Sorry if this is a naive question.   The independent variables are truly having different scale. They need to be standardized. The question is, does statsmodels.OLS do standardization for us as its first step, such that we don't need to do it ourselves?
In some literature, I have read that a regression with multiple explanatory variables, if in different units, needed to be standardized.  (Standardizing consists in subtracting the mean and dividing by the standard deviation.)  In which other cases do I need to standardize my data?  Are there cases in which I should only center my data (i.e., without dividing by standard deviation)?
Undefined Symbol ___gxx_personality_v0 on link I've been getting this undefined symbol building with this command line:  $ gcc test.cpp Undefined symbols:   "___gxx_personality_v0", referenced from:   etc...   test.cpp is simple and should build fine.  What is the deal? Is there a way to kill a process tree using the terminal?  By killing a process tree, I mean killing all descendants of a process along with the process it self.  I tagged this question htop because I am using that utility a lot these days and it would be cool if there was an easy way to kill a process tree inside htop (something better than just selecting all the processes in the subtree). Can't move files to trash without any permission issues This is not like one of the cases addressed before - I've checked them all.  I've suddenly begun getting that message "... can't be put in the trash. Do you want to delete it immediately?" this morning in my Home directory only.  I have a Home partition (ext4, mounted properly) with symlinks for user folders like Downloads, Documents, etc. to folders with the same names in a Data partition (ntfs, mounted properly).  For example, I cannot move a file in Downloads folder to Trash when I try via Home, but no problem if I try via Data partition, although the file in question has the same ownership and permissions at both locations.  Also no problem at all with files in my Home folder, including sub-folders like Public that are not symlinked to my Data partition.  Interesting puzzle for me...  PS: Just upgraded to 15.04 but I don't think it matters... On second thought, it might perhaps be something to do with upgrading from Nautilus 3.10 to 3.14?  PPS: This bug has been finally resolved some time later in version 16.10, and no longer exists under Ubuntu 17.04. Atiyah Macdonald, Exercise 8.3. Let $k$ be a field and $A$ a finitely generated $k$-algebra. Prove that the following are equivalent:   (1) $A$ is Artinian.   (2) $A$ is a finite $k$-algebra.   I have a question in the proof of (1$\Rightarrow$2): By using the structure theorem, we may assume that $(A,m)$ is an Artin local ring. Then $A/m$ is a finite algebraic extension of $k$ by . Since $A$ is Artinian, $m$ is the nilradical of $A$ and thus $m^n=0$ for some $n$. Thus we have a chain $A \supseteq m \supseteq m^2 \supseteq \cdots \supseteq m^n=0$. Since $A$ is Noetherian, $m$ is finitely generated and hence each $m^i/m^{i+1}$ is a finite dimensional $A/m$-vector space, hence a finite dimensional $k$-vector space.  But now how can I deduce that $A$ is a finite dimensional $k$-vector space? Bootstrap Paradox in Interstellar Linear algebra skew symmetric How do I combine standard deviations of two groups? I have 2 groups of people. I'm working with the data about their age. I know the means, the standard deviations and the number of people. I don't know the data of each person in the groups.  Group 1 :  Mean = 35 years old; SD = 14; n = 137 people  Group 2 :  Mean = 31 years old; SD = 11; n = 112 people  I want to combine those 2 groups to obtain a new mean and SD. It's easy for the mean, but is it possible for the SD? I do not know the distribution of those samples, and I can't assume those are normal distributions. Is there a formula for distributions that aren't necessarily normal? I'm currently going through notes on a physics course and I'm having trouble understanding the difference between a tensor, a vector, and a matrix. I know that a vector is a kind of tensor and that a matrix is also a form of tensor, but what I'm having trouble understanding is how they differ, and how a vector is related to a matrix. How come everyone easily takes or say the name of "Voldemort" without any fear in Scorpius's world? How to find all the available tools in mac terminal? I am trying to setup a bunch of development projects in my Mac. I have to run various tools like python, ruby, scala, groovy etc.  To see if a tool is available I use options like   ruby --version.    Instead I would like to see all the list of tools available in Mac terminal via a single command. What is the command/options for it? Open Finder window from current Terminal location? If I am in a specific path in a Terminal window, how can I open that same window in a new Finder window?   Note: This is the opposite of . Undergraduate research field different from PhD field I am a Physics undergrad who is interested in pursuing a PhD in pure maths in the future (algebraic geometry/topology) but I am a bit unsure. My question is quite general, and I don't wish to provide more background for fear of bias in the answers.  