what kind of correlation should I use in the case of having one dependent binary variable (has been to the doctor in the past few months) and one independent categorical variable, i.e, education?
I have a dataframe with many observations and many variables. Some of them are categorical (unordered) and the others are numerical.  I'm looking for associations between these variables. I've been able to compute correlation for numerical variables (Spearman's correlation) but :   I don't know how to measure correlation between unordered categorical variables. I don't know how to measure correlation between unordered categorical variables and numerical variables.   Does anyone know how this could be done? If so, are there R functions implementing these methods?
My professor has stated the following lemma:  Let $U$ and $V$ be two vector spaces and $B$ a basis for $U$. If $f:B\rightarrow V$ is a map, then there exists a unique linear map $A: U \rightarrow V$ such that $A(x)=f(x)\ \forall\ x\in B$  How can I prove this lemma? (This is not a homework problem.) Can you please explain this to me?          Could you please explain this to me?   I am unable to figure out which to use which situation. I did google, and some posts say they are both the same, even if the second one is more formal. Other posts say could is the past tense of can, but in the above example, I don't think could is used as past tense of can.  What is correct way to use these words? Installing debian package through Synaptic I want to install a .deb file. After going through various questions, I came across these three options: dpkg, GDebi and Ubuntu Software Center. However, I want to install the. Deb file via Synaptic Package Manager only. Is there any method by which I can install. Deb file as well as all it's dependencies via Synaptic Package Manager? Functional equations $f(x+y)= f(x) + f(y)$ and $f(xy)= f(x)f(y)$ Let $f:\mathbb{R}\to \mathbb{R}$ is a function such that for all real $x$ and $y$, $f(x+y)= f(x) + f(y)$ and $f(xy)= f(x)f(y)$, then prove that $f$ must be one of the two following functions:   $f:\mathbb{R}\to \mathbb{R}$ defined by $f(x)=0$ for all real $x$   OR   $f:\mathbb{R}\to\mathbb{R}$ defined by $f(x)=x$ for all real $x$   I got to the point where putting the two equations together, you get $f(x+y)f(x)= f(xy) + f(x)^2$ and plugging in $f(x)=x$ checks with it. So am I going in the right direction or am I just doing some guess work? Is there a more elegant way of doing it?   Thanks This is a follow-up to this question:   Hans Bethe wrote a paper in 1944, "Theory of Diffraction by Small Holes," Phys. Rev. 66, 163. I don't have access to the paper, but from descriptions online it sounds like he proved the following. Suppose a plane wave impinges on an absorbing sheet, and there is a hole in the sheet of diameter $d$, with $d&lt;\lambda$. Let $P_0$ be the power incident on the hole, and $P$ the power diffracted through the hole. Then the transmission is $T=P/P_0=(d/\lambda)^4$.  As a practical application, I think this explains why microwaves don't leak strongly through the metal grille in the front of a microwave oven.  Questions:   Does the thickness of the sheet matter? From references online, it sounds like the hole is treated as a waveguide...? This seems to relate to cutoff frequencies of waveguides, etc.? It seems to me that Huygens' principle would give $T=1$ for $d\ll\lambda$, since in this limit the wavelets are in phase. Why is Huygens' principle invalid here? Is this related to question #1? Is there a simple argument for the proportionality to $(d/\lambda)^4$? Or if not, how does one prove this using the gory details of Bessel functions, etc.? A number of questions "has been" or "have been" asked? Formally, is it correct to write:     A number of questions has been asked here.   or:     A number of questions have been asked here.   As a non-native speaker of English, I would prefer the former: the subject seems to be "number", therefore the verb ought to be singular, I'd say. However, the latter seems more common, and therefore I believe that my gut feeling is just plain wrong — but I would really like to have a definite answer.  Moreover, is it the same for "a myriad of", "a plethora of", and so on? Proving this identity $\sum_k\frac{1}{k}\binom{2k-2}{k-1}\binom{2n-2k+1}{n-k}=\binom{2n}{n-1}$ using lattice paths Why doesn't hydrogen gas exist in Earth's atmosphere? How do you sort a dictionary by value? I often have to sort a dictionary, consisting of keys &amp; values, by value. For example, I have a hash of words and respective frequencies, that I want to order by frequency.  