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I'm exploring the effects of removing the intercept in a logistic regression model.  Assume a model:  $$logit(Y = 1) = \beta_1 x + \beta_2z + 0$$  with $x$ and $z$ being categorical variables with 2 levels each and no intercept.  I understood that having no intercept with categorical predictors produce coefficients that compare the $P(Y = 1)$ in each level of the two predictor against a null case where $P(Y=1) = 0.5$ or $logit(Y=1) = 0$.  I noticed a phenomenon that can understand. Using glm() function in R if you change the order of the variable in the right hand part of the formula, the coefficients change too. But even more oddly, the coefficient of the first variable is always the same.  Here's an R demo:  y &lt;- as.factor(sample(rep(1:2), 30, T)) x &lt;- as.factor(sample(rep(1:2), 30, T)) z &lt;- as.factor(sample(rep(1:2), 30, T))  coef(glm(y ~ x + z - 1, binomial) #        x1         x2         z2  #-0.1764783  0.3260739 -0.1335192  coef(glm(y ~ z + x - 1, binomial)) #        z1         z2         x2  #-0.1764783 -0.3099976  0.5025523    As you can see the first predictors have the same coefficient while the other are different in the two models.  Here is what I expected and instead behave differently than what I though:   Since every level of the two predictors is compared to the same null case, I expected to have the same coefficients in the two models, independently from the order in which I use them. I expected to see the coefficients of every level of every predictor, instead the coefficient for the 1 level of the second predictor is not shown. I therefore assume that only the first variable is compared against the null case, while the second is compared against a reference level; but what is this level? Is it $P(Y = 1 | X = 1 \cap Z = 1)$? Reproducing one of the models WITH the intercept we get:  coef(glm(y ~ x + z - 1, binomial) #        x1         x2         z2  #-0.1764783  0.3260739 -0.1335192  coef(glm(y ~ x + z, binomial)) #(Intercept)         x2          z2  #-0.1764783   0.5025523  -0.1335192    As expected x1 become the intercept, and x2 is likely relative to x1. z1 is missing also in this case and z2 is the same as in the model without intercept.  Thus should I assume that the comparison against the null case $P(Y = 1) = 0.5$ is made only for the first variable in a formula, while the other are compared against the usual intercept? Is this behavior normal? What about the fact that the first coefficient has the same value whichever the order of the predictors in the formula? What if I want to compare all level of each predictor against the null case and have a coefficient for all levels? Or it's theoretically impossible for some reason I don't get? Extremizing sum and difference of lengths using triangle inequality We have three points $P=(2,3)$, $Q=(4,-2)$ and $R=(\alpha,0)$. We need to find the value of $\alpha$ such that:    Part 1: $|PR+QR|$ is maximized.  Part 2: $|PR-QR|$ is minimized.  I have  the solution for both. I have understood the solution for case 1 but not for case 2.  Case 1's solution :    Case 2's Solution:   I have understood case 1 completely but in case 2 why was there a need to take the image of point Q? I fail to understand this. History substitution fails when implemented in shell script The below command works in command line  rsync -avh -r /Source/09_03_2016/ /Destination/ echo $(basename !:3)      Output 09_03_2016   But when I do this in shell script it does not work  #! /bin/bash  /usr/bin/rsync -avh -r /Source/09_03_2016 /Destination/; echo $(basename !:3)      Output  !:3 What is a primary decomposition of the ideal $I = \langle xy, x - yz \rangle$? Rubbing eggplants in salt C/C++/Assembly Programatically detect if hyper-threading is active on Windows, Mac and Linux First, my understanding is that the long-term capital gains tax rate is 0% for those whose marginal rate on ordinary income is 10% or 15%, and (ignoring the highest 39.6% bracket) the rate is 15% for everyone else. (See  and .)  My interest is in what happens at the crucial break between the 15% and 25% bracket, which is $73,800 for married/joint returns in 2013 (and presumably will be higher in 2014, though I haven't been able to find out what that is or if it has even been set yet). Let's say a household has $64,000 in wage income, and sells stock for a $10,000 profit.   Does their income for the purposes of establishing their tax bracket go to $74,000? If so, is the entire $10,000 profit subject to the 15% long-term capital gains rate? Is any part of the wage income subject to the higher marginal tax rate?   Since the amount of income subject to the higher marginal rate is, well, marginal, part 3 seems somewhat less important than part 2. The real issue is whether the capital gains rate hits the entire profit, since, in that case, it seems the household should only sell enough stock to generate a $9000 profit, and sell the remainder in a future year. Explanation of method for showing that $\frac{0}{0}$ is undefined (This was asked due to the comments and downvotes on this  answer. I am not that good at maths, so was wondering if I had made any basic mistakes)  Ignoring limits, I would like to know if this is a valid explanation for why $\frac00$ is undefined:     $x = \frac00$    $x \cdot 0 = 0$        Hence There are an infinite number of values for $x$ as anything multiplied by $0$ is $0$.   However, it seems to have got comments, with two general themes.  Once is that you lose the values of $x$ by multiplying by $0$.  The other is that the last line is:      $x \cdot 0 = \frac00 \cdot 0$   as it involves a division by $0$.  Is there any merit to either argument? More to the point, are there any major flaws in my explanation and is there a better way of showing why $\frac00$ is undefined? My settlement was attacked by some Raiders and my defenses took care of them along with some of my NPC's. It seems like the Raiders didn't make it through to any of the buildings. What happens when they do?  