Suppose I have some dataset. I perform some regression on it. I have a separate test dataset. I test the regression on this set. Find the RMSE on the test data. How should I conclude that my learning algorithm has done well, I mean what properties of the data I should look at to conclude that the RMSE I have got is good for the data?
I've fitted my model and am trying to understand whether it's any good. I've calculated the recommended metrics to assess it ($R^2$/ AUC / accuracy / prediction error / etc) but do not know how to interpret them. In short, how do I tell if my model is any good based on the metric? Is an $R^2$ of 0.6 (for example) sufficient to let me proceed to draw inferences or base scientific/business decisions?     This question is intentionally broad, to cover a wide variety of situations that members frequently encounter; such questions could be closed as duplicates of this one. Edits to broaden the scope beyond the metrics mentioned here are welcome, as are additional answers - particularly those that offer insight about other classes of metrics.
I am having difficulty with this proof. I have previously proved that for an automorphism on the extension field $K$ of $F$ that when restricted to $F$ is the identity automorphism must take roots of $f(x)\in F[x]$ in $E$ to roots of $f(x)$ in $E$. I was thinking of using the minimal polynomial $x^{3}-2\in\mathbb{Q}[x]$ and the result of previous problem I solved, but I suspect there are automorphisms that don't fix the subfield, so the result can't be used or I need to prove that any automorphism of an extension field must fix the subfield that is being extended or always sends roots in $E$ to roots in $E$.  I am not asking for a solution to this, but maybe a hint or pointer in the right direction. This problem is introduced in the text prior to Galois theory, so please keep that in consideration. What SIM card would you recommend for a smartphone user for travel in Germany?  It would be probably the only or the most important connection to the Internet, so large amounts of data and relatively fast transfer is an issue.  I need to stay in touch with friends and family, so the calls to other EU countries should be as cheap as possible.   For to the first criteria, I found the T-Mobile offer interesting. The internet costs 10 Euros/month and after reaching the transfer limit it stays relatively fast. According to tests (Galileo from Pro7, AFAIR) it has also the best coverage. However, calls to other countries are very expensive.  For to second criteria, Lebara and Mobilka are interesting. The calls are very cheap, but there are problems with signal strength in many locations, where T-Mobile has no problem. The voice quality, at least in Lebara, is also limited. They both have mobile internet with unlimited transfer, but after reaching the high speed limit, the transfer is reduced to 64 kbps, which is too slow.  I've found out that O2 has foreign calls at moderate prices, but I haven't yet checked for details. There are so many other options, making it is hard to compare them all without spending the whole weekend on it. So, if someone has found a better option than having 2 SIM cards and constantly switching them, this answer would be greatly appreciated. I've had a very strange Finer error caused by recent macOS High Sierra betas that affected Macs running macOS 10.13 as well as macOS 10.12 Sierra. This error causes an entire Finder window to show visual artifacts when opening certain folders on either an APFS or HFS+ volume.  After moving the cursor or the affected Finder window, the window may look something like this;    Attempting to use Disk Utility to repair the affected volume does not resolve this issue, nor does restarting the affected Mac (even in Safe Mode).  Without formatting this disk, how can I prevent Finder from exhibiting this graphical error when opening particular folders? Prove $e^{x+y}=e^{x}e^{y}$ by using Exponential Series WMS and WFS queries needs SRS and BBOX parameters.  http://example.com/geoserver/wfs?   service=WFS&amp;   version=2.0.0&amp;   request=GetFeature&amp;   typeNames=namespace:featuretype&amp;   srsName=CRS&amp;   bbox=a1,b1,a2,b2&amp;   For example I have GeoServer to publish WFS. My data SRS is EPSG:4326 and my map SRS is EPSG:3857. So I send a WFS query.  