I want to investigate the relationship between stock traders' past success rate (i.e. the number of total winning trades divided by the total trades executed) on the status of their current trading decision. The current trading decision is the dependent variable and is a categorical variable that takes the value of 1 if the trade is a win, -1 if it is a loss and 0 if the trader decides not to trade.  I am conducting a multinomial regression where the dependent variable is the current trade decision (1,-1,0) as mentioned above and the independent variable is the trader's historical success rate.   I choose a multinomial model rather than an ordinal model since, in my opinion, the 3 states are really independent. If the trader traded and made a profit of 0, then it would make sense to categorize the decision as an ordinal variable. But since trading (whether win or lose) is not the same as not trading then I argue that this should be a multinomial variable. Nevertheless, the relationship between win and lose is relative/ordinal. Is my reasoning correct here?  Given that no-trade is the baseline, I obtain the following results from the R output    I am not very clear on how to interpret the output in this case. I tried to follow the example . The R output states that these are coefficient values and not log odds. Does this mean that a 1 unit increase in historical success rate increases the log odds of winning by 1.224 and decreases the log odds of losing by 0.622? Or are these coefficients? How should I interpret the results?  UPDATE: R results  Call: multinom(formula = formula, data = data)  Coefficients:   (Intercept)           Success Rate Cummulative_NumTrades -1  -3.601953                 -0.622         -1.304052e-05 1   -4.660911                  1.224         -1.342798e-05  Std. Errors:    (Intercept)           Success Rate Cummulative_NumTrades -1 8.630168e-08           2.734970e-08          1.341129e-06 1  1.016195e-07           4.889536e-08          1.161023e-06  Residual Deviance: 392352.8  AIC: 392376.8
This is somewhat of a beginner's question, but how does one interpret an exp(B) result of 6.012 in a multinomial logistic regression model?  1) is it 6.012-1.0 = 5.012 = 5012% increase in risk?  or  2) 6.012/(1+6.012) = 0.857 = 85.7% increase in risk?  In case both alternatives are incorrect, can someone please mention the correct way?  Ive searched many resources on the internet and I get to these two alternatives, and I am not entirely sure which one is correct.
How do I reset all progress in the game "just shapes and beats"? The game  has a very unique intro that I would like to show my friend again for the first time. I'm not sure how to reset all my progress on this game to achieve this though. Any thoughts? Merging dictionaries in C# What's the best way to merge 2 or more dictionaries (Dictionary&lt;T1,T2&gt;) in C#? (3.0 features like LINQ are fine).  I'm thinking of a method signature along the lines of:  public static Dictionary&lt;TKey,TValue&gt;                  Merge&lt;TKey,TValue&gt;(Dictionary&lt;TKey,TValue&gt;[] dictionaries);   or  public static Dictionary&lt;TKey,TValue&gt;                  Merge&lt;TKey,TValue&gt;(IEnumerable&lt;Dictionary&lt;TKey,TValue&gt;&gt; dictionaries);   EDIT: Got a cool solution from JaredPar and Jon Skeet, but I was thinking of something that handles duplicate keys. In case of collision, it doesn't matter which value is saved to the dict as long as it's consistent. Can I use the Unity launcher icon to minimize applications/windows? "They interviewed several candidates who/whom he thought had the experience he required." They interviewed several candidates who he thought had the experience and qualifications he required.   My test prep book says this should be "who" because of the subordinate clause's predicate:     They interviewed several candidates who he thought had the experience and qualifications he required.   I feel like it should be "whom" as it's the object of the main clause.     The interviewed several candidates whom he thought had the experience and qualifications he required.   Who's right? Case of the 'mice problem' for $n=3$ In France the higher education is like this:   3 years of "Licence" 2 years of "Master" 3 years of "Doctorat"   But what about in the United States?  