My regression model has pulse rate difference (continuous variable) as the DV and Body Mass Index (BMI, continuous variable) and Level of Exercise (low, moderate, high, categorical variable) as the 2 independent variables. Do I start with scatter plots and look for a linear pattern in the plots first or transform the non-normal data first? If all are non-normal (DV and IVs) do they all need to be transformed? n=110.
I am trying to perform a multiple regression in R. However, my dependent variable has the following plot:    Here is a scatterplot matrix with all my variables (WAR is the dependent variable):    I know that I need to perform a transformation on this variable (and possibly the independent variables?) but I am not sure of the exact transformation required. Can someone point me in the right direction? I am happy to provide any additional information about the relationship between the independent and dependent variables.  The diagnostic graphics from my regression look as follows:    EDIT  After transforming the dependent and independent variables using Yeo-Johnson transformations, the diagnostic plots look like this:    If I use a GLM with a log-link, the diagnostic graphics are:
What is the best way to solve equations like the following:  $9x \equiv 33 \pmod{43}$  The only way I know would be to try all multiples of $43$ and $9$ and compare until I get $33$ for the remainder.  Is there a more efficient way ?   Help would be greatly appreciated! How to make a field NULL using MySQL GUI Tools? I'm using the MySQL Query Browser (part of the ) and need to change a field to NULL, but I can't figure out how to do it - if I delete the value it tries to update it to ''. Typing "NULL" makes it try to update to 'NULL' (a string).  I know I could just write a query to do it, but that defeats the entire purpose of the tool, no? Let $R$ be a sub-ring of a ring $S$. Let $f,g$ be non-zero polynomials in $R[x]$ and assume that the leading coefficient of $f$ is a unit in $R$. If $f$ divides $g$ in $S[x]$, show that $f$ divides $g$ in $R[x]$.   Thoughts: If $f$ divides $g$ in $S[x]$, then  $g(x) = f(x)q(x)$ for some $q(x)$ in $S[x]$. From here I'm not sure what the question is asking. Do I have to show that $q(x)$ is an element of $R[x]$ ? Insights appreciated. Rubik's Cube Combination Could anyone explain why the number of legal or reachable combinations of a $3\times 3\times 3$ Rubik's Cube is $1/12\mbox{th}$ of the total. I understood the logic behind the total number of combinations: $8! \cdot 2^{12} + 3^{12} \cdot 12!$. What I am not able to understand is why do we divide this quantity by $2 \cdot 3\cdot 2$. I don't have any idea about parity or group/set theory. Is there another possible explanation for it? How can I switch between starting a coroutine vs running the routine all at once? This is sort of a follow-up to a feature request that resulted in obscuring spam / offensive content from 10K-visible answers:   Suggest the same to be done for questions. As of now, spam questions (, ) preserve their titles and content. Suggest to revise the titles to something like     This question was marked as spam or offensive and is therefore not shown   And the text to something like:     This question was marked as spam or offensive and is therefore not shown - you can see the revision history for details".   Where "the revision history" links to the question revision history.    For those interested, here is a link to screen shots of how spam shines through my flagging summary page and is displayed to me when I click the link to one of deleted questions: .  For the sake of precision, flagger having less than 10K rep would see only upper screen shot - the one that lists question titles ("Call giRℒs blah blah &lt;phone number&gt;") - in their  page. Kept back upgrade of fwupd What's wrong now with fwupd? It was OK since May 1st, 2020 on newly installed Ubuntu 20.04 The following packages have been kept back:    fwupd  0 upgraded, 0 newly installed, 0 to remove and 1 not upgraded. Is there a way to avoid SSH typing delay? Find the domain of composition of two functions Let $$f(x)= \frac{x}{x-9} \text{ and } g(x) = \frac{-6}{x+5} $$   Find the domain of $f \circ g.$    Please show the steps and substitution/algebra to the problem. Thank you. Convergence of sequence of real numbers and (sub)subsequence Let $(x_n)_{n\in \mathbb{N}}$ be a sequence of real numbers. A well known result is:     The sequence $(x_n)_{n\in \mathbb{N}}$ converges to $a\in \mathbb{R}$ if and only if every subsequence $(x_{n_k})_{k\in \mathbb{N}}$ converges to $a\in \mathbb{R}$.   Now, I'm working on an exercise which essentialy asks to prove the following:     The sequence $(x_n)_{n\in \mathbb{N}}$ converges to $a\in \mathbb{R}$ if and only if for every subsequence $(x_{n_k})_{k\in \mathbb{N}}$ there is a (sub)subsequence $(x_{n_{k_j}})_{j\in \mathbb{N}}$ which converges to $a$.   