I understand that $y_{i}$s are normally distributed because we assume that the residual is normally distributed which seems a decent assumption.   Question: Does that mean $Y$ is also normally distributed? In other words, if I plot a histogram of $Y$ values will they have a unimodal Gaussian shape?   Confusion: We generally apply linear regression on problems that involve predicting a continuous variable. Given the wide applicability of linear regression, I am finding it little difficult to believe that $Y$ tend to be normally distributed for all of them.   I believe that in case of Logistic Regression, I can say that $Y$ will be Bernoulli distributed, and $y_{i}$s will have the same distribution. In other words, I can say that $Y$ has a Bernoulli distribution with $P(y_{i}=1) = \theta$
I've got a weird question. Assume that you have a small sample where the dependent variable that you're going to analyze with a simple linear model is highly left skewed. Thus you assume that $u$ is not normally distributed, because this would result in normally distributed $y$. But when you compute the QQ-Normal plot there is evidence, that the residuals are normally distributed. Thus anyone can assume that the error term is normally distributed, although $y$ is not. So what does it mean, when the error term seems to be normally distributed, but $y$ does not?
Why the Principle of Least Action? Careers should allow me to add external (authored but not owned) GitHub projects under "other" Restricing domains for universal and existential quantifiers I am currently using Rosen's "Discrete Mathematics and Its Applications" (7th ed.) for my discrete mathematics course. We recently talked about quantifiers, more specifically the universal and existential quantifier. What confuses me is when we started talking about restricting the domain (i.e. instead of all real numbers, only all real positive numbers), where does the conditional statement come from when restricting the domain of a universal quantifier and where does the conjunction come from when restricting the domain of a existential quantifier?  This link did help:   However, the part that confuses here is how are the domains restricted in the answer given in the link above? Is there any way in unix to find out who accessed certain file in last 1 week? It may be user or some script ftp it to some other place. Can I get a list of user name who accessed certain file? How can I find out who is accessing particular file?? I eliminated a computer player that had a strong religion (Buddhism). My religion was weak, whereas this other one was taking over the continent quickly. Now that I have him overrun, I want, well wanted, to work on converting cities to mine, but I see now that all of the cities period have his religion! I tried making an Inquisitor just to test, but he is ineffectual at removing Buddhism, being that I can only buy him in Buddhist cities. (Because all of my cities are Buddhist and my religion, Shinto, has been wiped out.   Is there no way to recover your religion in such a situation? Existence of the moment generating function and variance How do I split a string by a multi-character delimiter in C#? Ok, I have to admit, I don't really delve too deep into the semantics of the spatial operators list below, I'm more of a user, I write software to drive the SQL most of the time and don't really think about it too much.  However, I have a situation where a spatial operation I'm doing is going dog slow, on a table that has great indexes on and has never caused a problem before now.  As a result, I'm trying to figure out which of the following is my best bet to use, that will give me the best performance, however, sometimes I find my searches don't return anything when I know they should, and sometimes return stuff when they shouldn't.  SO I'm reaching out, to ask if some one can give me the actual definition, such as criteria to match, fully within enclosing geometry, or within outer ring etc etc of each of the following operations:  Equals(Geom1, Geom2):int Disjoint(Geom1, Geom2):int Touches(Geom1, Geom2):int Within(Geom1, Geom2):int Overlaps(Geom1, Geom2):int Crosses(Geom1, Geom2):int Intersects(Geom1, Geom2):int Contains(Geom1, Geom2):int Relate(Geom1, Geom2):int   If you can give a concrete example of when they will and will not match too, that would be great.  For reference, I'm searching on a table of Linestrings, using a rectangular polygon, rotated to be pointing in the direction of travel (It's part of a traffic managment app)  For further reference, here is a sample of the SQL the app generates to perform a search:  SELECT recordID,AsBinary(geometry) AS geometry,Distance(GeomFromText('POINT(-1.84101 54.85078)',4326), geometry) AS distanceFromGps FROM linegrid WHERE Intersects(GeomFromText('POLYGON ((-1.8413149820810311 54.850782468607292, -1.8409507853094111 54.850952257034713, -1.8408279009723911 54.850864894077496, -1.8411920982612455 54.850695105650068, -1.8413149820810311 54.850782468607292))'), geometry)   You can see in this example I'm using intersects trying the others as mentioned doesn't quite give the results I expect, hence why I'm asking the question.  Please note, I'm not particularly bothered about actual faster/other ways of doing this at the moment, BUT if you do happen to spot a better way do feel free to shout up :-)  For now all I'm mostly trying to understand is the differences between each of the operations.  As for doing it faster/better I intend to open a different question for that at a later date.  For more reference, the Spatial engine this is working against is Spatilite 2.3.0, and I can't upgrade it due to the devices it's running on not having a more up to date build for it (Windows CE)    I'm going to choose mintix'es answer here as that provided a super easy to understand grid and description of all the various operations, which answered my question.  