I heard that they have things called "undergraduate", "graduate" and "postgraduate". How many years do each of those take? And what are the equivalencies between these and the "Licence - Master - Doctorat"?  Note: If the answer to this question depends on the field of studies, then the field is physics. Difference between '>' and '-gt' What's the difference between these:  SEC=$(mysql -hxxx -Pxxx -uxxx -pxxx -se "SELECT Seconds FROM tablename")  SEC=100   Both return the same result (100). But when I test it with:  if [ ${SEC} &gt; 1 ] then     echo "SEC GT 1" else     echo "SEC LT 1" fi   The first one returns:  "SEC GT 1"   The second one returns:  "SEC LT 1"   If however, I change it to:  if [ ${SEC} -gt 1 ]   then the result is reversed.  I'm assuming it's got something to do with the datatype, and that I presumbaly need to cast one or the other to get the same result.  It's just that at present it's messing up my testing, as I have to remember to change the IF section every time. How can I make environment variables "exported" in a shell script stick around? I have multiple Amazon EC2 accounts and want to quickly be able to switch variables, such as $EC2_HOME, using a script.  I have have a shell script set up like this:  #!/bin/sh export EC2_HOME=/home/me/.ec2 echo $EC2_HOME   When I run the script I know that EC2_HOME is set, but I thought that using export would make the variable stick around after the script completed. It does not, as running echo $EC_HOME does not show anything.  I know this must be very rudimentary Linux scripting knowledge, but I don't know it. I tried looking for related questions without luck - so my apologies if this is a duplicate. What Does it Really Mean to Have Different Kinds of Infinities? When should I publish in interdisciplinary versus subject-specific scientific journals? Get last n lines of a file, similar to tail I'm writing a log file viewer for a web application and for that I want to paginate through the lines of the log file.  The items in the file are line based with the newest item at the bottom. So I need a tail() method that can read n lines from the bottom and support an offset.  This is hat I came up with: def tail(f, n, offset=0):     &quot;&quot;&quot;Reads a n lines from f with an offset of offset lines.&quot;&quot;&quot;     avg_line_length = 74     to_read = n + offset     while 1:         try:             f.seek(-(avg_line_length * to_read), 2)         except IOError:             # woops.  apparently file is smaller than what we want             # to step back, go to the beginning instead             f.seek(0)         pos = f.tell()         lines = f.read().splitlines()         if len(lines) &gt;= to_read or pos == 0:             return lines[-to_read:offset and -offset or None]         avg_line_length *= 1.3  Is this a reasonable approach?  What is the recommended way to tail log files with offsets? In CSS what is the difference between "." and "#" when declaring a set of styles? What is the difference between # and . when declaring a set of styles for an element and what are the semantics that come into play when deciding which one to use? [Probability]need help to understand the following expression So assume $Y$ and $X$ are exponentially distributed with parameters $y_1$, and $x_1$ respecitively.  assume c is a constant.  I am having huge trouble to understand the integration of the following expression.  $P(Y&lt;c/u(X))$  $=\int_{t}^{\infty}f_X(x)\int_{0}^{c/u(x)}f_Y(y)dydx +\int_{0}^{t}f_X(x)\int_{c/u(x)}^{\infty}f_Y(y)dydx$  where t is the cross-point that $u(x)$ change sign    here $c/u(x)$ is given by the plot below, t is the point crossing the zero:   Confusion:   I don't understand the second integration of the second term "$\int_{c/u(x)}^{\infty}f_Y(y)dydx$", this isn't right because Y an X only defined for y>0, and x>0. So it's the first quadrant in this plot. I am using ArcMap 10.2 and want to represent a layer in a rotated dataframe with chart (graph) symbology. The problem is that the charts do not rotate with the dataframe:     I thought I could convert to graphics and rotate each chart individually, but   that is very tedious I don't find an option to convert a layer to graphics, works for the legend but not for the actual layer symbology Prove that $\binom{m+n}{m}=\sum\limits_{i=0}^m \binom{m}{i}\binom{n}{i}$ I need to proof this following equality :  $$\binom{m+n}{m}=\sum_{i=0}^m \left(\binom{m}{i}\binom{n}{i}\right)$$  This is what I did combinatoric proof:  Left : subset with $m$ members from $m+n$  Right : $\binom{m}{i} \rightarrow$ The number of subsets in set $m$ could also be written as $2^m$ AND $\binom{n}{i} \rightarrow$ the number of subsets with $m$ members from set $n$  In case $ n \leq m \implies \binom{n}{i}=2^n$  So this is what I came up with I still can't see why those expression are equal.  