Multiple repression training error
Multivariate multiple regression validation
I just sent a text to a friend, who didn't understand an acronym I used for a game:      "Ah, I said it in a previous text so thought it was ok to abbreviate   it."   Though, since it was an acronym I had created, could I have used the word 'acronymise/ze' to be more specific?   I'm pretty sure it isn't a (formally used) word, but I wondered, as you often refer to acronyms specifically as acronyms, rather than abbreviations. Can you be more specific with a verb, too?  It sounds too odd to me, so I'm guessing generally no. But I wondered—so perhaps I'm wrong. Or half wrong. What if the universe is rotating as a whole? Suppose in the milliseconds after the big bang the cosmic egg had aquired some large angular momentum. As it expanded, keeping the momentum constant (not external forces) the rate of rotation would have slowed down, but it would never reach zero.  What implications would that have to measurments to distant supernova and CMB radiation? Do we have any experimental data that definitely rules out such as scenario? And to what confidence level?  Edit A  suggests that the universe might indeed be spinning as a whole. Anyone care to poke holes at it?  Edit 2 Even more  places limits on possible rotation. Prove that the function $f(x)=\frac{x}{x^2+1}$ is continuous at $x=-1$. Prove  that the function $\displaystyle f(x)=\frac{x}{x^2+1}$ is continuous at $x=-1$. You should give a proof that is directly based on the  definition of continuity.   I saw many similar questions on this website, but none of them gave me a satisfactory answer. I more or less understand how epsilon-delta proofs work but my problem lies more in the algebraic manipulations probably. So here's my "attempt".  Definition of continuity; for $f:A \to \mathbb{R}$     $$\forall \varepsilon &gt;0 \ \exists\delta&gt;0\ \forall x \forall x_0 \in A:|x-x_0|&lt;\delta \Rightarrow |f(x)-f(x_0)|&lt;\varepsilon$$   So from what I understand, the procedure for epsilon-delta proofs are as follows: 1. Plug the point of interest $x_0$ into $|f(x)-f(x_0)|&lt;\varepsilon$ 2. Write $x$ in terms of $\varepsilon$ 3. Then plug $x$ into $|x-x_0|&lt;\delta$ 4. Find $\delta$ in terms of $\varepsilon$. Done    At step 1, we have $\left|\dfrac{x}{x^2+1}+\dfrac{1}{2}\right|&lt;\varepsilon$. Step 2 is where I'm stuck because of the 2nd degree polynomial in the denominator. First, I did this: $\left|\dfrac{x}{x^2+1}\right|&lt;\left|\dfrac{x}{x^2+1}+\dfrac{1}{2}\right|&lt;\varepsilon$. Then, I wasn't too sure about what to do, I thought about getting rid of the "$1$", but that would screw up my inequality. I thought about factoring $x^2+1$, but it doesn't have any real roots. I tried inverting the fraction, but that led me to nowhere. And I've already exhausted the tools I have. How do I proceed?  Apparently, epsilon-delta proofs are the most basic building blocks of analysis. And I'm already failing, this is both embarrassing and depressing... Question about Coulomb's law I am just very confsed about how to do these sort of questions where they give you a point in the middle of two charges. The farthest I've gotten in questions relating to coulomb's law, is using the formula \$F = {kq_1q_2 \over d^2}\$ to work out one of the unknowns when given two variables. Can someone please explain how you would do a question like this:  Two point charges of charge -2 µC and -3 µC respectively are separated by a distance of 15 cm. Point X is positioned at an equal distance away from each of the charges.      a. Determine the net electric field at X.     b. Find the point of equilibrium between the charges. The spell was cast without words, simply a flick of the Death Eater's wand, and a 'streak of purple flame' that lanced across her chest. It was later mentioned that the spell was weakened because of the lack of a verbal component, but still 'did enough damage as it was'. She was in the infirmary healing from the damage for some time. What spell was this? the teacher gave me this problem to solve. So i hope you can help me with it. Here is the problem: John poured 150ml ob boiling water in 2 cups made out of polystyrene. Cups are open on the top so heat goes out there. Temperature of the outside air is 20°C. In 1 cup he add 5 mm thick layer of hot oil. He measured starting temperatures and then he measured temperatures again after 10 min. He measured the mass of water and water+oil before and after 10 min.  