I'm still faced with getting performance on the routines up, but I do now have a few strategies to try on that one, I may still seek advice here from the group with regards to that.  @Vince deserves some credit too, as that white paper is definitely the definitive answer, but it's also quite challenging to read (I had to read through it several times) , for anyone wanting the real I am on these operations The Clementini paper is the way to go, if you need an easy to understand overview while developing solutions however, the FME link should be open in another browser tab. PostgreSQL multi-column unique constraint and NULL values I have a table like the following:  create table my_table (     id   int8 not null,     id_A int8 not null,     id_B int8 not null,     id_C int8 null,     constraint pk_my_table primary key (id),     constraint u_constrainte unique (id_A, id_B, id_C) );   And I want (id_A, id_B, id_C) to be distinct in any situation. So the following two inserts must result in an error:  INSERT INTO my_table VALUES (1, 1, 2, NULL); INSERT INTO my_table VALUES (2, 1, 2, NULL);   But it doesn't behave as expected because according to the documentation, two NULL values are not compared to each other, so both inserts pass without error.  How can I guarantee my unique constraint even if id_C can be NULL in this case? Actually, the real question is: can I guarantee this kind of uniqueness in "pure sql" or do I have to implement it on a higher level (java in my case)? To give you some background, I have a grasp on the basics of statistics and probability theory and even remember touching Bayes theorem at the university data mining course. But being a few years away from the university made my math got extremely rusty (so much for last-minute pre-exam cramming). While I remember various random basic concepts, there are a lot of gaps in my understanding of them.  What would be a good material (a book, a site, or otherwise equally accessible medium) to revise the fundamentals and go beyond basics? I'd like a book that can be actually read as a book (most statistics books are really dry and are close to being reference material, rather than a book). Is there to make the login screen appear on the external display in 18.04? I'm trying to prove that if $A\neq 0$ is a commutative ring and there is an injective $A$-module homomorphism $A^m\hookrightarrow A^n$ then $m\leq n$ must necessarily hold.    This is exercise 2.11 from Atiyah and MacDonald's Introduction to Commutative Algebra, but unfortunately all the solutions available online are either very sparse with regard to this question or seem to use (to my surprise) a generalized version of Cramer's rule. Is there perhaps some other "cleaner" approach to solving this problem? Use second argument for optional first argument if not provided in macro I'm trying to construct a command with one optional and one mandatory argument and I'd like the default if the optional argument is not provided to be #2.   Why does this not work?  (error: Illegal parameter number ...)  \documentclass{article}  \newcommand{\mycommand}[2][#2]{\label{#1}#2} \begin{document} \mycommand{mytext} \end{document}   And what would be a way around it?   EDIT: For clarification of my specific use case: I'm trying to define a command that passes a variable on as an option to an environment along those lines, where myenv can have options like optionone=X or optiontwo=Y so the default for the optional #1 should be optionone=#2 (not literally #2).   \newcommand{\mycommand}[2][optionone=#2]{\begin{myenv}[#1]\input{#2}\end{myenv}}   Maybe there's generally a better approach?   (The environment definition I'm using is from .) When should titles like "captain" or "admiral" be capitalized? Please excuse the contrived example below, but I am wondering if this example is properly capitalised? I'm assuming that capitals are used when addressing someone directly, but lower case is used elsewhere. Can someone give some rules on this?      The captain walked into the room.    "Hi, Captain," said the admiral.   "Hi, Sir," replied the captain.   "Call me Admiral."   "Hi Admiral."   The captain and admiral stepped forward.   "Prime Minister, this is Captain Jones," said Admiral Brown.   "Pleased to meet you," said the prime minister. Android/Java - Date Difference in days Subadditive sequences and the limit $\sup_{n\to\infty} a_n / n$ Let $\{ a_n, n\geq 1\}$ be a sub-additive sequence, i.e. for any $m,p\geq 1$ $$ a_{m+p} \leq a_m + a_p. $$ .Prove that $$\lim_{n\to\infty} \frac{a_n}{n} = \inf_n \frac{a_n}{n}.$$ I guess the first step is to state $$a_{n} = a_{mp+q} \leq a_{mp} + a_q$$ but I'm not sure where to go from here.... C# Settings.Default.Save() not saving? Google Apps Script Javascript compatibility error I have successfully created . Handy to avoid multiple calls to GAS services whit ordinary getRange calls.  While the code perfectly works in javascript, it throws an error in Google Apps Script upon saving.  The offending code is:  return matrix.slice(startRow, endRow + 1).map(i =&gt; i.slice(startCol, endCol + 1))   GAS seems rejecting code in the .map function. Moderators accepting answers on user's behalf after a certain time period I have a question regarding selections in ArcGIS for Desktop. Assumed I have one layer in ArcMap and I have selected two of five features.   Is it possible to get a list of all selected features by using Python?   It would be fine if there is a way to get one special (or all) attribute(s) of the selected features stored in a list that can be written into a txt file.  Is it possible to do this in ArcGIS for Desktop?