Now, one direction is trivial. If in fact $(x_n)_{n\in \mathbb{N}}$ converges to $a$, then by the result I've mentioned, every subsequence of $(x_{n})_{n\in \mathbb{N}}$ converges to $a$. Let then $(x_{n_k})_{k\in \mathbb{N}}$ be an arbitrary subsequence. In that case, we know that it is a subsequence of itself, and hence we've found a (sub)subsequence which converges to $a$.  The other way around seems quite complicated for me. The reason is as follows: I must assume that every subsequence $(x_{n_k})_{k\in \mathbb{N}}$ has a (sub)subsequence which converges to $a$ and the proof that the original one converges to $a$.  My problem is exactly that "a". If it had all (sub)subsequences converging to $a$, then by the result i've mentionted, the subsequence $(x_{n_k})_{k\in \mathbb{N}}$ would converge to $a$. In that case, we would have every subsequence converging to $a$ and the result would follow.  My idea to prove the claim was then:  First remember that a subsequence is the restriction of the original one $x: \mathbb{N}\to \mathbb{R}$ to an infinite subset $\mathbb{N}'\subset \mathbb{N}$. In that case a (sub)subsequence is the restriction of $\tilde{x} = x|\mathbb{N}'$ to an infinite subset $\mathbb{N}''\subset \mathbb{N}$. But since $\tilde{x}$ is the restriction of $x$ to $\mathbb{N}'$ and since $\mathbb{N}''\subset \mathbb{N}'$, the restriction of $\tilde{x}$ to $\mathbb{N}''$ is itself the restriction of $x$ to $\mathbb{N}''$.  In other words, every (sub)subsequence can be viewed as a subsequence of the original one. Considering this, by hypothesis every subsequence has a (sub)subsequence which converges to $a$. But by this argument, this means that we can replace every subsequence with a convergent one. And then we can use the result I stated.  Is my idea correct? Is this really the way to prove the claim? My only doubt is that I need every subsequence converging to $a$ to use the result. In this case I can't see how I can argue that this implies every subsequence converges to $a$.  How can I finish this proof? Sync +- 70 000 records from CSV into drupal I have a CSV file with approx. 70.000 records that I want to import into Drupal 7. Once this is done the client will provide a new CSV file on a daily base that has to sync the updated rows to Drupal.   I wrote a import with  and the  module, but in both cases it takes like forever to import the 70.000 rows. Is there any other solution to import the data faster in Drupal 7? Permutations with repeating digits My question is this : how many distinct two digit numbers can be produced from numbers $4, 3, 3, 1$? When applying the formula $$\frac{4!}{(4-2)!2!}$$ you come up with $6$, yet when doing the problem manually, I come up with $7$ numbers, namely $41, 43, 14, 13, 33, 31, 34$. Can anybody explain this discrepancy?  Thanks. Proving Geometric Hahn-Banach Implies Analytic Hahn-Banach I've come across a proof online of the H.B theorem using the goemetric version.   There is a step in the proof which im not sure why is true and it is as follows:   Let $X$ be a linear space and $M \subset X \times \Bbb R$ be a maximal subspace.  Then $M = G(F)$ for $F :X \to \Bbb R$ linear.   Someone can show me why this is true?   Maybe I misunderstood the proof, its the last paragraph of Matrin's answer here -.   Thanks a lot for helping! Can't watch youtube videos with chromium on ubuntu 13.04 64-bit I've digged all over google but I can't find any solution to my problem.   Firefox works pretty well. I have this issue only with chromium and only with youtube. I have no problem watching videos at any other site with chromium.   When I try to watch a video a black screen occurs and after a while it gives me the warning "an error occurred". Weirdly, sometimes when I try a couple of refreshing it starts to play but then the issue occurs again.  I tried removing-reinstalling chromium or the flash plugin but it did not do any good. My laptop is filled with viruses and Windows XP is just becoming impossible to work with.   I've been interested in Ubuntu for a while, so, would I be able to use something like Debian to clear my HDD and OS and then install Ubuntu and start fresh? I can copy, move, create, and delete them. I can rename them using the REN command from a command prompt. I cannot rename folders through Windows Explorer anywhere on my machine, including on other drives.   When I try to do so, I receive an error titled "Rename Folder" that says "Can't find the specified file. Make sure you specify the correct path and file name." Then when I click Try Again or Cancel, I get another error titled "Rename" that says "The file or folder does not exist."  As far as I can tell, nothing else is wrong with my computer, but I'm pulling my hair out trying to fix this problem. I don't know for sure if superuser is the right place to ask this question, but feel free to redirect me.  