,...$ (I understand why this is). Positive coefficients stay positive and negative stay negative. But the $p$-value changed and I do not understand why. Does the $p$-value suppose to change by making these changes? What does it mean? Basically I lack the understanding myself and I need your help to decide whether I can use the new data (for which the $p$ value is better) to conclude what I want. Thank you :)
Collinearity can pose certain problems in various kinds of regression problem. In particular, it can make the parameter estimates have high variance and be unstable.   Various methods have been proposed to deal with this including ridge regression, partial least squares regression, principal components regression, dropping variables and getting more data.   One method that is controversial is standardizing or scaling the independent variables, with various experts saying it is a good (e.g. Garcia) or bad (e.g. Belsley) idea. Belsley's issue seems to be (in non-technical terms) that changing the IVs just pushes the problem under the rug.  But other experts seem not to agree. And the authors tend to get rather heated in defending their own positions.   Back when I did my dissertation (on collinearity diagnostics) I found Belsley's arguments convincing, but that was long ago (I got my degree in 1999).  I'm looking either for expert guidance or for any current review article that is unbiased.
SF Story about human adapting to alien environment How do I have a camera follow my object in Unity? I have an object that automatically moves by itself and I want the main camera to automatically follow it.(Like in games such as geometry dash and jetpack joyride)  This is the code for the automatic moving object in case it is needed:  using UnityEngine; using System.Collections; public class automove : MonoBehaviour { public static int movespeed = 5; public Vector3 userDirection = Vector3.right;    public void Update() {     transform.Translate(userDirection * movespeed * Time.deltaTime);  } }   So does anyone know any good scripts I could add to the main camera to follow this object that automatically moves? Thanks in advance! Does everything with mass or energy have a gravitational pull? Finding the search terms behind 'not provided' We hold an L1 visa (Citizens of India) and are planning a cruise to the Bahamas this summer. Are there any Visa requirements to enter Bahamas. Calculating Latitude/Longitude X miles from point? I am wanting to find a latitude and longitude point given a bearing, a distance, and a starting latitude and longitude.  This appears to be the opposite of this question ().  I have already looked into the haversine formula and think it's approximation of the world is probably close enough.  I am assuming that I need to solve the haversine formula for my unknown lat/long, is this correct? Are there any good websites that talk about this sort of thing? It seems like it would be common, but my googling has only turned up questions similar to the one above.  What I am really looking for is just a formula for this. I'd like to give it a starting lat/lng, a bearing, and a distance (miles or kilometers) and I would like to get out of it a lat/lng pair that represent where one would have ended up had they traveled along that route. Short Story about interminable rain on Venus It's not All Summer in a Day.  This was a story about explorers on Venus, who are separated from their base (possibly they're lost, possibly they suffered equipment failure, possibly they're just traveling from base to base) and are slowly being driven insane because it never stops raining.  The story is old enough that Venus' clouds were still believed to indicate a wet climate.  I can't remember much more detail than that.  I have the impression that the narrator at one point either dreamed of or fantasized about walking into the destination base and being handed a very plush towel to dry off.  I can't remember the central plot points - only the (very wet) setting.  I would have read this in the late 1970's or early 1980's.  I thought it might be an H. Beam Piper short story but I've been through his catalog and don't see any likely suspects. Xerces error: org.apache.xerces.impl.dv.dtd.DTDDVFactoryImpl Prove normal matrix is 4th power of some self-adjoint matrix Let $A\in\mathbb{M}_n(\mathbb{C})$ be a matrix of order $n\geq 2$. Let $p_A(x) = (x-\lambda_1)\cdots (x-\lambda_n)$ be the characteristic polynomial of $A$ such that all $\lambda_i$ are positive real numbers.  Suppose that $A$ is a normal matrix. Prove that one can write $A=G^4$ for some self-adjoint matrix $G$.  My thinking is that since $A$ is normal, by Principal Axis Theorem, we have $A=UDU^\ast$, where $U$ is a unitary matrix and $D$ a diagonal matrix. However, I fail to see how to proceed. Could anyone help me out? My overall upgrade went well, but I am left with a critically lingering issue of mysql-server not being able to install itself, and nothing I am trying gets it to work.  This is the error I see when trying to install/reinstall it:  Setting up mysql-server-5.7 (5.7.11-0ubuntu6) ... Job for mysql.service failed because the control process exited with error code. See "systemctl status mysql.service" and "journalctl -xe" for details. invoke-rc.d: initscript mysql, action "start" failed. dpkg: error processing package mysql-server-5.7 (--configure):  subprocess installed post-installation script returned error exit status 1 dpkg: dependency problems prevent configuration of mysql-server:  mysql-server depends on mysql-server-5.7; however:   Package mysql-server-5.7 is not configured yet.  dpkg: error processing package mysql-server (--configure):  dependency problems - leaving unconfigured No apport report written because the error message indicates its a followup error from a previous failure.                    