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How to deal with high correlation among predictors in multiple regression? I found a reference in an article that goes like:     According to Tabachnick &amp; Fidell (1996) the independent variables with   a bivariate correlation more than .70 should not be included in   multiple regression analysis.   Problem: I used in a multiple regression design 3 variables correlated >.80, VIF's at about .2 - .3, Tolerance ~ 4- 5. I cannot exclude any of them (important predictors and outcome). When I regressed the outcome on the 2 predictors which correlated at .80, they remained both significant, each predicted important variances, and these same two variables have   the largest part and semipartial correlation coefficients amongst all 10 variables included (5 controls).   Question: Is my model valid despite high correlations? Any references greatly welcomed!    Thank you for the answers!  I did not use Tabachnick and Fidell as a guideline, I found this reference in an article dealing with high collinearity amongst predictors.   So, basically, I have too few cases for the number of predictors in the model (many categorical, dummy coded control variables- age, tenure, gender, etc) - 13 variables for 72 cases. The Condition Index is ~ 29 with all the controls in and ~23 without them (5 variables).   I cannot drop any variable or use factorial analysis to combine them because theoretically they have sense on their own. It is too late to get more data. Since I am conducting the analysis in SPSS perhaps it would be best to find a syntax for ridge regression (although I haven't done this before and interpreting the results would be new to me).   If it matters, when I conducted stepwise regression, the same 2 highly correlated variables remained the single significant predictors of the outcome.  And I still do not understand if the partial correlations which are high for each of these variables matter as an explanation for why I have kept them in the model (in case ridge regression can't be performed).   Would you say the "Regression diagnostic: identifying influential data and sources of collinearity / David A. Belsley, Edwin Kuh and Roy E. Welsch, 1980" would be helpful in understanding multicollinearity? Or might other references be useful? Postfix SMTP banner show multiple hostnames We have a Postfix SMTP server that's bound to two IP addresses and serves mail for two different domains. We can't change the domains to both use the same, single IP. Both IP addresses have reverse DNS   1.1.1.1 reverses to mail.domain1.com 2.2.2.2 reverses to mail.domain2.com   In our Postfix config I have  myhostname = mail.domain1.com myhostname = mail.domain2.com  inet_interfaces = 1.1.1.1, 2.2.2.2  smtpd_banner = $myhostname Mail Server   (And some other stuff, which I think is irrelevant)  Using , running the smtp test command on mail.domain2.com returns everything as OK, however running it on mail.domain1.com returns an error because Postfix is identifying itself as 'mail.domain2.com' in the SMTP banner, how do I get it to return the correct banner based on the external IP address used? Fuzzy string search library in Java Handling of special LaTeX characters in text How did the DeLorean travel to 1885? At the end of Back to the Future II, a lightning bolt hits the DeLorean which sends it back to 1885.  At the time though, the DeLorean wasn't moving; it was relatively stationary hovering in the storm.  Yet, it's emphasised repeatedly that the DeLorean must reach 88 miles per hour (which becomes a key plot point in Back to the Future III).  So, considering the DeLorean wasn't traveling at 88mph when the lightning struck the DeLorean sending it to 1885, what is the in-universe explanation of how it travelled there?  Some other factors to bear in mind:   If a lightning bolt was sufficient to send the DeLorean time traveling, then the 88mph business would be irrelevant Note that there are the firey tracks left after the DeLorean time travels in the '66' shape.  The thing to note about this though is that we never see these before the DeLorean disappears.  These tracks are always appearing after the DeLorean has traveled away.  This would seem to indicate that the DeLorean did move, but following the activation of the time circuits. Finite choice without AC Can anyone explain how we choose one sock from each of finitely many pairs without the axiom of choice?  I mean : To choose one sock from each of infinitely many pairs of socks requires the Axiom of Choice, but for shoes the Axiom is not needed.  The idea is that the two socks in a pair are identical in appearance, and so we must make an arbitrary choice if we wish to choose one of them. For shoes, we can use an explicit algorithm -- e.g., "always choose the left shoe." Why does Russell's statement mention infinitely many pairs? Well, if we only have finitely many pairs of socks, then AC is not needed -- we can choose one member of each pair using the definition of "nonempty," and we can repeat an operation finitely many times using the rules of formal logic (not discussed here). How to perform a true GIS clip of polygons layer using a polygon layer in R? I would like to do a true GIS Clip in R of soils polygons using a series of single boundary polygons, but I cannot find an R function to properly do it. It should work just like the clip function in ESRI's ArcMap. I've tried the over method in sp package but it doesn't seem to work for polys over polys.   One suggestion was to use the gIntersection in rgeos package as a clip using the following code:  #------------------------------------ library(rgeos) library(maptools)  #Read layers as SpatialPolygonsDataFrame (both the same Albers projection) Soils_poly = readShapePoly("Soils_polygons")  #Note - Has 400 polygons clipper_poly = readShapePoly("clipper_polygon")  #Note - Has 1 polygon  #Try gintersection as clip  Clipped_polys = gIntersection(Clipper_Tile_poly, Soils_poly)  #-----------------------------------   This takes 5 minutes to run (way too slow) and errors with this:     Error in RGEOSBinTopoFunc(spgeom1, spgeom2, byid, id, drop_not_poly, "rgeos_intersection") :      TopologyException: no outgoing dirEdge found at -721459.77681285271 2009506.5980877089   I also tried this code to check for overlap:  gIntersects(Clipper_Tile_poly, Soils_poly)   and the result was TRUE. clip function in ESRI ArcMap works fine for this data.   