My multiple regression analysis model has a statistically significant F value however all beta values are statistically non-significant.   All the regression assumptions are met. No multicollinearity was found. Correlations among all predictors are all less than 0.60.   What else might be the cause of the insignificant predictors?
In a multiple linear regression, why is it possible to have a highly significant F statistic (p&lt;.001) but have very high p-values on all the regressor's t tests?  In my model, there are 10 regressors. One has a p-value of 0.1 and the rest are above 0.9    For dealing with this problem see the .
Generator expressions vs. list comprehensions Should I use 'or' or 'nor' after a negative statement? Does the OS X log notifications from the Notification Center? understanding Debian dpkg package version numbers How to view CD key for a Steam game? I have purchased a game on Steam and can not find out the details of the file or purchase. How does one find their CD Key from a game purchased in Steam? Travelling with two different passports How do I show that $a^p + b^p > (a + b)^p$ for $a,b>0$ and $0<p<1$? A question on my math homework asks us to show that if $0 &lt; p &lt; 1$ and $a, b &gt; 0$, then $a^p + b^p &gt; (a + b)^p$. I have no idea how to do this, any pointers? How can I pad a String in Java? Is there some easy way to pad Strings in Java?  Seems like something that should be in some StringUtil-like API, but I can't find anything that does this. I'm currently working my way through Harvard's online abstract algebra lectures (if you're interested, you can find them ).  The lectures come complete with notes and homework problems.  Of course, since I don't actually go to Harvard, I can't hand in the homework assignments to find out if I'm doing them correctly.  So I've decided to try to crowd source the grading of my solutions.  I'll post individual questions as I finish them and wait for comments.  I would like to get critiques of not just my reasoning but the style of my write ups as well.  Also, any alternative approaches to the problem would be welcome.  I've looked for forums dedicated to these kinds of OCW courses but have not been able to find any.  This surprises me.  It seems like, with the advent of these free online educational resources, an online meeting place for those who take advantage of them would be a natural offshoot.  So this might be a bit of an experiment.  Unless I'm the 873rd person to post something like this here.  If that's the case, sorry for being so long winded.  Anyway, on with the question.  This one is assigned in the 4th lecture.     Let $V$ denote the Klein 4-group.  Show that $\operatorname{Aut}(V)$ is isomorphic to $S_3$.   (I've moved my solution below to keep this question from showing up in the unanswered list.)  Thanks... How to scp in Python? Connecting to sql server database mdf file without installing sql server on client machine? Unable to lock the administration directory (/var/lib/dpkg/) is another process using it? Open Mapping Theorem: counterexample The Open Mapping Theorem says that a linear continuous surjection between Banach spaces is an open mapping. I am writing some lecture notes on the Open Mapping Theorem. I guess it would be nice to have some counterexamples. After all, how can you appreciate it's meaning without a nice counterexample showing how the conclusion could fail and why the conclusion is not obvious at all.  Let $\ell^1 \subset \mathbb{R}^\infty$ be the set of sequences $(a_1, a_2, \dotsc)$, such that $\sum |a_j| &lt; \infty$. If we consider the $\ell^1$ norm $\|\cdot\|_1$ and the supremum norm $\|\cdot\|_s$, then, $(\ell^1, \|\cdot\|_1)$ is complete, while $(\ell^1, \|\cdot\|_s)$ is not complete.  In this case, the identity $$   \begin{array}{rrcl}     \mathrm{id}:&amp; (\ell^1, \|\cdot\|_1)&amp; \to &amp;(\ell^1, \|\cdot\|_s)     \\                 &amp; x &amp; \mapsto &amp; x   \end{array} $$ is a continuous bijection but it is not open.  I want a counterexample in the opposite direction. That is, I want a linear continuous bijection $T: E \to F$ between normed spaces $E$ and $F$ such that $F$ is Banach but $T$ is not open. This is equivalent to finding a vector space $E$ with non-equivalent norms $\|\cdot\|_c$ and $\|\cdot\|_n$, such that $E$ is complete when considered the norm $\|\cdot\|_c$, and such that $$   \|\cdot\|_c   \leq   \|\cdot\|_n. $$ The Open Mapping Theorem implies that $\|\cdot\|_n$ is not complete.  