I have 3 possible "final" models in binary logistic regression (N=176, Number of events = 36).  Now I am trying to decide which one to select. It´s clear,"All models are wrong, but some are useful", but I have to decide.  My goal is prediction and so parsimony over complexity.  Which criterion to use? Corrected AIC in combination with adjusted Pseudo-R2? And then AUC with calibration curve for each model in order to compare them?
Suppose we have $n$ covariates $x_1, \dots, x_n$ and a binary outcome variable $y$. Some of these covariates are categorical with multiple levels. Others are continuous. How would you choose the "best" model? In other words, how do you choose which covariates to include in the model?  Would you model $y$ with each of the covariates individually using simple logistic regression and choose the ones with a significant association?
For $u:\mathbb{R}\times [0,1]$ with boundary conditions $u(0,x)=\cos (2\pi x)$ and $u(t,0)=u(t,1)$.   Solve $u_t=u_{xx}+u_x$.  I had this on an exam and tried to write $u$ as a product of two single variate functions and convert to an ode using the usual methods but things got messy and I couldn't finish. I also tried to write $u$ as a Fourier series in $x$ with coefficients $a_k(t)$ depending on $t$, but this also didn't seem to yield anything.  Is there a more clever way to approach this, possibly with Fourier series? I heard from a friend there may be a Fourier transform method since the equation was "homogeneous in momentum space."   Thanks! I have some Java executable (jar) that is run my some shell script from a cron job once every night. That executable does not print log statements &quot;as usual&quot; just by printing them out in a sequential manner like line after line (print after print), but while it processes its data its printing a single line with status data and then &quot;overwrite&quot; or &quot;update&quot; just that single line over and over again, until its done with this part of processing. Examples: A common program would output something line this: Program XYZ started..&lt;cr+lf&gt; processing 1&lt;cr+lf&gt; processing 2&lt;cr+lf&gt; processing 3&lt;cr+lf&gt; im done&lt;cr+lf&gt;  Simple! I can easily redirect its output to a file and I'm done. But the program I will have to deal with does it more like this: Program XYZ started..&lt;cr+lf&gt; processing 1&lt;cr&gt; processing 1 - part a&lt;cr&gt; processing 1 - part b&lt;cr&gt; processing 1 - part c&lt;cr&gt; processing 1 - part d&lt;cr&gt; &lt;cr+lf&gt; processing 2&lt;cr&gt; processing 2 - part a&lt;cr&gt; processing 2 - part b&lt;cr&gt; processing 2 - part c&lt;cr&gt; processing 2 - part d&lt;cr&gt; &lt;cr+lf&gt; processing 3&lt;cr+lf&gt; im done&lt;cr+lf&gt;  but much more intensive than I showed here. So it just not always overwrite status lines, but does it a lot while processing. So just redirecting or appending its output to a log file does not seem to make a lot of sense here, since it will just clutter the log file with millions of screen-updates that can not be viewed and understood that easily by humans. So my question is: is there a way or tool for programs that may behave like that to &quot;log&quot; or maybe &quot;screenshot every 30 seconds&quot; their output to a log file? Continuous and preserves measurability $\implies$ preserves null sets. From reading the rules it would appear there are two kinds of damage and then straight loss of life:     118.3 If an effect causes a player to gain or lose life, that player's life total is adjusted accordingly.   From reading that I would guess that effects like Extort are not sources of damage. You simply lose the life.      119.2a Damage may be dealt as a result of combat. Each attacking and blocking creature deals combat damage equal to its power during the combat damage step.   So damage from creatures during combat is combat damage.     119.2b Damage may be dealt as an effect of a spell or ability. The spell or ability will specify which object deals that damage.   And that is direct damage from an object.  So the arguments are these:  Does loss of life as outlined by rule 118.3 (at top) count as being dealt damage? Do triggered abilities that redirect or reduce damage effect loss of life?  My second related question: You put  on a  and tap her to deal one damage to your opponent. Am I right in saying that because the damage was direct damage (not dealt during combat) then the triggered ability of preventing the combat phase of the damaged player is not triggered? Is my C1/D visa valid for transit in the US, if I want to go on a vacation to Mexico? Is the wave function of a particle re-created after a measurement stops? Some of the Puella Magi seem to have magical powers related to the wishes that they made. Sayaka has regeneration abilities, and she wished to heal someone. Homura has time manipulation abilities, and she wished to go back in time.  