When building a logistic regression, the probability of an observation belonging to a class can be calculated. But is there a way to determine how reliable that probability is? If the accuracy is of the model is low then how good is the probability?
I have a trained logistic regression model that I am applying to a testing data set. The dependent variable is binary (boolean). For each sample in the testing data set, I apply the logistic regression model to generates a % probability that the dependent variable will be true. Then I record whether the acutal value was true or false. I'm trying to calculate an $R^2$ or Adjusted $R^2$ figure as in a linear regression model.  This gives me a record for each sample in the testing set like:  prob_value_is_true         acutal_value    .34                          0    .45                          1    .11                          0    .84                          0     ....                        ....             I am wondering how to test the accuracy of the model. My first attempt was to use a contingency table and say "if prob_value_is_true > 0.80, guess that the actual value is true" and then measure the ratio of correct to incorrect classifications. But I don't like that, because it feels more like I'm just evaluating the 0.80 as a boundary, not the accuracy of the model as a whole and at all prob_value_is_true values.  Then I tried to just look at each prob_value_is_true discrete value, as an example, looking at all samples where prob_value_is_true=0.34 and measuring the % of those samples where the acutal value is true (in this case, perfect accuracy would be if the % of samples that was true = 34%). I might create a model accuracy score by summing the difference at each discrete value of prob_value_is_true. But sample sizes are a huge concern here, especially for the extremes (nearing 0% or 100%), such that the averages of the acutal values are not accurate, so using them to measure the model accuracy doesn't seem right.  I even tried creating huge ranges to ensure sufficient sample sizes (0-.25, .25-.50, .50-.75, .75-1.0), but how to measure "goodness" of that % of actual value stumps me. Say all samples where prob_value_is_true is between 0.25 and 0.50 have an average acutal_value of 0.45. Is that good since its in the range? Bad since its not near 37.5% (the center of the range)?  So I'm stuck at what seems like should be an easy question, and hoping someone can point me to a resource or method to calculate an accuracy stastic for a logistic regression model.
$\DeclareMathOperator{\Char}{char}$$\DeclareMathOperator{\Aut}{Aut}$ Let $G$ be a finite group, $H$ a subgroup, such that $H \Char G$. If $\phi \in \Aut(H)$ is there an automorphism $\widehat{\phi} \in \Aut(G)$ such that $\widehat{\phi}|_H$ = $\phi$?  In words, if $\phi$ is an automorphism of $H$, is there necessarily an automorphism $\widehat{\phi}$ of $G$ where $\widehat{\phi}$ maps the elements in $H$ to $H$ in exactly the same way?  I am thinking this is false (consider the non-finite example of $\bar{Q}$ and $\mathbb{C}$), but would like a counter example (for the finite case). Pokemon Go: Can't log in? Are everyone unable to log in right now? 2016 July 16. Where I live none can log in to the servers at the moment, and it all happened after the sudden release of the game in my country.   As I understand the game was recently released in 26 countries, so I guess they have problems and had the servers go offline in order to fix the issues. Is GTA Online cross-platform? threeparttablex table notes for tabu tabulars with less than \textwidth I read it in English in the United States, somewhere in the 1990s. I got it off of the big bookshelf in our family room, which means it could be a good bit older; some of the books were my Dad's. At the beginning, a young boy (maybe an early teen?) leaves his house, where he lives with his parent or parents, and takes a test to become a spaceship pilot for the military. Part of the test judges reaction speed, and he fails the test. He later learns (I think when he's approached by an agent of the government) that he "failed" because he has some sort of enhanced fortune that meant that he was actually giving the results before they could be displayed on the screen. At the time, I remember thinking that the book felt a bit like a Star Wars rip-off.  Years later, I read that one of the Star Wars books (probably now Legends) had Luke similarly failing the Imperial Academy test because he gave his answers too quickly, and it amused me that I was uncertain as to which had come first.  I don't remember anything concrete about the cover, although I have a general impression that it was white. Definitely futuristic. My impression was that the boy was wearing a white uniform for the testing and that the government agent who spoke to him had a grey beard, but I might be mixing bits of Star Wars in there. Is there a way to stop the gmail address field (on the login page) from displaying all the gmail addresses that you have ever typed in it?   When logging in with Google Chrome or trying to set up a new account, anything you type which starts with the same letter as the one that you are trying to use currently will show up in the auto-complete field, I don't want that.    I understand that this is a convenient feature in some cases, but the thing is--I know this shouldn't've happened, but it has actually happened more than once--I sometimes mistyped my password in the Gmail address field right after the address, mistakingly assuming that the prompt had already been moved to the password field, and then hit "Enter" without looking first. The next time I tried to enter my Gmail address, it popped up the address followed by my password as one of the entries on the list of email addresses that shows up, and I couldn't get rid of the entry.   