Summary of Failed Attempts:   Booted into Safe Mode  Made a New User Account System Restore Point (two days ago, 9 days ago)  Deleting / Restoring / Modifying FolderDescriptions registry entries SFC /scannow  Removing windows update KB2984006  Scanned for viruses using Nod32  Scanned for malware using MalwareBytes   Details:  Tried rolling back to two different system restore points, both immediately before I observed the problem and one release prior to that.  Tried restoring FolderDescriptions registry entries as found here:   Booting in safe mode as suggested here:   SFC /scannow as suggested here:   Tried removing registry keys and windows update KB2984006 as suggested here:   Tried exporting folderdescriptions from other machine and importing as suggested here:   Compared my exported registry with other machine's exported registry for both:  HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\CurrentVersion\Explorer\FolderDescriptions HKEY_LOCAL_MACHINE\SOFTWARE\Wow6432Node\Microsoft\Windows\CurrentVersion\Explorer\FolderDescriptions   My FolderDescriptions branch of the registry in both cases are binary equal to those exported from my wife's Windows 8.1 laptop which works fine. Since multiple inheritance is bad (it makes the source more complicated) C# does not provide such a pattern directly. But sometimes it would be helpful to have this ability. For instance I'm able to implement the missing multiple inheritance pattern using interfaces and three classes like that: public interface IFirst { void FirstMethod(); } public interface ISecond { void SecondMethod(); }  public class First:IFirst  {      public void FirstMethod() { Console.WriteLine(&quot;First&quot;); }  }  public class Second:ISecond  {      public void SecondMethod() { Console.WriteLine(&quot;Second&quot;); }  }  public class FirstAndSecond: IFirst, ISecond {     First first = new First();     Second second = new Second();     public void FirstMethod() { first.FirstMethod(); }     public void SecondMethod() { second.SecondMethod(); } }  Every time I add a method to one of the interfaces I need to change the class FirstAndSecond as well. Is there a way to inject multiple existing classes into one new class like it is possible in C++? Maybe there is a solution using some kind of code generation? Or it may look like this (imaginary c# syntax): public class FirstAndSecond: IFirst from First, ISecond from Second { }  So that there won't be a need to update the class FirstAndSecond when I modify one of the interfaces.  EDIT Maybe it would be better to consider a practical example: You have an existing class (e.g. a text based TCP client based on ITextTcpClient) which you do already use at different locations inside your project.  Now you feel the need to create a component of your class to be easy accessible for windows forms developers. As far as I know you currently have two ways to do this:  Write a new class that is inherited from components and implements the interface of the TextTcpClient class using an instance of the class itself as shown with FirstAndSecond.  Write a new class that inherits from TextTcpClient and somehow implements IComponent (haven't actually tried this yet).   In both cases you need to do work per method and not per class. Since you know that we will need all the methods of TextTcpClient and Component it would be the easiest solution to just combine those two into one class. To avoid conflicts this may be done by code generation where the result could be altered afterwards but typing this by hand is a pure pain in the ass. By the time, many files are still on my system and I don't need them anymore, so how to delete all files that are one year old at least? Why are pointers such a leading factor of confusion for many new, and even old, college level students in C or C++?  Are there any tools or thought processes that helped you understand how pointers work at the variable, function, and beyond level?  What are some good practice things that can be done to bring somebody to the level of, "Ah-hah, I got it," without getting them bogged down in the overall concept? Basically, drill like scenarios. How to simulate a rope? I'm trying to simulate a rope (that later might get pulled on the ends*) that interacts with some obstacles. So far I created a plane as the floor and a cube as an obstacle, and activated "collision" in the physics menu for both of them.   *(In the end the goal is simulating a .)  For modelling the rope, I tried using a long cylinder with enough subdivisions, and activate "cloth" in the physics menu. This resulted in the cylinder collapsing like a sleeve of a sweater, but I would like the cross section to remain roughly circular. Is there a way to directly avoid this?   Another approach I tried now was just using a a line made up of vertices and edges (with the idea of later adding modifiers to give it a thickness), but this just fell through all the collision objects as it has no faces. Is there good way to do this?