Here are the resaults:   -cup 1 (only water)  starting temp: 96°C  finnish temp: 64°C  starting mass: 149.4g  finnish mass: 142.42g  -cup 2(with oil on top)  starting temp.: 96°C  finnish temp.:91°C  starting mass: 164.72g  finnish mass: 164.70g  The surface of the both cups is 0.003 m2  Questions: 1.Why did the water covered with oil cooled down slower that the one with no oil? Show with calculations. 2.Why did John use oil with temperature around 100°C and not oil with room temperature? How would the resaults change if he used room temeprature oil? 3. Which other physical values, which are relevant, can you calculate from this informations? Basiccaly i need the physics behing why does this happen. Why does SharePoint always prompt me to download SharePoint Designer when I already have it installed? For example, if I click Edit page -&gt; Edit in SharePoint Designer from within my SharePoint site, I'm always presented with a dialog prompting me to download Designer.  I already have Designer installed.  Seems like it should a.) launch it for me, or b.) at least stop prompting me to  download it.  UPDATE: Turns out this stemmed back to the 64-bit IE compatibility issue that was causing me grief here: If Chrome is already open, it opens new sites (e.g. from Windows shortcuts, application shortcuts, or from the Run dialog) in new tabs of the existing instance.   I'd prefer to open new sites in a separate window (a new instance of Chrome).   I don't see that in the options - is it possible? Work done changes between reference frames? (This is not homework; a friend shared with me this puzzler and neither of us can figure it out.) Suppose you are in a plane traveling at velocity $v_1$ relative to the ground. The flight attendent pushes a cart of mass, say, $m$, accelerating it from rest to $v_2$, relative to the plane (so relative to the ground, its velocity goes from $v_1$ to $v_1+v_2$). From your perspective, the work done is then $$W = \Delta E = \dfrac{1}{2}mv_2^2$$ but from the perspective of the ground, the work done is $$W = \Delta E = \dfrac{1}{2}m(v_1+v_2)^2 - \dfrac{1}{2}mv_1^2 = \dfrac{1}{2}mv_2^2 + mv_1v_2.$$ Why are these quantities unequal?  I've seen some similar problems, like a body colliding with a wall in different reference frames, but I don't have the physics experience to tell if that question is analogous to this one. So, my apologies if this is a duplicate. :) In Texas Hold'em poker, there are some cases where a particular card, often called kicker, acts as a tiebreaker between players to determine who wins the pot, or if the pot has to be shared.  For some combinations such as three or four of a kind, there is no doubt: the kicker is the 5th card of the chosen combination, and determines the winner.  Example     Alice has 7 and 10   Bob has 7 and K   On the board are 7, 7, 2, 3, 4   In that case, both have a three of a kind. But because Bob has a king and Alice only a 10, he wins.  Most of poker websites explaining the rules clearly mention the role of the kicker applying to three of a kind and double pairs. But much fewer say something about colors, straights and full houses, and I found many contradicting answers. I also asked the question to some used online poker players and they also gave me contradicting answers.  I have tried to search for official tournament rules, but most of them only explain what happens with bad behaviors, bad deals, incorrect or confusing betting, showing cards when you shouldn't, acting when it's not your turn, etc. without mentioning subtleties about combinations at all.  To simplify my question, I will take three examples; I think it's better to start with examples before getting to the general answer if one exists. So, what's happening in the following 3 examples? Could you give a more generalized answer?  Example 1 - Flushes     Alice has 2&clubs; and 3&clubs;   Bob has 4&clubs; and 5&clubs;   On the board are 6&clubs;, 8&clubs;, 10&clubs;, 2&hearts;, 5&diams;   Contradicting answer 1: it's a tie, because the highest card included in the flush is the 10, which everybody chooses to include in their 5 showdown cards. Contradicting answer 2: Bob wins, because he has the greatest private card that is part of the flush  Example 2 - Straight     Alice has 6 and K   Bob has 6 and J   On the board are 4, 5, 7, 8, 10   Contradicting answer 1: it's a tie, because the greatest card in the straight is the 8 for both Alice and Bob Contradicting answer 2: Alice wins, because she owns an extra king, compared to the jack of Bob  Example 3 - Full house     Alice has 3 and 7   Bob has 3 and 6   On the board are 3, 3, 2, 2, 5   Contradicting answer 1: it's a tie, because one is supposed to choose only five cards to make a combination, and a full house is already five cards. There couldn't be any kicker, and thus their showdowns are strictly equals. Contradicting answer 2: Alice wins because of her extra 7, compared to the 6 of Bob  Thank you very much for your answers.  