But other magical girls, like Mami and Kyouko, don't appear to have powers related to their respective wishes.  So, is there a connection, or is it only a coincidence for Sayaka and Homura? If it's the former, how do Mami and Kouko's wishes relate to their powers? As the output of df -h shows here, something is eating up 5GB of free space. So, it's not available to use.   I'm also noticing sometimes that the hard disk gets filled up to 100% sometimes. So, I had to restart the machine or delete some unncessary files. Only noticed these in /home partition. Don't know whether these two are related, but appreciate if anyone can put some insight into this.  $ df -h Filesystem            Size  Used Avail Use% Mounted on /dev/sda8             100G   92G  2.7G  98% /home Calculating $\lim_{x\to+\infty}(\sqrt{x^2-3x}-x)$ Let $f(x) = \sqrt{x^2-3x}$ and $g(x) = x$. Calculate the following limits, showing all working.  I've done the first two -   $$\lim_{x\to0}f(x)\\ =\lim_{x\to0}\sqrt{x^2-3x}=0$$  $$\lim_{x\to-\infty}\frac{f(x)}{g(x)}\\ =\lim_{x\to-\infty}\frac{\sqrt{x^2-3x}}{x}=\sqrt{1-\frac{3}{x}}=1$$  How do I calculate this one?  $$\lim_{x\to+\infty}(f(x)-g(x))$$ Java FileInputStream ObjectInputStream reaches end of file EOF The direction of static friction? How can I return NULL from a generic method in C#? How to get glare on "Quick Smoke" (Fire & Smoke explosion) Manual/automatic line breaks and text alignment in TikZ nodes How can I insert a line break in a TikZ node? Simply putting \\ where I want the break doesn't work (see MWE).  Is there a way to make lines break automatically at some specified width?  And can I control the alignment of the text (left, right, centered, justified)?  \documentclass{article} \usepackage{tikz} \begin{document} \begin{tikzpicture} \node {First line\\second line}; \end{tikzpicture} \end{document} If $f(x)\to 0$ as $x\to\infty$ and $f''$ is bounded, show that $f'(x)\to0$ as $x\to\infty$ Let $f\colon\mathbb R\to\mathbb R$ be twice differentiable with $f(x)\to 0$ as $x\to\infty$ and $f''$ bounded. Show that $f'(x)\to0$ as $x\to\infty$. (This is inspired by  to a different question) I'm looking for some help disproving an answer provided on a  I posted about computing the number of double square combinations for a given integer.    The original question is from the Facebook Hacker Cup       Source: Facebook Hacker Cup   Qualification Round 2011      A double-square number is an integer $X$   which can be expressed as the sum of   two perfect squares. For example, 10   is a double-square because $10 = 3^2 + 1^2$.   Given $X$, how can we determine the   number of ways in which it can be   written as the sum of two squares? For   example, $10$ can only be written as $3^2 + 1^2$   (we don't count $1^2 + 3^2$ as being different). On the other hand,   $25$ can be written as $5^2 + 0^2$ or as   $4^2 + 3^2$.      You need to solve this problem for $0 \leq X \leq 2,147,483,647$.      Examples:      $10 \Rightarrow 1$      $25 \Rightarrow 2$      $3 \Rightarrow 0$      $0 \Rightarrow 1$      $1 \Rightarrow 1$   In response to my original question about optimizing this for F#, I got the following response which I'm unable to confirm solves the given problem correctly.       Source:       Again, the number of integer solutions   of $x^2 + y^2 = k$ is four times the   number of prime divisors of $k$ which   are equal to $1 \bmod 4$.      Knowing this, writing a program which   gives the number of solutions is easy:   compute prime numbers up to $46341$ once   and for all.      Given $k$, compute the prime divisors of   $k$ by using the above list (test up to   $\sqrt{k}$). Count the ones which are   equal to $1 \bmod 4$, and sum. Multiply   answer by $4$.   When I go through this algorithm for $25$, I get $8$ which is not correct.          For each prime factor (pf) of $25$ ($5$, $5$ are prime factors of $25$)         if pf % $4$ = $1$ (true for both $5$'s), add $1$ to count      return $4$ * count (count would be $2$ here).          So for $25$, this would be $8$ I've encountered different usages of preposition + Home and I want to learn which of them are correct.  Some examples:     Back home   Back at home   Back to home Microsoft Edge keeps taking over PDF file open/association How should I cite a website URL? What are good basic statistics to use for ordinal data?