I understand the usual procedure to code categorical variables is to convert n categories into n-1 coded variables. For example, the categorical variable colour with levels red/green/blue could be coded as            V1  V2  red   -&gt; 1   0 blue  -&gt; 0   1 green -&gt; 0   0   which in a regression setting means that the effect of green on the response is factored into the intercept.  I know that if we created an additional binary variable V3 such that green is coded           V1  V2  V3  red   -&gt; 1   0   0 blue  -&gt; 0   1   0 green -&gt; 0   0   1   then we should fit a regression model with no intercept.   What happens if I take the latter coding (i.e. 3 variables V1, V2, V3 for 3 levels of colour) and fit a regression model with an intercept? I can't figure out why we shouldn't do this.
I have an independent variable called "quality"; this variable has 3 modalities of response (bad quality; medium quality; high quality). I want to introduce this independent variable into my multiple linear regression. When I have a binary independent variable (dummy variable, I can code 0 / 1) it is easy to introduce it into a multiple linear regression model.  But with 3 modalities of response, I have tried to code this variable like this :  Bad quality      Medium quality      High quality       0                1                  0      1                0                  0      0                0                  1      0                1                  0   But there is a problem when I try to do my multiple linear regression: the modality Medium quality gives me NA:    Coefficients: (1 not defined because of singularities)    How can I code this variable "quality" with 3 modalities? Do I have to create a variable as a factor (factor in R) but then can I introduce this factor in a multiple linear regression?
Consider I've set variable site and needs to be printed by echo or printf, but If I use single quote to write something and want to use variable then how?  Example:  $ site=unix.stackexchange.com $ echo "visit:$site" visit:unix.stackexchange.com   But If I use single quote:  $ echo 'visit:$site' visit:$site   Then we know that '' is strong quote and will not expand the variable   I've tried something:  $ echo 'visit:"$site"' visit:"$site"   but do not succeed. So, I am looking for way to print value inside variable while using single quote. Can domain masking be used to move content from a subdomain to a subdirectory? example.com is hosted on IP address c.c.c.c at host1, no access any windows server admin at all blog.example.com is  on IP a.a.a.a at host2, full access to Linux server admin, using WordPress   So basically, I can fiddle with subdomain all I want.  I can't 301 redirect because the content on host 1 is an eCommerce site that I have no server control over. Can't put WordPress on it, can't run scripts, can't do anything on the server period.  Is there a method to "mask" all the URLs on root blog.example.com so they appear as example.com/blog/ folder?  They can't actually be sent to example.com/blog/ as that doesn't exist. It just needs to look to the surfer as if they are there.  Can this be done with some kind of masking or something?  Will this be better for SEO as hopefully search engines will see the blog in a directory on the main domain? How to change css property using javascript Sequence Limit Problem: If $0 \leq x_{m+n} \leq x_n + x_m$ then limit of $x_n/n$ exists Redefine default color of todonotes Android EditText listener for cursor position change I have a Git repo that I have deleted four files from using rm (not git rm), and my Git status looks like this:  #    deleted:    file1.txt #    deleted:    file2.txt #    deleted:    file3.txt #    deleted:    file4.txt   How do I remove these files from Git without having to manually go through and add each file like this:  git rm file1 file2 file3 file4   Ideally, I'm looking for something that works in the same way that git add . does, if that's possible. REST API composite query: How do I use the result of a query subrequest in the referenceId of another subrequest? How can I disable landscape mode in Android? How can I disable landscape mode for some of the views in my Android app? For which $f,g \in k[t]$, $k[f,g]$ is integrally closed? Let $f,g \in k[t]$, $k$ is a field of characteristic zero, $\deg(f)=n \geq 2$, $\deg(g)=m \geq 2$.     Is it possible to characterize all such $f$ and $g$ for which $k[f,g]$ is integrally closed in its field of fractions $k(f,g)$?   