Note: I'm unable to post next to you, so I edit my own post; strange not be able to answer to an answer.  Ok, So if I summarize what you are saying :   In the flush case, Bob wins because at some point, their hand differs. Technically, I can continue comparing the highest private card to decide who wins. I had it correct. In the straight case, if the highest card of the straight is public, then it's technically always a tie, no matter what the players had as second private card (asuming that only one of the two cards was part of the straight). In a full house if both players have the same triplet and the same pair, it's always a tie, no matter what the players had as second private card (assuming again that only one of the two was part of the full house).   Please confirm me that what I summarized is correct.  Thank you for your answer. Finite Sets, Equal Cardinality, Injective $\iff$ Surjective. Get names of all keys in the collection I am trying to define the probability distribution of $Z$ such as $Z = X_1\cdot X_2$ where $X_1$ and $X_2$ are two independent and identically exponentially distributed variables.  $$P(X_1=x) = \lambda e^{-\lambda x}$$ $$P(X_2=x) = \lambda e^{-\lambda x}$$  I tried something like that….  $$P(Z=x) = P(X_1 = a) \cdot P(X_2 = x/a)$$  Is this first equation correct?  $$P(Z=x) = \lambda e^{-\lambda a} \cdot \lambda e^{-\lambda x/a} = \lambda^2 e^{-\lambda (a+x/a)}$$  I doesn't feel like I found the solution as the dummy variable $a$ remains in the final result. Can you please help me solving this problem? Proof for SSS Congruence? How to find the frequency and type of my current RAM? How shall I find out the frequency and type of my current RAM? My OS is Ubuntu 12.04. Whenever the Doppler effect is mentioned, it's typically in the context of sound waves or electromagnetic radiation. On the cosmological scale, red-shifting is also important because of the enormous speed of receding galaxies, thanks to the expansion of the universe.   Yet, red-shift is always discussed as the red-shifting of electromagnetic waves. Can gravitational waves be red-shifted? If so, could observations of them be used like red-shifted electromagnetic waves from distant sources are; that is, to figure out how fast an object is receding? I think this story dates from the 1950s, plus or minus a decade - I read it about 30-35 years ago in a (then) fairly old story collection. It involves explorers on a planet falling into a gelatinous object that dissolves most of their bodies except for their brains and nervous systems. About four of them fall in to the same creature, and they discover that by thinking about it they can grow limbs and other body parts. At first they try to fight each other, by growing arms so they can hit each other's brains - and one of them realises that growing a skull would be a good idea - but later they agree to grow legs and move the creature around co-operatively. I would love to identify this story. Alternate proofs (other than diagonalization and topological nested sets) for uncountability of the reals? I recently started studying set theory and am having quite a bit of difficulty accepting Cantor's diagonal proof for the uncountability of the reals. I also saw a topological proof via nested sets for uncountability which still does not satisfy me completely, given that just like the diagonal it relies on a never ending process. In fact, the nested sets proof sounds very much like the diagonalization proof to me.  Do all proofs of the uncountability of the reals involve diagonalization? Are there any other proofs I can look at to understand? I couldn't find any on searching stack exchange. Thanks. Sum of two closed sets in $\mathbb R$ is closed? Is there a counterexample for the claim in the question subject, that a sum of two closed sets in $\mathbb R$ is closed? If not, how can we prove it?  (By sum of sets $X+Y$ I mean the set of all sums $x+y$ where $x$ is in $X$ and $y$ is in $Y$)  Thanks! Is there a way to get a background in CSS to stretch or scale to fill its container?