Any ideas? Thanks. I'm too spoiled by Windows utilities that take a digital snapshot of your entire drive, which you can then restore from in the event of a drive crash.  (e.g. like Time Machine for Mac OS X).  Is there a similar way of doing this in Linux? What's the right way to hard boil eggs? How to make the BibTeX reference list visible in a LaTeX document Im very new at LaTeX and I would appreciate some help solving this problem. I have created a BibTeX file containing all references to a document. In this text file BibTeX items are inserted and no other text are written, for instance @article{...}. When I call for this bib file from the main.tex file I use the commands:  \bibliographystyle{plain} \bibliography{thebibliography}   Now to my question. All i get when I compile this main.tex is the title (bibliography) for this chapter, otherwise the textfield is blank. Is this error occurring because I should write anything in the bib file or have I missed any lines in the main.tex file. $G$ a group and $H, K\mathrel{\unlhd}G$. Assuming that $H \cap K = \{1_G\}$ and $G = \langle H, K \rangle$, prove that $G \cong H \times K$ I am trying to prove the following statement:     Let $G$ be a group and $H, K\mathrel{\unlhd}G$. Assuming that $H \cap K =  \{1_G\}$ and $G = \langle H, K \rangle$, prove that $G \cong H \times K$.   From this, we get that $HK \cong H \times K$. Naturally, it would be ideal if I could prove that $HK \cong G$. One issue that I am facing here is the meaning of $G = \langle H, K \rangle$. How is this defined (I mean, more explicitly)? Is my strategy correct or Questions about proving $\lnot \lnot a = a$ This is all in the context of a Hilbert system with modus ponens $A, A\to B \vdash B$ and axioms:  Axiom $1$: $A \to (B \to A)$   Axiom $2$: $(A \to (B \to C)) \to ((A \to B) \to (A \to C))$   Axiom $3$: $(\lnot B \to \lnot A) \to (A \to B)$  So I tried to prove double-negation elimination by doing the following:  \begin{array}{ccc} 1 &amp; \{ \lnot \lnot a \} \vdash \lnot \lnot a &amp; \text{Premise}\\ 2 &amp; \{ \lnot \lnot a \} \vdash \lnot \lnot a \to (\lnot \lnot \lnot \lnot a \to \lnot \lnot a)  &amp; \text{ Axiom } 1\\ 3 &amp; \{ \lnot \lnot a \} \vdash \lnot \lnot \lnot \lnot a \to \lnot \lnot a  &amp; \text{ Modus Ponens } 1, 2\\ 4 &amp; \{ \lnot \lnot a \} \vdash (\lnot \lnot \lnot \lnot a \to \lnot \lnot a) \to (\lnot a \to \lnot \lnot \lnot a)  &amp; \text{ Axiom } 3\\ 5 &amp; \{ \lnot \lnot a \} \vdash \lnot a \to \lnot \lnot \lnot a  &amp; \text{ Modus Ponens } 3, 4\\ 6 &amp; \{ \lnot \lnot a \} \vdash (\lnot a \to \lnot \lnot \lnot a) \to (\lnot \lnot a \to  a)  &amp; \text{ Axiom } 3\\ 7 &amp; \{ \lnot \lnot a \} \vdash \lnot \lnot a \to  a  &amp; \text{ Modus Ponens } 5, 6\\ 8 &amp; \{ \lnot \lnot a \} \vdash a  &amp; \text{ Modus Ponens } 1, 7\\ 9 &amp; \vdash \lnot \lnot a \to a  &amp; \text{ Deduction Theorem } \\ \end{array}  And then I continued on, to prove double negation introduction:  \begin{array}{ccc} 10 &amp; \vdash \lnot \lnot \lnot a \to \lnot a &amp; \text{Double Negation Elimination}\\ 11 &amp; \vdash (\lnot\lnot \lnot a \to \lnot a) \to (a \to \lnot \lnot a) &amp; \text{ Axiom } 3\\ 12 &amp; \vdash a \to \lnot \lnot a &amp; \text{ Modus Ponens } 10, 11\\ \end{array}  My questions:   Am I allowed to invoke the deduction theorem in the middle of a proof like this (step $9$)? Is this considered a context change? Is context-changing allowed? Are the proofs even right/correct? Assuming it's all correct: Are we able to combine them to say that $a \to \lnot \lnot a$ and $\lnot \lnot a \to a$, therefore $a \iff \lnot \lnot a$ or is this symbol not allowed? What ultimately let us say $\lnot \lnot a = a$, the use of the equal sign here?