There is a SortedList which is good for a single value (say frequency), that I want to map it back to the word.   orders by key, not value. Some resort to a , but is there a cleaner way? Adding layers to GeoPackage using PyQGIS I am having some issues trying to show multiple fields for a single label in QGIS. In QGIS2.6, attempting to display labels for a feature consisting of multiple fields results in an empty label if one of the fields is null. So for example, in the label expression dialog:  concat("Temp Site",'\n',"Notes",'\n',"Function")   will function normally unless one of the fields is null, then it results in no label being shown. Using the '||' operator instead in the expression dialog also results in the same behaviour:  "Temp Site" || '\n'  ||  "Notes" || '\n'  ||  "Function"   Is there a way to display the labels even if one of the fields is null? This System Information is from Process Explorer. There is still physical memory available but the system shows nearly no RAM left.  Task Manager also shows that about 74% of total RAM is used.  Since installing Windows 8.1, the computer had 4+8=12 GB of RAM. I upgraded it by changing the 4 GB to an 8 GB module. Could that be the problem? Or is this behavior normal and I've just misunderstood the meaning of available physical memory? Significance of assumption in competition inequality questions Refer to the problem below (IMO 2009 Shortlist)     Let $a, b, c$ be positive real numbers such that $$\frac{1}{a} + \frac{1}{b} + \frac{1}{c} = a + b+ c$$   Prove that    $$\frac{1}{(2a+b+c)^2} + \frac{1}{(2a+b+c)^2} + \frac{1}{(2a+b+c)^2} \leqslant \frac{3}{16} $$    In the solution given by the  (Pg 16), it states that      Without loss of generality, we choose $$a +b+c = 1$$.    Thus, the problem becomes    $$ \frac{1}{(1 + a)^2} + \frac{1}{(1 + b)^2} +\frac{1}{(1 + b)^2} \leqslant \frac{3}{16}(\frac{1}{a} + \frac{1}{b} + \frac{1}{c})$$    Applying Jensen’s inequality to the function $$f(x) = \frac{x}{ (1+ x)^2}$$   ,which is concave for $0 ≤ x ≤ 2$   and increasing for $0 ≤ x ≤ 1$, we obtain   $$α \frac{a}{(1 + a)^2} + β \frac{b}{(1 + b)^2} + γ \frac{c}{(1 + c)^2} \leqslant (α + β + γ) \frac{A}{(1 + A)^2}$$   , where $A =\frac{αa + βb + γc}{α + β + γ}.$   Choosing $α = \frac{1}{a} , β =\frac{1}{b},$ and  $γ = \frac{1}{c}$   , we can apply the harmonic-arithmetic-mean inequality   $$A =\frac{3}{\frac{1}{a} + \frac{1}{b} + \frac{1}{c}} ≤ \frac{a + b + c }{3} = \frac{1}{3} &lt; 1$$   Finally we prove:   $$ \frac{1}{(1 + a)^2} + \frac{1}{(1 + b)^2} +\frac{1}{(1 + b)^2} \leqslant ( \frac{1}{a} + \frac{1}{b} + \frac{1}{c}) \frac{A}{(1 + A)^2} \leqslant ( \frac{1}{a} + \frac{1}{b} + \frac{1}{c})\frac{A}{(1 + \frac{1}{3})^2} = \frac{3}{16}(\frac{1}{a} + \frac{1}{b} + \frac{1}{c}) $$   However,  (Pg 4) differs by having $a +b+c=3$ and setting $f(x) = \frac{1}{16x} - \frac{1}{(x+3)^2}$ and allowing Jensen to resolve the rest.   The questions are as follows;   How do you choose before hand which $a + b+ c =$ to choose?  Why particularly does the assumption differ between the 2 solutions? How does one know before hand the choosing of $α = \frac{1}{a} , β =\frac{1}{b},$ and  $γ = \frac{1}{c}$?  Where and how did $A =\frac{αa + βb + γc}{α + β + γ}$ come from?   Any help would be much appreciated. Updating Location of Point Features using XY Fields? I have changed the coordinates of couple points in the attribute table and I want to update the location. I have found the script that is working in field calculator.   Does anybody know how to write it using a Python script in ArcGIS Desktop (not in Field Calculator)?  def XYsetVALUE( shape, X_value, Y_value):    point = shape.getPart(0)    point.X = X_value    point.Y = Y_value    return point  __esri_field_calculator_splitter__ XYsetVALUE ( !SHAPE!, !X_COORD!, !Y_COORD! )   COORDINATE FIELD TYPE ------ STRING !!!! Backgrounder:  The  (Pointer to IMPLementation) is a technique for implementation hiding in which a public class wraps a structure or class that cannot be seen outside the library the public class is part of.  This hides internal implementation details and data from the user of the library.  When implementing this idiom why would you place the public methods on the pimpl class and not the public class since the public classes method implementations would be compiled into the library and the user only has the header file?  To illustrate, this code puts the Purr() implementation on the impl class and wraps it as well.  Why not implement Purr directly on the public class?  // header file: class Cat {     private:         class CatImpl;  // Not defined here         CatImpl *cat_;  // Handle      public:         Cat();            // Constructor         ~Cat();           // Destructor         // Other operations...         Purr(); };   // CPP file: #include "cat.h"  class Cat::CatImpl {     Purr(); ...     // The actual implementation can be anything };  Cat::Cat() {     cat_ = new CatImpl; }  Cat::~Cat() {     delete cat_; }  Cat::Purr(){ cat_-&gt;Purr(); } CatImpl::Purr(){    printf("purrrrrr"); } Why is "be" here? People be like Endofunctors of $\textsf{FinVec}$ which are not $C^n$ Prove continuous functions $f$ and $g$ are equal Suppose $f,g$: $\Bbb R$ → $\Bbb R$ are continuous functions such that $f(r) = g(r)$ for all $r$ in $\Bbb Q$. That is to say, $f$ and $g$ are equal on the rational numbers.   Prove that  $f(x) = g(x)$  for all $x$ in $\Bbb R$ How do I access folders created on Ubuntu with Windows? How do I use F3 to get my coordinates when my laptop makes F3 a special key?