Processing triggers for systemd (229-4ubuntu4) ... Processing triggers for ureadahead (0.100.0-19) ... Errors were encountered while processing:  mysql-server-5.7  mysql-server E: Sub-process /usr/bin/dpkg returned an error code (1)   I've tried completely removing it, though doing so attempts to install MariaDB because of dependencies (?). Any suggestions on what I can do to fix this would be most welcome.  EDIT: Looks like I'm not the only one: How to close view windows? Google Sheets QUERY won't display cell text if other cells have numbers I'm not sure what is happening in my Google Sheet query and could really use some help. I have  that demonstrates and explains the issue.   Basically, I'm using a query to pull data from a Google Spreadsheet that is populated by a Google Form. If the form submits only numbers (100), there is no problem. However, if someone submits a string ($100 or 100 dollars), the query will not display the string. It will only display form submissions that are 100% numbers.   Also, if the 1st submission is a string (not 100% numbers) the query will work.   Here is my query  =query(data!B2:CL,"select B, C, D, E, F, G, H, I, J, CI, BZ, CA, BA  where J = 'Industry Certification'",false)   Any ideas on why this is happening?  Also, I'm aware that I can limit the form to numbers only. I'm trying to avoid that and learn 'why' this is happening. I'm completely new and lost in Ubuntu 12.04, I'm having trouble navigating to my Sublime folder which I know is in my /opt folder. Yet I've tried to no avail to navigate into it via Terminal window. The directory is colored in blue, no idea what this means...but I am able to access the folder using the GUI explorer...?  k@k-Ubuntu:~$ cd /opt k@k-Ubuntu:/opt$ ls Sublime Text 2 k@k-Ubuntu:/opt$ cd Sublime Text 2 bash: cd: Sublime: No such file or directory k@k-Ubuntu:/opt$ cd /Sublime Text 2 bash: cd: /Sublime: No such file or directory How can $\pi$ be irrational if it can be calculated using an infinite series of rational numbers? Expressing $1.24\overline{123}=1.24\;123\;123\;123\;\ldots$ as the ratio of two integers How do American English and British English use the definite article differently? I decided to make sure that I know this important difference between American and British English, so I wrote what I have found out so far and I would be grateful to anyone who reads this and tells me whether I am wrong, or not.  In British English when people say  to hospital or in hospital when  talking  about somebody being there as a patient they don't use the definite article : "I had to go to hospital", "She spent two weeks in hospital". And the meaning is that somebody was there as a patient.   If then for some other reasons British English speakers  will use the definite article which will change the meaning itself, I noticed that, in American English, native speakers often use the  the and if they need to show that somebody is in church to pray,  in school as a student, in hospital as a patient, in prison as a prisoner, they use 'in' and not 'at'. Do American English speakers use 'at' like British English speakers use 'the' to give the sentences a different meaning?    Are my sentences correct? Do they show American English usage?   He is in the school. (enrolled as a student) He is at the school. (for some different reasons) He is in the hospital. (as a patient) He is at the hospital. (visiting somebody) He is in the church. (to pray) He is at the church. (for some different reasons) He is in the university. (as a student) He is at the university. (not as a student) He is in the college. (as a student) He is at the college. (Not as a student) He is in the prison. (as a prisoner) He is at the prison. (not as a prisoner) I need help to find the Galois Group of $x^5 +1$. I know that it has a 5-cycle and a 4 cycle and is not a subgroup of $A_5$. Thanks! Submitting ACM Conference papers to ArXiv I'm a little confused. The  states:     ACM authors hold the right to post copies of their own peer-reviewed accepted ACM works on any non-commercial repository or aggregation that does not duplicate ACM tables of contents, i.e., whose patterns of links do not substantially duplicate an ACM-copyrighted volume or issue. Non-commercial repositories are here understood as repositories owned by non-profit organizations that do not charge a fee for accessing deposited articles and that do not sell advertising or otherwise profit from serving articles.   However, the  site states:     Can I publish the published version of my publication on arXiv?       No. An ACM author cannot grant arXiv.org or any other publisher rights to distribute their works that have been published by ACM.   SHERPA/Romeo shows ACM as being a "Green Publisher", which would support the case that I can upload to ArXiv.   states that I can upload pre- or postprints under certain circumstances, but does not explicitly mention Arxiv, positively or negatively.  So, what is it? Can I submit a paper I published with an ACM Conference (ACM WiSec, if that makes a difference) to ArXiv or not? As I understand it, ArXiv is a non-profit, so it would fit the terms of the publishing policy. Or is this related to the rights you have to grant ArXiv upon submission?  If I can only publish a specific version of the paper, which one? Can I buy a plane ticket from A-B-C but get on the plane at B? Moon photography Hi I am a photography hoobyist. At the moment I am using a Nikon D3100 with the standard kit lens (18-55mm). I am interested in taking photos of the moon. I am debating whether to buy a 55-200mm lens or a 55-300mm lens. Which one would be better?  P.S I am on a tight budget and I am looking for a lens for personal use, not commercial.  Would appreciate any answers!  Thank you!