Normalization Interval variable
When conducting multiple regression, when should you center your predictor variables & when should you standardize them?
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! Proper analyses for 2x2 contingency tables So I have multiple questions about the different types of analyses that can be used on a 2x2 contingency table and when different analyses should be used.   To open, I'll note that this stems from my efforts to find the appropriate analyses to run for research using categorical data in a 2x2 contingency table. In my case I have two conditions: control and experimental and within the experimental group there are two items of interest (say, Item A and Item B). In all cases I'm investigating whether an outcome occurs or not: How many experimental participants show the outcome on Item A? How many experimental participants show the outcome on Item B? How many control participants show the outcome? So in addition to comparing Item A with the Control group (A vs. C) and Item B with the Control group (B vs. C), I also want to compare Item A with Item B (A vs. B).   My understanding is that for between-subjects comparisons (e.g., A vs. C   &amp;   B vs. C) a  is traditionally used and that for within-subjects comparisons (e.g., A vs. B) that  is a common choice.   Question 1: is this an accurate understanding of the common choices for statistical tests using 2x2 contingency tables?    My follow-up questions, and where most of my confusion lies, are related to what to do when multiple observed cell counts are low (less than 10). I've explored numerous threads here, the Wikipedia pages for different topics (Yates's correction, Fisher's exact, etc.), a few journal articles, and descriptions in R-packages, but I have found conflicting views.   Some sources indicate that you should use , others say it's out-dated because, in addition to being overly conservative, it was only preferred because the other options were computationally intense.   Others say that you should use , but I've seen additional information suggesting that Fisher's exact test is only appropriate if you know both the row and column totals and that other options (Boschloo, Barnard, etc.) are generally more powerful. However, which of those to use is also not clear.  Finally, even others suggest that the Pearson's $\chi^{2}$ test is appropriate as long as the expected cell counts are not low.   I've seen some indication that these arguments occur for McNemar's test as well (e.g., continuity correction &amp; McNemar's exact test).  Question 2: Is the assumption regarding cell counts about expected cell counts or observed cell counts? If the observed cell counts are low, does that matter to the type of test that should be used?  Question 3: What is an exact test and when should exact tests be used?    In addition to answers to these questions, I would also greatly appreciate any suggestions as to books or articles I can read to learn more about this. Part of my struggle with all of this has been just general difficult finding clear information about these topics and how they relate to one another. Club filter of $\kappa$ is $\kappa$-complete I'm trying to show that club filter of $\kappa$ is $\kappa$-complete for uncountable regular cardinal $\kappa$:  Let $\kappa$ be uncountable regular cardinal, let $C(\kappa)$ be the club filter generated by $\kappa$.  To show that $C(\kappa)$ is $\kappa$-complete it is enough to show that for every sequence $\langle \alpha_i\mid i&lt;\gamma\rangle$ with $\gamma&lt;\kappa$ and $\alpha_i$ club of $\kappa$ the set $\alpha=\bigcap_{i&lt;\gamma}\alpha_i$ is a club of $\kappa$.  Showing that $\alpha$ is close is easy:     If $\beta_n$ is a sequence in $\alpha$ then for every $i$ we that $\beta_n$ is a sequence in $\alpha_i$, because $\alpha_i$ is a club it is close hence $\lim \beta_n$ is in $\alpha_i$ for every $i$ so it is also in $\alpha$   But I have a problem with unboundedness, my guess will be for each $\lambda&lt;\kappa$ to find a sequence for each $\alpha_i$ such that all of the sequences converge to some $\mu&gt;\lambda$, that way $\beta&lt;\mu\in\alpha$. I think I'll have to use the fact $\kappa$ is regular, but I don't know how to proceed and prove my idea.  So, is my idea correct, and if yes how can I proceed? I don't know the command to set our spawn in Minecraft 1.12.1.  Is it /set spawn? I honestly can't figure it out. Thanks! Shape with a slanted side (responsive) Inspired by  which states limb loss as a recurring theme, I started thinking about the final lightsaber battle. After watching The Force Awakens the second time, I was not sure if      Kylo Ren   lost a limb or just lost his lightsaber. We definitely see      Rey slash at Ren’s right hand.   So knowing that context:      Did Kylo Ren actually lose his arm/hand? Ignored and watched tags seem broken For the longest time my ignored tags have been working but today they are not. They work on the home page but not the /questions page. However, if you choose the &quot;Gray out questions&quot; option then that fails. Arqade is the only site I've ever had a long-standing ignore list so I don't think I can blame cache. The same behavior seems to be exhibited on Stack Overflow but I added those ignore tags just moment ago so cache could be an issue. If it matters, I am using Chrome x64 v91.0.4472.77 on Windows 10 Via comments, this issue has been confirmed for Watched Tags as well. What do parentheses surrounding an object/function/class declaration mean? I'm new to both JavaScript and . In YUI library examples, you can find many uses of this construct:  (function() {     var Dom = YAHOO.util.Dom,     Event = YAHOO.util.Event,     layout = null,         ... })();   I think the last couple of parentheses are to execute the function just after the declaration.  ... But what about the previous set of parentheses surrounding the function declaration?  