My question: Is it is advisable/possible/unfavorable/favorable to apply for a PhD in a field, different from that in which you have done most of your undergraduate research?  My research (includes just reading and understanding papers, writing summaries until now, I havent published anything) mostly includes Quantum field theory, and gauge theory. Would the selection committee turn down an application to a pure maths field, if I have no research experience whatsoever?  I would also like to ask the question other way round. What if I concentrate my undergraduate research SOLELY on topics in pure maths such as algebraic geometry/topology and take other physics courses, would I be able to apply to a string theory PhD with a high chance of success?  Should I consider spending time on both of these (which is almost an impossible task), to improve my chances in both the areas or would research in one area, and grad level courses in the other suffice?  In brief: Should the PhD field you are applying to be the same as your undergraduate research area? How to get city name from latitude and longitude coordinates in Google Maps? How assign shortcut to custom function? After monitor calibration colors on my two monitors are still different, why? I have a pair of pretty nice monitors (HP ZR30w) which I calibrated with a pretty good calibrator (i1-Pro) and after I calibrated both they still show colors every so slightly differently.  My left monitor has a little more magenta color to it in photos.  Is monitor calibration only ment to get things 'close'?  Other people in the office have experienced similar issues with their pairs of monitors, both HP ZR30w and Dell 3007WFP-HC monitors.  If I can't even get colors to match between my two exact same monitors connected to the same computer I have little confidence that colors on my monitors will look the same on somebody else's calibrated monitor :p Extracting Data Between two Characters in Excel I have the following format in Excel and I am trying to extract the data between the characters:  First Last &lt;flastname@xxxx.com&gt;   I need to extract the email address between &lt; and > into its own cell  Thanks! DOS of Van Hove singularity in 2D square lattice tight binding model For the simplest example, 2D square lattice tight binding model gives the energy band as $$\varepsilon_k=-2t(\cos k_x+\cos k_y) \, .$$ We know that $\mathbf{k}=(0,\pi)$ and related momentum points are saddle points which give $|\nabla_k \varepsilon_k|=0$ and thus some kind of singularity in density of state (DOS) since $$\rho(\varepsilon)\propto \int_{\varepsilon=\text{const}} \frac{d S}{|\nabla_k \varepsilon_k|} \, .$$ How can I get the $\ln$ divergence for DOS near $\varepsilon=0$? Should I only care about those singularity points and omit the integral from normal parts and do Taylor expansion near those saddle points?   Moreover, why are points like $(\pi/2,-\pi/2)$ or $(2\pi/3,-\pi/3)$ not called Van Hove points when those points are also lie in the $\varepsilon=0$ line and give $|\nabla_k \varepsilon_k|=0$? In Markov inequality proof, why is $\int_a^\infty xp(x) \, dx \ge \int_a^\infty ap(x) \, dx$ Markov inequality,   $$\Pr(X \ge a) \le \frac{E[x]}{a}$$  Proof  $$\begin{aligned}      E(X) &amp;= \int_0^\infty xp(x)\,dx = \int_0^a xp(x)\,dx + \int_a^\infty xp(x)\,dx \\       &amp;\ge \int_a^\infty xp(x)\,dx \ge \int_a^\infty ap(x) \, dx  \end{aligned}$$  Why is the last inequality true? Why is it ok to change $x$ to $a$, and we know it is less than or equal to? How did they figure it out? Thanks! $\operatorname{Aut}(\mathbb Z_n)$ is isomorphic to $U_n$. I've tried, but I can't solve the question. Please help me prove that:  $\operatorname{Aut}(\mathbb Z_n)$ is isomorphic to  $U_n$. Canonical copies of sets Sometimes one needs two disjoint copies of a given set $X$. This can be canonically done by taking $\{0\} × X$ and $\{1\} × X$. Sometimes we want to identify one of the copies with the original set $X$. So I wonder, is it possible to take a disjoint copy of $X$ straight ahead? And can this be done canonically? More precisely, are the following claims true? $ \def\dom{\operatorname{dom}} \def\rng{\operatorname{rng}} \def\On{\mathbf{On}} $   For every $X$ there is a one-to-one function $f$ such that $\dom(f) = X$ and $\rng(X) ∩ X = ∅$. There is an explicit formula $φ(X, f)$ such that for every $X$ there is exactly one $f$ satisfying $φ(X, f)$ and this $f$ satisfies 1. for $X$.   Since such construction of a disjoint copy is intuitively trivial, I'm interested in proofs of 1. and 2. without using regularity, choice, or infinity.   Some ideas:   We may simply put $f(x) := (x, X)$, but we need regularity to show that $(x, X) ∉ X$. We may consider $α = \sup(X ∩ \On)$ and pair members of $X$ with some ordinals above $α$, but we need AC to well-order $X$, and we need global choice to obtain 2. Let $&lt;$ be the transitive hull of $∈$. If the relation $&lt;$ is narrow, i.e. $\{y: y &lt; x\}$ is a set for every $x$, then we may choose $z ∉ ⋃\{(\leftarrow, x)_&lt;: x ∈ X\}$ and put $f(x) := (x, z)$ since $(x, z) = y ∈ X$ would imply $z &lt; y$. Note that we don't need the axiom of infinity to define $&lt;$, but I don't know how to prove its narrowness without infinity.