There are a few books out there on how to do multivariate regression, but of course the literature isn't as massive and detailed as univariate regression models.  So why bother with multivariate regression at all? Sure, what you gain from the ability to be able to model the strong correlation structure between the responses, you probably lose from your lack of ability to use the wide class of models and techniques available for univariate regressions, no?  So, my question is, if a multivariate response is highly correlated, is it really the end of the world if we just do separate but proper and highly informative univariate regressions?
I just browsed through this wonderful book: . The irony is, I am still not able to understand the motivation for using multivariate (regression) models instead of separate univariate (regression) models. I went through stats.statexchange posts  and  that explain (a) difference between multiple and multivariate regression and (b) interpretation of multivariate regression results, but I am not able to tweak out the use of multivariate statistical models from all the information I get online about them.   My questions are:   Why do we need multivariate regression? What is the advantage of considering outcomes simultaneously rather than individually, in order to draw inferences. When to use multivariate models and when to use multiple univariate models (for multiple outcomes).  Take an example given in the  with three outcomes: locus of control, self-concept, and motivation. With respect to 1. and 2., can we compare the analysis when we do three univariate multiple regression versus one multivariate multiple regression? How to justify one over another? I haven't come across many scholarly papers that utilize multivariate statistical models. Is this because of the multivariate normality assumption, the complexity of model fitting/interpretation or any other specific reason?
Find all natural numbers $x,y$ such that   $$3^x=2y^2+1$$  solutions are $(1,1)$, $(2,2)$, $(5,11)$. I found that parity of both is same and If $x$ Is odd it is of the form $4k+1$. Why are objects at rest in motion through spacetime at the speed of light? I read that an object at rest has such a stupendous amount of energy, $E=mc^2$ because it's effectively in motion through space-time at the speed of light and it's traveling through the time dimension of space-time at 1 second per second as time goes forward.  What troubles me here, is the fact that it is traveling through space-time at the speed of light. Why is it at the speed of light? While using the mobile site on my Android phone, I saw a comment that I wanted to flag but there was no flag button. After searching, I saw  that says flagging comments is not supported on mobile site.  Could the ability to flag comments be added to the mobile site? Is there a 'rule of thumb' that I can use to estimate depth of field while shooting? I can use a DoF calculator, or crunch the heavy math by hand if I really want to know exactly what my DoF is going to be... but most of the time knowing exactly is actually overkill, and taking the time to pull out a DoF calculator is impractical. I'm wondering if anyone knows of a 'rule of thumb' that is common for quickly figuring out a rough estimate of what my DoF will be when I'm in the field... Disable storage of invisible files "._" on my cfs or smb network storage I need to run a query like:  SELECT p.id, p.name,         (SELECT name            FROM sites s           WHERE s.id = p.site_id) AS site_list   FROM publications p   But I'd like the sub-select to return a comma separated list, instead of a column of data.  Is this even possible, and if so, how? How can I show that "A center of a free group that is non-cyclic is trivial" ? Can US stocks list on one stock exchange but trade on other US stock exchanges? I am trying to understand how the US stock market works. From my understanding, there is one stock exchange where a company is &quot;listed&quot;. This stock exchange listing requires the company to adhere to the regulations of the stock exchange where it is listed. Once a company is &quot;listed&quot;, its shares can start to trade on any stock exchange. For example, once a company lists on NASDAQ, its shares can be traded on NASDAQ, NYSE, Boston Stock Exchange, Philadelphia Stock Exchange, National Stock Exchange, EDGX Exchange, EDGA Exchange, NYSE Arca, etc. Is my understanding correct? Is it true that once a stock is listed on a US stock exchange, the stock can then trade on any US stock exchange? Consider the Level 2 quotes for Microsoft (NASDAQ: MSFT). Microsoft is only listed on NASDAQ, but it also trades on the NYSE and other stock exchanges:  My questions are:  Does this mean that companies only need to be listed on one stock exchange in order for their stock to trade on other stock exchanges?  