http://example.com/geoserver/wfs?   service=WFS&amp;   version=2.0.0&amp;   request=GetFeature&amp;   typeNames=namespace:featuretype&amp;   srsName=EPSG:3857&amp;   bbox=978393.9621,2680799.4560,-430493.3433,3326539.4710&amp;   Does GeoServer or ArcGIS server give an error? Because my data has EPSG:4326 . Or does GeoServer convert these coordinates internally and find data and send me as EPSG:3857 How to represent it with UNIQUE indexes and foreign keys? "Group" is a group of pupils. "Topic" is a topic of lessons.  To every group corresponds exactly one topic. (So there may be multiple groups per topic.)  To a pupil corresponds multiple groups, but maximum one group per topic.  How to implement this in terms of UNIQUE indexes and foreign keys in MySQL? I have a question about the pattern "turn &lt;something&gt; on &lt;somebody&gt;" :     Then he allegedly turned the body-building equipment on his 44 year-old wife, identified by sources as Feng Liang, and his elderly mother-in-law, Feng Kun Zaehng,77, the sources said.     I understand the phrase "*turn the gun on &lt;somebody&gt;", am not sure about "turn the equipment on &lt;somebody&gt;".  Could the example be wrong? Which are the word orders that can be found in English? The internals of bcrypt I'm attempting to get a better understanding of cryptography and have run into some questions about bcrypt.   Bcrypt relies on the blowfish cipher, which is a reversible method of encryption. But bcrypt is not reversible. How is that possible? Or am I mistaken? What does bcrypt do on top of blowfish to make it irreversible? Why does bcrypt use blowfish instead of twofish or threefish? Annoying FrontEnd bugs in Mathematica 10 How to describe arbitrary accelerations in special relativity Implicit newline at the end of each paragraph? In certain styles of text I define \parindent 0pt in the preamble and write the text in this manner:  paragraph 1\\  paragraph 2\\   and so forth. I wonder if there is anything I can include in the preamble for instance to modify how the end of paragraphs are interpreted so I don't have to include the \\ at the end of each? A mysterious app named &quot;10102&quot; shows up in my data usage. It bears only the standard Android app icon (the Bugdroid logo with a cube on its torso). From what the graph tells me, it has used 36 megabytes of data in the background and zero on the foreground. I think I haven't uninstalled anything for months. Is it malware? I haven't sideloaded anything and only authorized my laptop as a USB debugger. If it's malware, how do I remove it? I have no idea how to find its package name and 10102 isn't in the list of downloaded apps in settings. I'm running stock &amp; never-been-rooted Android 4.4.4 on Nexus 4. Is there a way to enter the default keyring password using the command line?   For instance:  You have a remote setup of Ubuntu 10.10 thats set to auto login. You don't want to remove  the keyring password.  All right the system boots up and logs in automatically, then asks for the keyring password now at this point you can create ssh connections but you can't remote desktop.   What can you do to enter the keyring password at this point?  Also, to better clarify, this is from a remote connection using the command line. Most efficient way to see if an ArrayList contains an object in Java PHP validation/regex for URL I've been looking for a simple regex for URLs, does anybody have one handy that works well?  I didn't find one with the zend framework validation classes and have seen several implementations. My computer no longer boots Windows or the installed operating system. Instead, I may get this error:  PXE-E61: Media test failure, check cable -or- Check cable connection!  PXE-M0F: Exiting PXE ROM.   and/or one of the following messages or similar:  Operating System not found  No boot device available- No bootable devices--strike F1 to retry boot, F2 for setup utility  No bootable device -- insert boot disk and press any key  No Boot Device Found. Press any key to reboot the machine  Default Boot Device Missing or Boot Failed  Reboot and Select proper Boot device or Insert Boot Media in selected Boot device   What does this mean and what can I do?     This question comes up often and the answers are usually the same. This post is meant to provide a definitive, canonical answer for this problem. Feel free to edit the answer to add additional details. What methods of ‘clearfix’ can I use? Could it be that Goldbach conjecture is undecidable? How can I get a significant overall ANOVA but no significant pairwise differences with Tukey's procedure?