I do not mind to further assume that $k(f,g)=k(t)$ (but I do not want to assume that $k[f,g]=k[t]$, which makes my question trivial).  Thank you very much!  Edit: (i)  is relevant.  (ii) If also $k(f,g)=k(t)$, then being integrally closed is equivalent to $k[f,g]=k[t]$. Indeed: (a) If $k[f,g]=k[t]$ then $k[f,g]$ is integrally closed (since $k[t]$ is). (b) If $k[f,g]$ is integrally closed then, in particular, since $t \in k(t)=k(f,g)$ (= the field of fractions of $k[f,g]$) and obviously $t$ is integral over $k[f,g]$ (for example, $t$ is a root of $f(T)-f \in k[f,g][T]$) hence $t \in k[f,g]$, so $k[f,g]=k[t]$.  For example: $f(t)=t^2+1$, $g(t)=t^3-4t$. We have, $t= \frac{t(t^2-4)}{t^2+1-5}=\frac{g}{f-5}$, so $k(f,g)=k(t)$. By Abhyankar-Moh-Suzuki theorem, $k[f,g] \neq k[t]$, so $k[f,g]$ is not integrally closed. Similarly, for every $f,g$ such that $k(f,g)=k(t)$ and one of the degrees does not divides the other, then $k[f,g]$ is not integrally closed.  (iii) If also $k(f,g)=k(t)$ and $k$ is algebraically closed, then being integrally closed is equivalent to $H(t)=(f(t),g(t))$ is injective and $H'(t)=(f'(t),g'(t)) \neq (0,0)$ for every $t \in k$. Indeed, $k[f,g]=k[t]$ is equivalent to the new conditions (it is important that $k$ is algebraically closed!!).  Edit: What if we replace $k$ by an integral domain $D$ (which is a $k$-algebra)? See also  question. How do I run a batch file from my Java Application? Can we create a subsection of the References Cited section with different reference numbering? How can I duplicate a mesh along a curve? I want to outline a curve in the form of text with a mesh (UV-sphere, cube etc.). How can I do that while saving mesh geometry without using the Curve modifier? I've been doing some practice questions in the textbook for an upcoming predicate calculus lecture and I think I've managed to get A and B (possibly C) correct but I am clueless on how I can manage D and E.   For A I got: ∃x(R(x)∧¬B)  For B I got: ∀x(¬R(x)∧B)  For C I got: ∃x(R(x)∧(x=y))   - Not sure if this is even remotely correct    R(X) : ”X is rich”  X = Y : ”X equals Y”  B : ”Bill Gates”  a) Someone besides Bill Gates is rich.  b) Bill Gates alone is rich.  c) At least two people are rich.  d) Exactly one person is rich.  e) Exactly two persons are rich.  The universe of discourse is the set of all people. How do I disable client side decoration globally in GNOME? I'm using Ubuntu GNOME 17.04. One encounters client side decoration (CSD) as most of the official GNOME applications (Nautilus, gedit, Evince etc.) use  (a combined title bar and toolbar, see linked screenshots) whereas other applications don't. This feature is disabled in Unity, all the applications use traditional separate title bars.  Screenshots (from ):     Nautilus with GtkHeaderBar   Nautilus without GtkHeaderBar     For consistency I want to disable GtkHeaderBars globally (in all the applications using it) and use separate title bars. Is there a way to achieve that?  I have heard of gtk3-nocsd package, but couldn't make it work with GNOME for all the applications. Every finite group is isomorphic to some Galois group for some finite normal extension of some field. The following are two methods of building a link that has the sole purpose of running JavaScript code. Which is better, in terms of functionality, page load speed, validation purposes, etc.?    function myJsFunc() {     alert("myJsFunc"); } &lt;a href="#" onclick="myJsFunc();"&gt;Run JavaScript Code&lt;/a&gt;     or    function myJsFunc() {     alert("myJsFunc"); }  &lt;a href="javascript:void(0)" onclick="myJsFunc();"&gt;Run JavaScript Code&lt;/a&gt; How to work with iAds using xcode 3.1.3 How can I specify a custom date formate to be validated with the  for jQuery? Construct a field of 25 elements. We need to construct a field of 25 elements.  By using a result : For a prime p and a monic irreducible polynomial $p(x)$ in $\Bbb F_p [x]$ of degree $n$ , then the ring $(\Bbb F_p [x] / &lt;p(x)&gt;)$ is a field of order $p^{n}$.  So , for the question problem above , we need a irreducible polynomial of degree $2$ in $\Bbb Z_5 [x]$.  Solution says , $x^{2} + x +1$ does our job , since it's irreducible in $\Bbb Z_5 [x]$.  My question : Can't we take $ x^{2} + 2$ , it has no zeroes in $\Bbb Z_5$ , and is irreducible. In every solution I've gone through , the polynomial $x^{2} + x+1$ is taken. Can't we consider $ x^{2} + 2$ ?