If so, do companies need to adhere to the &quot;listing requirements&quot; of all the stock exchanges where their stock is traded, even though they are not &quot;listed&quot; on those stock exchanges? Does Microsoft have to follow the listing requirements of the NYSE even though it is not listed there?  If stocks can trade on any US stock exchange regardless of which US stock exchange the stock is listed on, why don't NYSE-listed companies reduce their yearly listing fees by listing on NASDAQ instead? How to select the rows with maximum values in each group with dplyr? How can we recover the Newtonian gravitational potential from the metric of general relativity? The Newtonian description of gravity can be formulated in terms of a potential function $\phi$ whose partial derivatives give the acceleration:  $$\frac{d^2\vec{x}}{dt^2}=\vec{g}=-\vec{\nabla}\phi(x)=\left(\frac{\partial\phi}{\partial x}\hat{x}+\frac{\partial\phi}{\partial y}\hat{y}+\frac{\partial\phi}{\partial z}\hat{z}\right)$$  However, in general relativity, we describe gravity by means of the metric. This description is radically different from the Newtonian one, and I don't see how we can recover the latter from the former. Could someone explain how we can obtain the Newtonian potential from general relativity, starting from the metric $g_{\mu\nu}$? Given a pointed category $X$, is $|N(X)|$ contractible ($N(X)$ is the nerve of $X$)? Or are there counter-examples? Uninstall, Activate, Deactivate a plugin: typical features & how-to I'm making a WordPress plugin. What are typical things I should include in the uninstall feature?  For example, should I delete any tables I created in the install function?  Do I clean up my option entries?  Anything else? Finding a tricky limit I have a homework in real analysis and I'm very confused about it. I would be very thankful, if you could give me any ideas or solutions how to get this task done. The task is as follows:     Find the limit:   $$\lim_{x\to 0} \frac{1}{x} \int_{0}^{x} (1+ \sin(t))^{1/t} dt.$$   A hint that has been given is to use L'Hospital's Rule. Moreover, it must be substantiated why we can use L'Hospital' Rule in this situation. It is also important to mention that $(1 + \sin(t))$ has a removable point of discontinuity at $0$ and therefore the integral can be interpreted as a Riemann integral. 32-bit vs. 64-bit systems What are the differences between 32-bit and 64-bit systems?  If you have used both of them, what kind of sharp differences have you experienced?   Would it be a problem to use 32-bit programs on 64-bit systems in some cases? Start a git commit message with a hashmark (#) Why can't Discovery's Data Core be separated from the ship? Movie with "Where do the tubes go?" I'm trying to find a movie with an underground facility with people wearing white suits. The people have been affected such that they show no curiosity. There is one person that does and asks one of his co-workers where a tube leads to.      At the end there is an uprising where everyone gets to see the surface and sunlight.   What is the name of this movie? derivative of a determinant of matrix Let $A,B\in M_{n\times n}(\mathbb{R})$, prove that $$(\frac{d}{dt}\det(A+tB))_{t=0} = Tr(cof(A)^{T}\cdot B), $$ where $cof(A)$ is the cofactor matrix of $A$. I tried expanding it using row expansion, but it gets messed up. Any help? Can low-gravity planets sustain a breathable atmosphere? If astronauts could deliver a large quantity of breathable air to somewhere with lower gravity, such as Earth's moon, would the air form an atmosphere, or would it float away and disappear? Is there a minimum amount of gravity necessary to trap a breathable atmosphere on a planet? I just replaced a broken light fixture in my closet. (The switch in the light fixture broke when I pulled too hard on the chain.)   When replacing the light fixture I noticed that there is only 30 V AC between the white and black wires. The ground wire is cut back and is not being used. By the way, the wiring in my house is all aluminum.   I know the new light fixture works. I checked it out with my multimeter, and I tried it in a different closet. But the light bulb won't turn on because there is only 30 V. (Even if I disconnect the light fixture completely there is still only 30 V.   It seems to me that it must be a problem with the wiring.  My attic does provide some (difficult) access to the wiring, but I am not sure where to start looking for the problem or what to look for. Can anyone offer some suggestions?