Intuitively, I can't really wrap my head around this. If I regress y on x and the beta is less that one, shouldn't the beta from a regression of x on y be greater than one. Mathematically, I know the relationship:  i.e. beta = cov(x,y)/var(x)   so that as long as var(y) and var(x) are greater than cov(x,y), both betas will be less than one. But intuitively, this doesn't seem to make sense to me. The context I'm looking that is in stock returns. If I get a beta of less than 1, doesn't that mean the stock that is the independent variable is less volatile than the dependent? And if that's the case should the inverse regression yield a beta greater than one?  What am I missing? Is there an easy way to conceptualize this?
The Pearson correlation coefficient of x and y is the same, whether you compute pearson(x, y) or pearson(y, x). This suggests that doing a linear regression of y given x or x given y should be the same, but I don't think that's the case.   Can someone shed light on when the relationship is not symmetric, and how that relates to the Pearson correlation coefficient (which I always think of as summarizing the best fit line)?
Where can I see my flag count / history? Is there a section or page that lists my flag count and / or history? Why does "stigmata" [often] have penult stress? I have been studying the pronunciation of Greek-derived words in English, and I've found an odd anomaly. There are (at least) two possible pronunciation patterns for plural word-forms that end in -&#8288;mata (which correspond to singular word-forms that end in -&#8288;ma).   Antepenult stress (expected)  It appears that it is always possible to place the stress on the antepenult (third-to-last) syllable, such as:    /ˈlɛmə/, /ˈlɛmətə/  /ˈskiːmə/, /ˈskiːmətə/  /ˌtɛrəˈtoʊmə/, /ˌtɛrəˈtoʊmətə/~/ˌtɛrəˈtɒmətə/  /ˈstɪɡmə/, /ˈstɪɡmətə/   This is what would be expected from  (I believe most or all of these words came through Latin before entering English), since the penultimate "a" in the original Greek words is short.  Maybe Latin vowel quality and stress rules are not very relevant; certainly, few English speakers know about them nowadays. And even with antepenult stress, some of these pronunciations do not seem to follow all of the traditional rules for pronouncing Latin-derived terms in English. I was reminded by some comments in this  that  in antepenult stressed syllables, we would expect tense ("long") vowels to be shortened due to  (TSL), yielding pronunciations like /ˌtɛrəˈtɒmətə/ (which I just noticed is in fact listed in the Oxford English dictionary) and ?/ˈskɛmətə/ (which is not). (Compare to genus~genera /dʒiːnəs/~/dʒɛnərə/, and perhaps opus~opera /oʊpəs/~/ɒpərə/). However, there are other Latinate plural forms that typically don't have trisyllabic laxing (matrices, also I think helices), or where both the lax- and tense-voweled pronunciations coexist (codices, apices), so I guess the apparent lack of it in schemata should not be surprising. (There are even some exceptions to TSL in singular nouns like obesity.)  Penult stress (unexpected)  The other pronunciation seems to exist only for a couple of words, in which the penultimate "a" is commonly stressed and broadened: stigma ~ stigmáta  (listed by both the Merriam-Webster dictionary and the ), and also sometimes schéma ~ schemáta /skiːˈmɑːtə/ (listed only by the ). (Neither the Merriam-Webster dictionary nor the Oxford Learner's Dictionaries list *"lemmáta").  I'm wondering why this pronunciation exists. It's an irregular plural either way, and putting the stress on the penultimate syllable creates a stress change between the singular and the plural forms.  (It's true that all of these words are rare, and some people might pronounce some of their plurals differently. The pronunciations I give here are simply the ones listed in dictionaries.)  The plural form "stigmata" is probably most common in religious or theological contexts (where it refers to the wounds of Christ), so at first I wondered if the penultimate stress was supposed to be closer to the original Greek pronunciation, but according to , the stress is on the antepenult in Greek as well.  So, what's up with this? Did the stress perhaps change in Latin over time, is this a tradition of Greek accentuation that I'm not familiar with, is this a simple matter of ignorance of the original position of the stress that has now become entrenched with time and usage, or is this somehow explainable by established English stress patterns? (For example, do English speakers have some natural preference for a penultimate stress on polysyllabic words?)  If nobody knows of a reason, I suppose I can just put it down to people encountering the word mainly in text, not knowing which syllable to stress, and choosing the penult because it sounds better to them.  (I asked this question a while back on , but nobody knew of any reason.) I am a physics Master's student.  I have good grades, with CGPA above 9(/10)(However, all courses in my university are graded on a curve so the actual marks are significantly lower than 90%). This has been my marks throughout my undergraduate and graduate courses and I was happy because this was above average. Also, my summer projects in UG were usually computational and any difficulty I had in theoretical aspects I attributed it to my inexperience in advanced Physics.   However, recently I have started to work on pure theoretical project and while reading for the project I realized that I consistently miss some details from each topic. I understand the general idea, can re-derive most of the equations(with some effort) however when I discuss things with my professor or when I read further topics I realize that I have missed certain key-details. This is exactly similar to the case of me missing a few key questions in my exams and getting that 9 grade point instead of 10(or at-least I think so). I was not worried about this before but now I realize that there is some flaw in the way I study (but I do not know what).   Since I want to apply for Physics PhD I realized that I will need to have solid concepts and it would be best to correct my mistakes but I do not know how or even what could be the reason for my imperfect understanding.  Any direct suggestion would help or even certain general guidelines on what I can do.    Things I've tried recently -   1) I've started to written down almost everything I read. This is slightly laborious but is certainly helping. It also helps me to gloss over the things I read previously when I come back the next day.  2) I completely avoid smartphone when I'm library/study room so that I won't get distracted. Not sure if it helps me solve the above problem but certainly helps me study better in general.  