I have a dataset with many variables. Some of these variables are linked to each other in various ways, but I don't know in advance those that are.  For example, these are some relationships:   $A=B$ -- obvious and easy to spot/remove; $A=B\cdot\mathrm{constant}$ -- again easy to remove using a correlation matrix; The problem comes with $A = B+C+D+E$ or even $A = B+(0.5\cdot C)+(0.5\cdot D+E).$   The last set are difficult to identify and PCA doesn't provide me with all the clues to identify what A is made up of.   For example, a simple $A = B + C$ will not always show a link. If half of the B values are 0.1 with the other half distributed from 0.5-1.5 randomly and C is a normal distribution with mean 1 no correlation is detected between B and A. However, correlation is often detected in A and C due to the distribution in C still being present in A.  Without knowing in advance these relationships are present how do identify these underlying relationships?  In essence, I am trying to remove these relationships before running PCA and later modelling with remaining uncorrelated variables.
I have a correlation matrix of security returns whose determinant is zero. (This is a bit surprising since the sample correlation matrix and the corresponding covariance matrix should theoretically be positive definite.)  My hypothesis is that at least one security is linearly dependent on other securities. Is there a function in R that sequentially tests each column a matrix for linear dependence?  For example, one approach would be to build up a correlation matrix one security at a time and calculate the determinant at each step. When the determinant = 0 then stop as you have identified the security who is a linear combination of other securities.  Any other techniques to identify linear dependence in such a matrix are appreciated.
Would a compass with unmagnetized needle work? We know that the needle that is used in a compass is a permanently magnetized ferromagnetic material and commonly steel is used.  If we used an unmagnetized iron needle instead, would it still align with Earth's magnetic field lines? If yes, how? Mis-aligned shapefiles in QGIS? Let $M$ be the space of all $m\times n$ matrices. And $C=\{X\in M|rank(X)\leq k\}$ where $k\leq \min\{m,n\}$. How to proof that C is a closed subset of M? Have we completed Diablo 3 in 9 hours? My friend and i decided to play some Diablo 3. We played for almost 9 hours straight and killed Diablo on the hard difficult. We reached level 41.  We think 9 hours is short for a game like Diablo 3.   Have we missed something? Why are we only level 41? Is there more story? Sometimes I have asked a question which got no answers, but is answered in the comments to the question.  How should I handle these questions? I can't accept an answer, so it is never an accepted question.  For example this one:   (ok here the answer in the comments is from me, but nevertheless I also have others of them) Possible to click on an object in the viewport and the object list hierarchy automatically goes to that object also? Does installing and using Wine open up your Linux platform to Windows viruses? Just wondering if installing Wine might open up a fairly solid Linux desktop to the world of Windows viruses.  Any confirmed reports about that?  Would you then install a Windows antivirus product under Wine? How can I fix an out-of-focus blurred photo in Photoshop? How can I fix this picture?  Somebody else took this picture and well he wasn't able to do it very well, and it's blurred.    I have photoshop I  want to download free app in my iPod touch device and i have the following doubts.  Kindly resolve me doubts.   when i try to download it asks my credit card security number. since i am trying to download free app , why do i need to provide my credit card security code? Will i be debited for downloading the free app from app store?   I cant able to find any information regarding this on apple.  Please provide me some references about this from apple and please resolve my doubts.  Thanks a lot. Comment authors are not getting migrated Why does reversing serial upvoting not reverse the Mortarboard badge? user has serial up-voting reversed, but he still have badge Mortarboard.   Is it correct behavior of badges? I suppose it should be reversed too.  And will this 200 daily reputation (2012-03-20) score for the Epic, and Legendary badges? How to work out sqft/m of land coverage? I am currently self teaching myself on qgis whilst volenteering on a project on a river catchment and your help is hugely appreciated!  I need to be able to work out the percentage of land cover or sqft/m coverage. I have all the land uses on as a vector layer over my river catchment.   Many thanks and let me know what other info i need to give as a newbie! Finding the search terms behind 'not provided' How to know what program is listening on a given port? I suspect a program is listening on port 8000 on my machine.  When I run the following command, I get this error:  &gt; python -m SimpleHTTPServer # Lots of python error socket.error: [Errno 98] Address already in use   If I use another port (8000 is the default), the web server runs fine.  If I run wget localhost:8000 from the command line, it returns 404 Not Found.  What can I do (or what tools are available) to find what program is listening on port 8000, and from there where that program is configured? In sampling without replacement the probability of any fixed element in the population to be included in a random sample of size $r$ is $\frac{r}{n}$. In sampling with replacement the corresponding probability is $\left[1- \left(\frac{1}{1-n}\right)^r\right]$.  Please help me show how this is proved. How to take the gradient of the quadratic form? It's stated that the gradient of:  $$\frac{1}{2}x^TAx - b^Tx +c$$  is   $$\frac{1}{2}A^Tx + \frac{1}{2}Ax - b$$  How do you grind out this equation? Or specifically, how do you get from $x^TAx$ to $A^Tx + Ax$? I cannot boot to the desktop because I filled the file system. How do I reclaim some space? My memory is completely full when I tried following the data recovery and copied the wrong file using command line tool Test Disk. As it was taking so long to copy, I turned it off and I realized I copied the wrong file. Now my laptop memory is now full and lead me to more problems.  I have had similar problems to :       Now my screen keeps blinking:   Can anybody help? Many thanks. Wish you all the best. Reading Photoshop PSD Files with Layers (There are a few existing questions on Photoshop alternatives, but none seem to focus on reading PSD files specifically)  Say I'm a programmer working with a web designer and would like to implement a design she's produced as a PSD file using Photoshop. It's a fairly complicated design using overlays/animating layers, so the ability to examine the PSD file and turn individual layers on and off is necessary.   Is there an app available in Ubuntu that can read PSD files created by Photoshop?  Alternatively, is there a more linux-friendly file format that Photoshop can export to and still preserve layers? Can you claim a Double Sacrifice Bonus? Two very closely related questions:  If a card has two different "Sacrifice this creature for X" abilities on it, does sacrificing it give both benefits?  Likewise, if a card requires a creature to be sacrificed, but that creature has a "Sacrifice this creature for X" ability, do you get the sacrifice benefit when you sacrifice it for the other requirement? Equivalent of "both" when referring to three or more items?