Consider the linear regression model,  $y = \beta_0 + \beta_1x_1 + \beta_2x_2 + u, u \sim N(0, \sigma^2 )$  If we estimate the model twice using OLS on two mutually exclusive groups (say, group 1 and group 2) and then estimate the same model using the pooled sample of group 1 and group 2, should the $\hat{\beta_1}$ from the pooled regression be bounded by the $\hat{\beta_1}$'s we obtain by estimating the model on each group separately?  My intuition tells me no, but any form of proof/evidence is eluding me.  Thanks in advance for any help.
In a multiple regression, the regression coefficient of the two subsamples is opposite to that of the full sample. Both coefficients are significant. The sum of the number of obs in the two subsamples is equal to that of the full sample. Is this normal? What are the possible causes? Thanks.
Interchanging the order of differentiation and summation Where to place 'only' Deleting a comment (mine) shouldn't count as a comment vote Programmatically disable apt unattended upgrades How can I programmatically/script disable apt unattended upgrades? Running Ubuntu 16.04. A Terms of Service update restricting companies that scrape your profile information without your permission How to convert ISO 8601 date (string) to Date? Is it possible to schedule my laptop to mute and unmute at a specific time? I always used to wake up to my favorite radio station on my alarm clock. However, I have moved and can no longer get that radio station over the air. To solve this problem, I would like to stream the station on my laptop, but have it muted overnight, then set it to unmute at a specific time in the morning, so that it will act as an alarm clock. Is there a way to schedule my laptop (Windows 7 64-bit) to unmute at a specific time? I have used the code shown below to draw a static CMOS inverter. I have tried to use the TikZ library calc to calculate the point at which drains of the PMOS and the NMOS devices meet; and the mid-point of the line which connects the gates of the two devices. Apparently calc gets the y coordinates of the points right. However, calc seems to get the x coordinates of the points wrong. What could I be doing wrong?  Here is the TikZ code:  \documentclass{standalone} \usepackage[americaninductors]{circuitikz} \usetikzlibrary{calc} \begin{document} \begin{circuitikz} \draw % Draw MOSFETs: (0,0) node [pigfete,yscale=-1,anchor=S] (M1) {} (M1.D) node[nigfete,anchor=D] (M2) {} (M1.G)--(M2.G) % The line connecting the gates of the MOSFETs. ; % Draw the power rails: \draw ($(M1.S)-(2.0,0)$) -- (M1.S) -- ($(M1.S)+(1.2,0)$); \draw ($(M2.S)-(2.0,0)$) -- (M2.S) -- ($(M2.S)+(1.2,0)$); % Input and output nodes: \node (I) at ($0.5*(M2.G)+0.5*(M1.G)$) {}; % The mid-point between the gates. \node (O) at (M1.D) {}; % The point at which the drains of the MOSFETs are conneted. % The Input and output lines. \draw ($(I)-(.8,0)$) -- (I); \draw (O) -- ($(O)+(0.8,0)$); \end{circuitikz} \end{document}   Here is the figure that I get: Note that that input and the output lines are not connected to the rest of the circuit. Can we attribute the problem of the lines not being connected, to the rest of the circuit, to the way I am using calc? algebra - matrices and polynoms $T:\mathbb P_2[x]↦\mathbb P_2[x]$ s.t.:   $T(1)=3+2x+4x^2$, $T(x)=2+2x^2$, $T(x^2)=4+2x+3x^2$.   Is there base $B$ of $\mathbb P_2[x]$ that $[T]_B$= \begin{bmatrix}     2 &amp; 0 &amp; 0\\     -1 &amp; 1 &amp; 0\\     5 &amp; 0 &amp; 4\\  \end{bmatrix}  Please help. Thanks. double movement in Scrabble Can you resolve a dispute between myself and my girlfriend? She recently won a game with what I think is a double movement (although there's no mention of this in the rule book).  She put one two letters down to make one word, which also scored linked to another letter. But she then added another letter immediately to the left of the finished word, which then extended the second word. I just don't think you can make a second movement like this in scrabble!    My sister placed down W, D and E, the ones that I circled in red. Is she allowed to do that? I told her it was impossible is it?  Can you resolve this for me please? Contraction mapping in the context of $f(x_n)=x_{n+1}$. I'm interested in convergence of $f(x_n)=x_{n+1}$ and often hear this term referenced.  