3) I've tried to read the topics from several sources. The books I am reading is somewhat like a collection of research papers and hence does not have a exercises. So I though reading from various sources might help get better ideas but it's not really helping because most other sources are too high level as an introductory text. But this will probably help me in cases where it's practical to do this.  4) Somewhat similar to point (1)- I am trying reread, whenever I can, what I've done until that point. But not sure how much this will help me in filling the gaps. How to simplify the summation kk! without using induction? How to adjust the gap between figure and caption within the same subfloat The total number of subsets is $2^n$ for $n$ elements In my probability book, it says that to count the total number of subsets of n elements is a process of $n$ stages with binary choice of either adding this element to the subset or not to add it. Therefore, the total number is $$2^n$$  But, for instance, we have 3 elements, according to this formula, there are 2 to the power of 3 elements, namely 8, which are $${\emptyset},A,B,C, AB, AC, BC, ABC$$  However, I have a hard time of imagining the process or N stages binary choice that form this many subsets. Can anyone explain/help me to understand it? I mean, ABC, if we are making the choice of A, put it in or do not put it in, exactly which subset are we choosing to put in or not? Thank you. Device that makes metal malleable Is $f(x)=10$ a periodic function? I am not getting satisficatory explanation for this. Clearly $f(x+T) = f(x)$ for all values of $T$.  If we assume it is periodic, does this mean period =  $0$? Since I upgraded to the latest version of Ubuntu, I cannot install the Java OpenJDK package needed to compile Android custom ROMs. When I run sudo apt-get install openjdk-7-jdk, the following error appears:  Reading package lists... Done Building dependency tree        Reading state information... Done Some packages could not be installed. This may mean that you have requested an impossible situation or if you are using the unstable distribution that some required packages have not yet been created or been moved out of Incoming. The following information may help to resolve the situation:  The following packages have unmet dependencies:  openjdk-7-jdk :  Depends: openjdk-7-jre (= 7u51-2.4.6-1ubuntu4) E: Unable to correct  problems, you have held broken packages.   How do I fix this problem? Trying to plot the sin(x) function, I get this result:    The MWE is here:  \documentclass{standalone} \usepackage{ pgfplots} \begin{document} \begin{tikzpicture} \begin{axis} \addplot[samples=500]{sin(x)}; \end{axis} \end{tikzpicture} \end{document}   cos(x) looks like an inverted parabola and tan looks just like sin.  I'm using pdflatex and MiKTeX. Any ideas? Subject–verb agreement not clear in "Is two bars OK?" Is the following correct?     Can I get some chocolate for myself? Yes, you can but not much.   Is two bars OK?   Is there any rule to explain the sentence above?  The dialogue's taken from Grammar Textbook Round-Up Level #3. What can I do to manage my phone's internal storage? Can I get more than 1000 records from a DirectorySearcher? I just noticed that the return list for results is limited to 1000. I have more than 1000 groups in my domain (HUGE domain). How can I get more than 1000 records? Can I start at a later record? Can I cut it up into multiple searches?  Here is my query:  DirectoryEntry dirEnt = new DirectoryEntry("LDAP://dhuba1kwtn004"); string[] loadProps = new string[] { "cn", "samaccountname", "name", "distinguishedname" }; DirectorySearcher srch = new DirectorySearcher(dirEnt, "(objectClass=Group)", loadProps); var results = srch.FindAll();   I have tried to set srch.SizeLimit = 2000;, but that doesn't seem to work. Any ideas? How do I protect random people pointing their domain to my server? Prove that the multiplicative inverse of $a$ modulo $m$ exists if and only if $a$ and $m$ are coprime. Prove that the multiplicative inverse of $a$ modulo $m$ exists if and only if $a$ and $m$ are coprime.  Can someone help me with this? Total MU Calculation when Outer CF is linked to Inner CF What happens to the Y MU from the outer field when 2 fields are connected AFTER both fields are made. What would be the total MU gained in the checkpoint in the third step? Attribute Table Default Order in QGIS I'm having an issue with QGIS version 3.2 Bonn. For my class, a question asks, "What city corresponds to row number 1713 for the Colleges and Universities shapefile?". I'm having issues answering this, because each time I load the shapefile into QGIS, the attribute table order is randomized, giving me a different city each time.   How can I open the "default" version of the attribute table for this layer, so that the order of rows is not randomized each time? Could Dark Matter form black hole? Some people speculate that the mysterious dark matter in the universe could be tiny black holes. But on the other side, could dark matter particles attract each other by gravity and finally form a black hole? Since dark matter is even more abundant than normal matter, the dark matter black hole should not be rare. Please add TeX rendering on the Android app MathJax isn't currently working on the Android app, which makes it totally useless for the 'technical' sites like  or .  For example, in the Android app:    Same post in a (mobile) browser:     Please add this functionality! The email for getting notifications can be changed by clicking the "preferences" tab in your profile. After entering a new email address, the "Save email settings" button becomes clickable:    Clicking the button turns it grey:    So all looks well. But if you don't confirm the email by clicking on the link sent to your email inbox, the next time you go back to the preferences, you will see your old email address with no indication that it changed.  You can subscribe to the weekly newsletter from the "edit" tab of your profile. If you click the option and save, the next time you visit the edit page before confirming your email you get this message:    Once you confirm the email, the resend link disappears so you know the subscription is set up:    Ideally, the two systems would be unified so that all email subscriptions happen the same way. But short of that, it would be very helpful to indicate that an email address is unconfirmed for notification emails just like newsletters.