I think it is a matter of scope; that's to hide inside variables to outside functions and possibly global objects. Is it? More generally, what are the mechanics of those parentheses? Why is it necessary to sample from the posterior distribution if we already KNOW the posterior distribution? My understanding is that when using a Bayesian approach to estimate parameter values:   The posterior distribution is the combination of the prior distribution and the likelihood distribution. We simulate this by generating a sample from the posterior distribution (e.g., using a Metropolis-Hasting algorithm to generate values, and accept them if they are above a certain threshold of probability to belong to the posterior distribution). Once we have generated this sample, we use it to approximate the posterior distribution, and things like its mean.   But, I feel like I must be misunderstanding something. It sounds like we have a posterior distribution and then sample from it, and then use that sample as an approximation of the posterior distribution. But if we have the posterior distribution to begin with why do we need to sample from it to approximate it? Proving the series $\sum_{n=0}^{\infty}\sin(e\pi n!)$ converges Did all Headmasters get a portrait in Hogwarts? Throughout the Harry Potter series, we see that deceased Headmasters of the school get a semi-sentient portrait of themselves in the Headmaster's Office, at the service of the current Headmaster. Do all Headmasters get a portrait? What are the conditions of getting one? For instance, there are a couple of times when Dumbledore is temporarily deposed as Headmaster: Dolores Umbridge takes over the job in Order of the Phoenix, and Minerva McGonagall takes the job in Chamber of Secrets and Half Blood Prince. Will Umbridge and McGonagall have portraits in the Headmaster's Office when they expire? Can I change directory to a Windows drive in Ubuntu Bash on WSL? I am a super newbie for Ubuntu and basically need Ubuntu for a Python package.  I would like to run a Python file in say e:/username/folder1/folder2/python.py. I tried every method online and the only reply is bash: cd./e: No such file or directory. I am not sure whether it is because of the bash windows or virtualenv.  When I use bash on Ubuntu on Windows, ls, it says VIRTUALENV_DIR. cd, it says /home/username. The cd .. etc changes the directory a little, but not another drive, nor the folder I would like it to find. Here is the documents needed.     Here are the documents needed.       Which is grammatically correct and why? My guess would be the second one because of the plural form. Why is diamond transparent while graphite is not? Diamond and graphite are both made of the same atom, carbon. Diamond has a tetrahedron structure while graphite has a flat hexagonal structure. Why is diamond transparent while graphite is not (at least not with more than a couple of layers)? In many situations, JavaScript parsers will insert semicolons for you if you leave them out. My question is, do you leave them out?  If you're unfamiliar with the rules, there's a description of semicolon insertion on the . Here's the key point:     If the first through the nth tokens of a JavaScript program form are grammatically valid but the first through the n+1st tokens are not and there is a line break between the nth tokens and the n+1st tokens, then the parser tries to parse the program again after inserting a virtual semicolon token between the nth and the n+1st tokens.   That description may be incomplete, because it doesn't explain @Dreas's example. Anybody have a link to the complete rules, or see why the example gets a semicolon? (I tried it in JScript.NET.)   is related, but only talks about a specific scenario. This comes from a brain teaser but I'm not sure I can solve it:     You are in a rowing boat on a lake. A large heavy rock is also in the boat. You heave the rock overboard. It sinks to the bottom of the lake. What happens to the water level in the lake? Does it rise, fall or stay the same?   I'd say that the water level drops, because when you drop the stone in the lake, the water level rises according to the volume of the stone, BUT the water level decreases by a volume of water weighting the stone's weight, when you take it off the boat.  Is that correct? We put all of our unit tests in their own projects.  We find that we have to make certain classes public instead of internal just for the unit tests.  Is there anyway to avoid having to do this.  What are the memory implication by making classes public instead of sealed? Find all number $n\in \mathbb N$ such that $\varphi (n)=14$ I am looking for the combinatorial argument for the identity:  \begin{equation} k\binom{n}{k} = n\binom{n-1}{k-1} \end{equation}  This is easy to show algebraically as:  \begin{equation} \binom{n}{k} = \dfrac{n(n-1)(n-2)(n-k+1)}{k(k-1)!} \end{equation}   What is the combinatorial argument? What are some general ideas to get started?   Here is a clarification of 2. From what I have seen so far, proving (combinatorially) an identity with an addition sign usually implies that we need to partition a set (this makes sense because of the addition rule and provides a nice visual). On the contrary, the previous observation leads me to believe that multiplication in identities can be resolved with the multiplication principle, but what is the "visual/interpretation" for this? Could someone provide such an interpretation for the example identity given above? Determine wether the differential equation is stable or not for the following conditions:  $x'''(0) = x''(0) = x'(0) = x(0) =0$  $\frac{d^3x(t)}{dt^3}+\frac{d^2x(t)}{dt^2}+4\frac{dx(t)}{dt}+4x(t) = e^t(H(t)-H(t-3))$  Now, I got that the solution to this differential equation reduces x(t) by use of Laplace Transforms, however, how do I determine whether or not it is stable?  $x(t) = 0.1e^{-t} + 0.1e^t - 0.1\sin(2t) + 0.1e^3 (\sin(2(t-3)) + e^{-t+3}-e^{t-3})*H(t-3)$  Now I first thought I would look at it graphically and I used Matlab software to get a plot as shown below:    And from the plot above it clearly appears to diverge (though this is not a proof).  Anyone have an idea as to an elegant proof to show the solution is unstable?  Anyone help would be greatly appreciated!