What does it mean to be a contraction mapping in the context of the sequence of real numbers given by $f(x_n)=x_{n+1}$? And what does it tell us about such sequence?  A search online gives the answer given by Wikipedia, that it is a function $f$ defined on a metric space $(M,d)$ from $M$ to itself with the property that for some real number $k \in [0,1)$,  $$d(f(x),f(y)) \leq k d(x,y)$$  This definition is quite unhelpful because I barely know what a metric space is. I feel like this definition is to generalized, and I'm interested in in the specific case of recursively defined real sequences $f(x_n)=x_{n+1}$ that there should be a more specific answer to my question. How do I suppress the "New release '12.10' available" message? How can i get my community Base URL in apex I am using  Salesforce Community and I have network Id of the community but I don't know how can I get Base URL of my community. Any one know how can I get my community base URL using its id in apex as a internal user.  Is there any other way in which salesforce internal user can get the base URL of all his community in the apex also i don't find any object in which Community Base URL is stored. I checked network sObject but it only store community path prefix not the complete URL so how can i get the base URL for my community? Circular duplicate link allowed How do I install Guest Additions in a VirtualBox VM? I've recently installed Ubuntu on Oracle's Virtualbox.  Now I want to install the guest additions.  I started up my Ubuntu guest OS, clicked "Devices" and chose "Install Guest Additions". Nothing happened, and I don't see the CD icon on my desktop.  How can I make this work? Execute a large SQL script (with GO commands) Using conjugates to find a limit with a cubic root: $\lim_{h\to 0}\frac{\sqrt[3]{h+1}-1}{h}$ I currently have $$\lim_{h\to 0}\frac{\sqrt[3]{h+1}-1}{h}$$  Now, I know that when you have square root instead of a cubic root it's easy. You just multiply by the conjugate and simplify afterwards. If it were a sqrt I know that the limit is 1/2. I know that the result here is 1/3 but I can't seem to get there. I always end up with 1/4 due to getting something like: $$\frac{h+1-1}{h(\sqrt[3]{h+1}+1)(\sqrt[3]{h+1}+1)}$$  After simplifying and evaluating the limit you end up with $$\frac{1}{(\sqrt[3]{0+1}+1)(\sqrt[3]{0+1}+1)}$$  which turns out to be $1/4$.  What am I doing wrong? How is Google Scholar compared to other academic search engines and catalogues such as ScienceDirect, Scopus, and universities' own online catalogues--in terms of the following?   comprehensiveness of search (i.e. can fetch all the ever published relevant titles, whether the user have access to full-texts or not) accuracy and precision of results advanced search features usability  Are there good reasons for (or against) using Google Scholar as the only literature search tool for PhD research? Does the answer of (2) depend on the research discipline? Why are local variables not initialized in Java? Was there any reason why the designers of Java felt that local variables should not be given a default value? Seriously, if instance variables can be given a default value, then why can't we do the same for local variables?  And it also leads to problems as explained in :     Well this rule is most frustrating when trying to close a resource in a finally block. If I instantiate the resource inside a try, but try to close it within the finally, I get this error. If I move the instantiation outside the try, I get another error stating that a it must be within a try.      Very frustrating. Exercise 12 from SEC. 82 of Finite-Dimensional Vector Spaces - 2nd Edition by Paul R. Halmos.  If $A$ and $B$ are linear transformations on a finite-dimensional inner product space, and if $\textbf{0} \le A \leq B$, then $\det A \leq \det B$.  Notation: $0 \le A$ means that $A$ is positive.  If $\det B = 0$, choose $x \in \ker B$, then $0 \le ((B-A)x,x) = (Bx, x) - (Ax, x) = -(Ax, x) \le 0$. Therefore $\ker B \subseteq \ker A$ and $0 = det A \le det B = 0$. How to prove for the case when $B$ is invertible? Intuitively, I feel that since both $A$ and $B$ are positive their proper values are also positive and $B$'s proper values should be greater the $A$'s and same for determinants.