Can you lose your items if you stored them in a house?  Can the NPC's die?  Do the enemies destroy your buildings? My cursor is moving by every selection by large increments!  Normally when I use Blender, I am able to select and move objects to any coordinate. Now, all of the sudden, when I select an object or mesh the selection moves by an inch or so in each direction.  How do I reset it to normal? I have a few satellites and stations orbiting my planets, but I'd like to add onto them. I've seen numerous videos on using docking clamps to attach my new ship to the existing station, but can I do that on a part-by-part basis? For example, I take an extra fuel tank up there, can I attach just the tank to my station, then send my vessel back to Kerbin? I'm not talking about refueling, but rather transferring individual parts from my ship to the station in orbit.  I'd prefer to not have to use an unmanned probe and jettison everything but the desired part in space after docking if possible, but if that's the only way I guess I don't have a choice. How do I uninstall Ubuntu Wubi? What is the Physical Meaning of Commutation of Two Operators? I understand the mathematics of commutation relations and anti-commutation relations, but what does it physically mean for an observable (self-adjoint operator) to commute with another observable (self-adjoint operator) in quantum mechanics?   E.g. an operator $A$ with the Hamiltonian $H$? Doubly stochastic matrix proof A transition matrix $P$ is said to be doubly stochastic if the sum   over each column equals one, that is $\sum_i P_{ij}=1\space\forall i$.   If such a chain is irreducible and aperiodic and consists of $M+1$   states $0,1,\dots,M$ show that the limiting probabilities are given by   $$\pi_j=\frac{1}{1+M},j=0,1,\dots,M$$   I have no idea how to prove it but   If a chain is irreducible then all states communicate i.e $$P_{ij}&gt;0\space \text{and}\space P_{ji}&gt;0\space\forall i,j$$ If $d$ denotes the period of any state, if a chain is irreducible aperiodic, then $d(i)=1\forall i$   If $P_{(M+1)\times (M+1)}$ matrix and $\pi$ is the stationary distribution  $$\pi_j=\sum_iP_{ij}\pi_i\space j=0,1,\dots,M+1$$  but how I can get this expression? Alternative methods to prove that $Z_m$ is a field under addition and multiplication $\bmod\ m$ iff $m$ is a prime I am looking for ways to prove that $\mathbb{Z}_m=\{0,1,2,\dots,m-1\}$ is a field under addition and multiplication $\bmod\ m$ iff $m$ is a prime.   I tried it this way: If $m$ is a prime $p$,it is obvious that most importantly, we need to prove that every non-zero element in $\mathbb{Z_p}$ has an inverse in $\mathbb{Z_p}$.We note that if $a,b\in \mathbb{Z_p}$, then $a\cdot b\in \mathbb{Z_p} \dots \boxed{*}$. Next, $a^p\equiv a \bmod p$ for prime $p$(the proof follows by induction on $a$).As  $\displaystyle 0\leq a\leq p-1$,$a\not =p$. Thus $$a^{p-1}\equiv 1 \bmod p$$ for prime $p$ which,together with $\boxed{*}$ guarantees the existence of an inverse in $\mathbb{Z_p}$.Proving the other properties is simple.  Conversely,if $\mathbb{Z_m}$ is a field,then every non-zero element of $\mathbb{Z_m}$ has an inverse.Note that inverse of an element is unique.For if $a\cdot b\equiv a\cdot c\equiv 1 \bmod m$,then $(a\cdot b)\cdot c\equiv c\equiv (a\cdot c)\cdot b\equiv b \bmod m$ i.e $m|(b-c)\implies b-c=0(0\leq a\leq m-1,a\in \mathbb{Z_m})$.So, inverses must be unique and every element is either an inverse of itself or has in inverse in the field.That allows us to conclude that $[(m-1)!]^2\equiv 1 \bmod m$ which can only mean that either  $(m-1)!\equiv 1 \bmod m$ or $(m-1)!\equiv -1 \bmod m$. If $m$ is not a prime, it has a prime factor, say $p$. $ 0\leq p\leq m-1\implies p|(m-1)!\implies p|1$or $-1$ which is absurd, a contradiction.Thus $m$ is prime.  I feel that this method is too involved and complicated. Can anyone please suggest some other method?(Some context: This is a problem from Finite Dimensional Vector Spaces by Paul Halmos. I am learning linear algebra for the first time.It seems some of the comments have been posted on the assumption that I know rings and fields; I don't. ) While I basically understand what a determinant is, I wonder how this idea was developed?  What was the principal idea behind its origination?  I would like to know this so that I can have a better conceptualization of the determinant. What is the meaning of the third derivative of a function at a point (Originally  by AJAY.)  What is the geometric, physical, or other meaning of the third derivative of a function at a point?  If you have interesting things to say about the meaning of the first and second derivatives, please do so. Extract substring in Bash Given a filename in the form someletters_12345_moreleters.ext, I want to extract the 5 digits and put them into a variable.  So to emphasize the point, I have a filename with x number of characters then a five digit sequence surrounded by a single underscore on either side then another set of x number of characters.  I want to take the 5 digit number and put that into a variable.  I am very interested in the number of different ways that this can be accomplished. There's a fairly standard two or three-semester curriculum for introductory quantum field theory, which covers topics such as:   classical field theory background canonical quantization, path integrals the Dirac field quantum electrodynamics computing $S$-matrix elements in perturbation theory, decay rates, cross sections renormalization at one loop Yang-Mills theory spontaneous symmetry breaking the Standard Model   What is a good, complete and comprehensive book that covers topics such as these? Why didn't Sauron find Bilbo when he put on the ring like Frodo?