Working with systems with Perfect Multicollinearity I am working with a time-series dataset that is based on demand-supply dynamics with variables: Production, Ending Stocks, Exports, Imports etc. I was working on a regression with this data and wanted to find the relative importance of regressors using relaimpo package in R. However, I soon realized I can't use regression setting because of near to perfect collinearity in my dataset - the standard errors will be inflated and hence will be the relative importance of each regressor. Is there a way to go around this? Or, can I use any other method (instead of regression)? Any suggestions will be useful.
Working with systems with Perfect Multicollinearity I am working with a time-series dataset that is based on demand-supply dynamics with several variables.  THe sample data for one time period is: &gt; data # A tibble: 19 x 6    Pred_error_A Pred_error_B  Pred_error_C  Pred_error_D  Pred_error_E  Pred_error_Target                  &lt;dbl&gt;         &lt;dbl&gt;          &lt;dbl&gt;      &lt;dbl&gt;      &lt;dbl&gt;           &lt;dbl&gt;  1            -0.45           1.72          -0.170      1.85       -0.01          -0.7    2            -0.45           1.72          -0.170      2.35       -0.01          -1.2    3            -0.45           1.92          -0.170      2.35       -0.01          -1      4            -0.0500         0.37          -0.12       1.65       -0.01          -1.5    5             0             -0.840         -0.12       0.950      -0.01          -1.7    6             0             -0.200         -0.12       1.35       -0.01          -1.5    7             0             -0.460         -0.12       1.35       -0.01          -1.8    8             0             -0.520         -0.12       1.05       -0.01          -1.5    9             0             -0.340         -0.12       1.05       -0.01          -1.4   10             0             -0.340         -0.12       1.35       -0.01          -1.7   11             0             -0.110         -0.12       1.05       -0.01          -1.2   12             0             -0.110         -0.12       0.850      -0.01          -1     13             0              0             -0.12       0.350      -0.01          -0.4   14             0              0             -0.12      -0.15       -0.01           0.100 15             0              0             -0.12      -0.350      -0.01           0.300 16             0              0             -0.02       0          -0.01          -0.1   17             0              0              0          0           0              0     18             0              0              0          0           0              0     19             0              0              0          0           0              0   I was working on a regression for each time period with data and wanted to find the relative importance of regressors in explaining the target variable ( Pred_error_A through E and dependent variable is Pred_error_Target ) using relaimpo package in R. However, I soon realized I can't use regression setting because of near to perfect collinearity and hence no relative importance values. Is there a way to go around this? Or, can I use any other method (instead of regression)? Any suggestions will be useful. The predictors are near to perfect and each one is important. I can't exclude any single one and I need the relative importance of all 5 regressors. I am also trying XGBoost as an alternative. However, I am not sure if it takes care of multicollinearity.
Parallel website running a copy of my original website We have been working on a gaming website. Recently while making note of the major traffic sources, I noticed a website that I found to be a carbon-copy of our website. It uses our logo, and everything else the same as ours, but with a different domain name.   Their domain name is not however pointing to our site because at several places the links are like: carbonccopy-website/our-links. This website even has links to some images as: carbonccopy-website/our-images.   How could they have done that, and what can I do to stop it? How large would the steam explosion at Chernobyl have been? So the  of the HBO series began to cover the  that led to them sending three divers into the water below the reactor to drain the tanks.  This occurred after the initial explosion that destroyed the reactor, and after the fire in the core had been put out. But at this point the decay heat and remaining fission reaction kept the core at more than 1200°C, causing it to melt through the concrete floors below the reactor.  And below the reactor were water tanks which contained 7,000 cubic meters of water (according to the TV show. If anyone has a real figure, I'd love to hear). When the lava of the melted core hit it, it would cause an enormous .  Finally, my question: About how large would this explosion have been? The character in the show says "2-4 megatons" (of TNT equivalent, I assume). I'm pretty sure this is absurd and impossible. But real estimates are hard to come by. Other sources vary wildly, some repeating the "megatons" idea, and others saying it would've "". This still seems crazy.  tl;dr:  I know a lot of it hinges on unknowns and the dynamics of the structures and materials involved, so I can simplify it to a constrained physics question:  Assuming 7,000 cubic meters of water instantly flashes to steam, how much potential energy is momentarily stored in that volume of steam occupying the same volume as the water did?  I don't know what to assume the temperature of the steam is. There were hundreds of tons of core material at temperatures near 1200°C, so worst case scenario you could assume all the steam becomes that temperature as the materials mix. Best case scenario, I guess we could assume normal atmospheric boiling point (100°C)? How do I root my Nexus 7? I am wanting to gain root privileges on my Google Nexus 7 tablet, running Android 4.1-4.2.1. How can I do this? Problem:Let $k$ be an odd positive integer. Prove that $(1+2+3...+n)|(1^k+2^k+3^k+...+n^k)$ for all positive integers $n$.  My Attempt: Proof (By Induction on $k$): Let $P(k)$ be the proposition that $(1+2+3...+n)|(1^k+2^k+3^k+...