So, is anyone aware of such a counterexample? grep: memory exhausted Evaluating $ \lim_{x \rightarrow 0}\left (\frac{\sin(x)}{x}\right)^\frac{1}{x^2}$ Euler-Lagrange equation in curved spacetime: how to calculate $\partial \mathcal{L}/\partial(\nabla_\nu A_\mu)$? My problem is mostly with notation. When we apply the Euler-Lagrange equation to the Lagrangian scalar $$\mathcal{L}= -\frac{1}{4}F^{\mu\nu}F_{\mu\nu}$$ Where $$F_{\mu\nu} = \partial_\mu A_\nu -\partial_\nu A_\mu= \nabla_\mu A_\nu -\nabla_\nu A_\mu$$ and I start with $$\frac{\partial\mathcal{L}}{\partial A_\mu}=\nabla_\nu\left(\frac{\partial \mathcal{L}}{\partial(\nabla_\nu A_\mu)}\right).$$   Now I rewrite the lagrangian as $\mathcal{L} = -\frac{1}{4}g^{\mu\alpha}g^{ \nu\beta}(\nabla_\mu A_\nu-\nabla_\nu A_\mu)(\nabla_\alpha A_\beta-\nabla_\beta A_\alpha)$ $$\mathcal{L}= -\frac{1}{4}g^{\mu\alpha}g^{\nu\beta}\left[(\nabla_\mu A_\nu)(\nabla_\alpha A_\beta)-(\nabla_\mu A_\nu)(\nabla_\beta A_\alpha)-(\nabla_\nu A_\mu)(\nabla_\alpha A_\beta)+(\nabla_\nu A_\mu)(\nabla_\beta A_\alpha) \right]$$ My problem is calculating $\frac{\partial \mathcal{L}}{\partial(\nabla_\nu A_\mu)}$, how are the rules of partial derivatives generalised to covariant ones? Also, is $\frac{\partial\mathcal{L}}{\partial A_\mu}=0$, is that correct ? Infinitely number of primes in the form $4n+1$ proof Question: Are there infinitely many primes of the form $4n+3$ and $4n+1$?  My attempt: Suppose the contrary that there exist finitely many primes of the form $4n+3$, say $k+1$ of them: $3,p_1,p_2,....,p_k$  Consider $N = 4p_1p_2p_3...p_k+3$, $N$ cannot be a prime of this form. So suppose that $N$=$q_1...q_r$, where $q_i∈P$  Claim: At least one of the $q_i$'s is of the form $4n+3$:  Proof for my claim: $N$ is odd $\Rightarrow q_1,...,q_r$ are odd $\Rightarrow q_i \equiv 1\ (\text{mod }4)$ or $q_i ≡ 3\ (\text{mod }4)$  If all $q_1,...q_r$ are of the form $4n+1$, then $(4n+1)(4m+1)=16nm+4n+4m+1 = 4(\cdots) +1$  Therefore, $N=q_1...q_r = 4m+1$. But $N=4p_1..p_k+3$, i.e. $N≡3\ (\text{mod }4)$, $N$ is congruent to $1\ \text{mod }4$ which is a contradiction.  Therefore, at least one of $q_i \equiv 3\ (\text{mod }4)$. Suppose $q_j\equiv 3\ (\text{mod }4)$  $\Rightarrow$ $q_j=p_i$ for some $1\leq i \leq k$ or $q_j =3$  If $q_j=p_i≠3$ then $q_j$ | $N = 4p_1...p_k + 3 \Rightarrow q_j=3$ Contradiction!  If $q_j=3$ ($\neq p_i$, $1\leq i \leq k$) then $q_j | N = 4 p_1...p_k + 3 \Rightarrow q_j=p_t$ for some $1 \leq i \leq k$ Contradiction!  In fact, there must be also infinitely many primes of the form $4n+1$ (according to my search), but the above method does not work for its proof. I could not understand why it does not work. Could you please show me?  Regards Polar Plot x and y ticks and units So I have Destiny on PS3. If I were to buy the Legendary Edition (Containing House of Wolves and Dark Below Expansion) will I be able to play with my characters from my original Destiny disc? May sound silly, but I need confirmation. Can't login using ssh as root I am trying to virtualize an old linux server, and the PtoV software requires a password login as root via ssh. However, the root login is being prevented with a "Permission Denied" error on the client end, and a "Failed Password for root" on the server end (when sshd is running in debug mode).  I HAVE set PermitRootLogin yes in /etc/ssh/sshd_config.  This is an old RedHat 7.3 server that has had hardening scripts like Bastille run on it years and years ago, and has many remnants of old OS's (like ipchains - no longer supported by the kernel) lying around. All to say I have little idea what has been altered from the original system, but there is a lot.   I can log in fine as root from the console I can su to root fine from within the console or ssh session I can ssh fine as a regular user.   My question is: What else could be preventing my root login on this server?  More information: /etc/pam.d/sshd   auth       required     pam_stack.so service=system-auth  auth       required     pam_nologin.so  account    required     pam_stack.so service=system-auth  password   required     pam_stack.so service=system-auth  session    required     pam_stack.so service=system-auth  session    required     pam_limits.so  session    optional     pam_console.so   /etc/pam.d/system-auth  auth        required      /lib/security/pam_env.so auth        sufficient    /lib/security/pam_unix.so likeauth nullok auth        required      /lib/security/pam_deny.so account     required      /lib/security/pam_unix.so password    required      /lib/security/pam_cracklib.so retry=3 type= password    sufficient    /lib/security/pam_unix.so nullok use_authtok md5 shadow password    required      /lib/security/pam_deny.so session     required      /lib/security/pam_limits.so session     required      /lib/security/pam_unix.so     Can anybody tell me if the hashing algorithm could be the culprit?  Keeping in mind that I can log in as an unprivileged user.