Is there a way to remove these? The autofill feature in Chrome is a time saver, and so I don't really want to turn it off. It would be helpful to be able to edit out some of the typed info, though, so it won't show up again -- is this possible to do? How to create vertical and horizontal dotted lines in a matrix? Requires installation of untrusted packages? I tried installing VLC Player yesterday, and I got the Requires installation of untrusted packages error.  I searched for hours for a solution to this problem, and finally came upon a suggestion that said to change servers for downloading updates from.  I did this, and it gave me a 404 error when I clicked on "Check" in the Update Manager.  I tried switching my server back to the main one (and after that, several other ones), but I am now still getting a 404 error:   And the other error I get when downloading or updating:   Edit: Output of cat /etc/apt/sources.list:  deb-src http://us.archive.ubuntu.com/ubuntu/ precise main restricted #Added by software-properties  # See http://help.ubuntu.com/community/UpgradeNotes for how to upgrade to # newer versions of the distribution. deb http://us.archive.ubuntu.com/ubuntu/ precise main restricted multiverse deb-src http://us.archive.ubuntu.com/ubuntu/ precise multiverse universe #Added by software-properties  ## Major bug fix updates produced after the final release of the ## distribution. deb http://us.archive.ubuntu.com/ubuntu/ precise-updates main restricted multiverse deb-src http://us.archive.ubuntu.com/ubuntu/ precise-updates restricted main multiverse universe #Added by software-properties  ## N.B. software from this repository is ENTIRELY UNSUPPORTED by the Ubuntu ## team. Also, please note that software in universe WILL NOT receive any ## review or updates from the Ubuntu security team. deb http://us.archive.ubuntu.com/ubuntu/ precise universe deb http://us.archive.ubuntu.com/ubuntu/ precise-updates universe  ## N.B. software from this repository is ENTIRELY UNSUPPORTED by the Ubuntu  ## team, and may not be under a free licence. Please satisfy yourself as to  ## your rights to use the software. Also, please note that software in  ## multiverse WILL NOT receive any review or updates from the Ubuntu ## security team.  ## N.B. software from this repository may not have been tested as ## extensively as that contained in the main release, although it includes ## newer versions of some applications which may provide useful features. ## Also, please note that software in backports WILL NOT receive any review ## or updates from the Ubuntu security team. deb http://us.archive.ubuntu.com/ubuntu/ precise-backports main restricted universe multiverse deb-src http://us.archive.ubuntu.com/ubuntu/ precise-backports main restricted universe multiverse #Added by software-properties  deb http://us.archive.ubuntu.com/ubuntu/ precise-security main restricted multiverse deb-src http://us.archive.ubuntu.com/ubuntu/ precise-security restricted main multiverse universe #Added by software-properties deb http://us.archive.ubuntu.com/ubuntu/ precise-security universe  ## Uncomment the following two lines to add software from Canonical's ## 'partner' repository. ## This software is not part of Ubuntu, but is offered by Canonical and the ## respective vendors as a service to Ubuntu users. deb http://archive.canonical.com/ubuntu precise partner deb-src http://archive.canonical.com/ubuntu precise partner  ## This software is not part of Ubuntu, but is offered by third-party ## developers who want to ship their latest software. How do I get the coordinates of a mouse click on a canvas element? What's the simplest way to add a click event handler to a canvas element that will return the x and y coordinates of the click (relative to the canvas element)?  No legacy browser compatibility required, Safari, Opera and Firefox will do. How can I quickly level up in World of Warcraft? I've been playing for months and I'm barely at level 40, while my classmates play less than I do and have multiple lvl 80 characters.  Is there a better way to level fast in World of Warcraft than just completing quests? How do you handle "that that"? The double "that" problem How to push a copy of an object into array in PHP How to make \hl (highlighting) to automatically place incompatible commands in \mbox? The soul package provides a useful command \hl for highlighting text. However, \cite, \ref, and some other commands (maybe equations too) must be placed within an \mbox in order for \hl to work properly.  Is there any way to make this automatic? Meaning that to modify \hl (and other commands provided by soul) to put everything except plain text in an \mbox?  \documentclass[12pt]{article} \usepackage{soul} \begin{document}  \section{1}\label{sec} This is to show that \textbackslash{hl} fails to highlight texts containing citations or reference!  \hl{ This is one line containing a citation \mbox{\cite{}}}  \hl{ This is one line containing a reference \mbox{\ref{sec}}}   \end{document} not able to execute multiple commands on multiple linux machines? Optional argument to \item Smallest positive element of $ \{ax + by: x,y \in \mathbb{Z}\}$ is $\gcd(a,b)$ Let $S = \{ax + by: x,y \in \mathbb{Z}\}$  and let $e &gt; 0$ be the smallest element in $S$. Prove that $e \mid a$, and hence prove that $e = \gcd(a,b)$  I'm afraid I can't provide much of my initial working here because I'm at a loss of how to start.  I suppose that to show $e\mid a$ I would have to show that $eg = a$ for some $g \in \mathbb{Z}$. But I have no idea how I would do this. Best books for mathematical background? Add desktop notifications for Chrome or Firefox How do I transfer iPhone contacts to an Android phone? How to find Oracle's installed version and release from a program?