+n^k)$ for all positive integers $n$ when $k$ is odd. Then $P(1)$ and $P(3)$ are trivially true. So for $k\geq 5$, we assume that $P(k)$ holds. We would like to show that $P(k+2)$ also holds. In order to do that consider the following sums  $$1^{2}(1^k+2^k+3^k+...+n^k)=1^{k+2}+2^k+3^k+...+n^k$$ $$2^{2}(1^k+2^k+3^k+...+n^k)=2^2*1^k+2^{k+2}+2^2*3^k+...+2^2*n^k$$ $$..$$ $$n^2(1^k+2^k+3^k+...+n^k)=n^2*1^k+n^2*2^k+n^2*3^k+...+n^{k+2}$$ Note that $$1^2(1^k+2^k+3^k+...+n^k)+2^2(1^k+2^k+3^k+...+n^k)+...+n^2(1^k+2^k+3^k+...+n^k)\equiv 0\pmod {\frac{n(n+1)}{2}}$$  Therefore, if we denote $\sum_{i=1}^{n}i^2=s$, then    $(t)(1^k+2^k+3^k+...+n^k)-t+\sum_{i=1}^{n}i^{k+2}\equiv 0\pmod {\frac{n(n+1)}{2}}$ which implies that $P(k+2)$ holds. Hence by PMI we are done.  Now I am a bit hesitant in convincing myself whether this proof is correct or not. This is because I have never seen induction performed in this manner. Any reasons as to why this argument falls would be much appreciated. Viber notification is not in the right position Perpendicular Chord parabola If $r_1,r_2$ be the length of the perpendicular chords drawn through the vertex of a parabola $y^2=4ax$, then show that $$(r_1r_2)^{4/3}=16a^2(r_1^{2/3}+r_2^{2/3})$$ Bitlocker won't initialize on a 4TB drive with 4K sectors Is the universe finite or infinite? I thought the universe was finite, but then I read this:    And they seem to assume it is infinite. So which is it? I have a JavaScript object like the following:  var p = {     "p1": "value1",     "p2": "value2",     "p3": "value3" };   Now I want to loop through all p elements (p1, p2, p3...) And get their keys and values. How can I do that?  I can modify the JavaScript object if necessary. My ultimate goal is to loop through some key value pairs and if possible I want to avoid using eval. I want to burn a Windows ISO to a USB device in Ubuntu. How do I do this?   I know how to burn a Ubuntu ISO into a USB device, but with a Windows ISO it's not the same. Why no tag Badges for Good questions Why not make  but for questions too?  I love that everything is well though behind SO but I can't see no reason as to why great questions can't be prized with "Badges by subject". Code   find / -name netcdf   Output  find: `/root/.dbus': Permission denied find: `/root/.gconf': Permission denied find: `/root/.gconfd': Permission denied find: `/root/.gnome': Permission denied find: `/root/.gnome2': Permission denied find: `/root/.gnome2_private': Permission denied How to disable Mac OS X's autocorrect but still show spelling suggestions? I welcome popup spelling suggestions, but I dislike the OS replacing text as I type without any real confirmation from me.   I'm aware both behaviors can be enabled/disabled together as one option in System Prefs &gt; Keyboard &gt; Text, but would anyone know a way to disable the autocorrect while leaving the tooltip-style suggestions intact…perhaps via the Terminal? Thank you.   Mac OS X 9.4 (Mavericks) Java synchronized static methods: lock on object or class The Java documentation says:      It is not possible for two invocations of synchronized methods on the   same object to interleave.   What does this mean for a static method?  Since a static method has no associated object, will the synchronized keyword lock on the class, instead of the object? jQuery get specific option tag text All right, say I have this:  &lt;select id='list'&gt;     &lt;option value='1'&gt;Option A&lt;/option&gt;     &lt;option value='2'&gt;Option B&lt;/option&gt;     &lt;option value='3'&gt;Option C&lt;/option&gt; &lt;/select&gt;   What would the selector look like if I wanted to get "Option B" when I have the value '2'?  Please note that this is not asking how to get the selected text value, but just any one of them, whether selected or not, depending on the value attribute. I tried:  $("#list[value='2']").text();   But it is not working. A commercial airport being any airport that has regular scheduled passenger flights.  The mathematics of  got me thinking: is the network of scheduled flights a connected graph?  That is, is there a pair (or triplet or even larger set) of airports such that they only have scheduled flights with each other?  Or can you get from any airport to any other?  Ignore vagaries like cargo and general aviation. I'm looking for two airports that I can shuttle between, but would have to drive (or sail) to get to one or the other of them. I’m making a little movie with using multiple computers. I can't use the network so I've divided the frames of the animation over the computers. Unfortunately now there are frames missing. What I'd like to do is using 1 machine to render all the missing frames. For example: 4-24-35-64-143 but ideally in such a way that I don't have to re-start blender multiple times. Is this possible somehow? My professor was lecturing today and he made this statement which I was unable to verify.  (I worded it nicer)  There is no map which is both smooth and onto from $S^1$ to $S^1$$\times$ $S^1$.  When he said this he included the original "one can clearly see" statement which is usually when the most people seem to be confused in his class.  Thus, I was hesitant to ask why.  So, please no one lecture me on the fact that I should have asked anyway.  If it is really that obvious, I would rather look stupid here than in class :) Motley fool says you can make $15,978 more per year with Social Security. Is this for real? The Motley fool has an ad campaign that says you can make $15,978 more per year on Social Security by doing 17 minutes of work using a legal loophole.  I don't want to link to their ad (although, you can find it by searching ).  What are they talking about here?  Is there any truth to this?  If someone could explain it to me without me having to watch the entire ad video or subscribe to their newsletter, I'd appreciate it. Why does thermal radiation only occur at infrared and visible frequencies? The resources that I've checked out seem to say thermal radiation only occurs in the infrared and visible spectrum. For example my heat transfer textbook and the Wikipedia page on .  In my mind thermal radiation is just energy emitted as a result of internal collisions from temperature. So, since temperature can range from 0K to huge numbers, I would think you would have a similar range of emitted energies. So then thermal radiation could occur throughout the whole of the electromagnetic spectrum.