Anyone knows of an R function to properly do a clip on spatial polygons using spatial polygons? Updating directly from SP1 to SP3 I am considering applying the Service Pack 3 in a SQL Server 2008 with Service Pack 1; however, I was not able to find if there are any drawbacks in this process, specially regarding to Replication Services and Reporting Services.   Has someone done this kind of update? Was it smooth or did it generate many issues? How to set the monitor to its native resolution which is not listed in the resolutions list? After installing Ubuntu 10.04 with my Samsung SyncMaster B2030, native resolution (1600X900) is not found in the list of resolutions. From Drupal 8 beta 6 (released today), I have this error :     Error message UnexpectedValueException: Untrusted Host "localhost" in   Symfony\Component\HttpFoundation\Request->getHost() (line 1221 of   core/vendor/symfony/http-foundation/Symfony/Component/HttpFoundation/Request.php).   I use this local url to call my site:   Inside my setting file, I have:       $settings['trusted_host_patterns'] = array(         'theming\.dev$',      );   Note, this error is displayed only when I uncomment this lines:   if (file_exists(__DIR__ . '/settings.local.php')) {    include __DIR__ . '/settings.local.php';  }   What is the problem please ? Thanks. Non constant analytic function from $\{z\in\mathbb{C}:z\neq 0\}$ to $\{z\in\mathbb{C}:|z|>1\}.$ How to monitor process/program execution in windows? We are trying to develop a small application that can monitor the programs/processes that are executing in a windows machine.  If the program/process is not supposed to run, it should be blocked. It works similar to an antivirus.  This is the basic idea.  I want to know the ways to hook into the OS to get notified about every single program/process trying to run in the machine. How do I install Adobe Acrobat Reader from the repository? How do I install Adobe Acrobat Reader in Ubuntu 14.04 using a Trusty apt repository?  This is NOT a duplicate of . In Synaptic &gt; Repositories &gt; Other software I enabled "Canonical Partners", but I still cannot install acroread as it is not available on my 64-bit system.  Here's the output from the console:   root@liv-inspiron:/home/liv# apt-get install acroread Reading package lists... Done Building dependency tree        Reading state information... Done E: Unable to locate package acroread root@liv-inspiron:/home/liv# apt-get install acroread:i386 Reading package lists... Done Building dependency tree        Reading state information... Done E: Unable to locate package acroread What are the benefits of modeling in one piece, or as separate parts? Is there any benefit of creating model in one piece or I can create separate pieces and just overlap them to create a visually joint part.  For example, the below image were made from two parts 1. Blade 2. Spinner  Is there any benefit to model them (e.g. extrude from the spinner) or it is actually ok to have them separated since visually I can achieve the same effect (See picture 2) Custom command does not reference a label created with a previous custom command Parenthesis vs brackets for matrices When I first learned linear algebra, both the professor and the book used brackets like [ and ] to enclose matrices. However, in my current differential equations textbook, matrices are enclosed by parenthesis, and I suddenly realize everybody else are using them too.  So are brackets/parenthesis for enclosing matrices always totally interchangeable? Is there a shortcut for switching between these three modes? I had originally coded the program wrongly. Instead of returning the Fibonacci numbers between a range (ie. startNumber 1, endNumber 20 should = only those numbers between 1 &amp; 20), I have written for the program to display all Fibonacci numbers between a range (ie. startNumber 1, endNumber 20 displays = First 20 Fibonacci numbers). I thought I had a sure-fire code. I also do not see why this is happening.  startNumber = int(raw_input("Enter the start number here ")) endNumber = int(raw_input("Enter the end number here "))  def fib(n):     if n &lt; 2:         return n     return fib(n-2) + fib(n-1)  print map(fib, range(startNumber, endNumber))   Someone pointed out in my Part II (which was closed for being a duplicate - ) that I need to pass the startNumber and endNumber through a generator using a while loop. Can someone please point me in the direction on how to do this? Any help is welcome.    I'm a learning programmer and I've run into a bit of a jumble. I am asked to write a program that will compute and display Fibonacci's Sequence by a user inputted start number and end number (ie. startNumber = 20 endNumber = 100 and it will display only the numbers between that range). The trick is to use it inclusively (which I do not know how to do in Python? - I'm assuming this means to use an inclusive range?).  What I have so far is no actual coding but rather:   Write Fib sequence formula to infinite Display startNumber to endNumber only from Fib sequence.   I have no idea where to start and I am asking for ideas or insight into how to write this. I also have tried to write the Fib sequence forumla but I get lost on that as well. Can someone point me to a paper, or show here, why symmetric matrices have orthogonal eigenvectors? In particular, I'd like to see proof that for a symmetric matrix $A$ there exists decomposition $A = Q\Lambda Q^{-1} = Q\Lambda Q^{T}$ where $\Lambda$ is diagonal. Question involving the Cauchy-Goursat Theorem Show $\int_C \frac{dz}{(z-z_0)^n} = 2\pi i$ when $n = 1$ and 0 when $n \gt 1$   I'm not entirely sure how to approach this one.  Any help would be much appreciated.