I have a multiple regression equation that reads as follows: ln10(DV) = 0.437 + 0.394(ln10(IV_1)) + 0.061(IV_2) - 0.145(IV_3) I performed the ln10 transformations for the DV and for IV_1 to get around heavy skewness in the original data. The ln10 transformed data is normally distributed. IV_2 is a principal component (which hasn't been transformed) IV_3 is a variable that represents 0 = &quot;disagree&quot; and 1 = &quot;agree&quot; The ln10 transformation helped me to perform the regression but I'm now struggling to interpret what this means in practical terms, all help appreciated! (The model is significant, but has a fairly modest R^2 of .33)
I'm wondering if it makes a difference in interpretation whether only the dependent, both the dependent and independent, or only the independent variables are log transformed.  Consider the case of  log(DV) = Intercept + B1*IV + Error    I can interpret the IV as the percent increase but how does this change when I have   log(DV) = Intercept + B1*log(IV) + Error   or when I have   DV = Intercept + B1*log(IV) + Error   ?
MSO Review Queue Privileges are Misleading Central Moments of Symmetric Distributions I am trying to show that the central moment of a symmetric distribution:     $${\bf f}_x{\bf (a+x)} = {\bf f}_x{\bf(a-x)}$$ is zero for odd numbers. So for instance the third central moment $${\bf E[(X-u)^3] = 0}.$$ I started by trying to show that $${\bf E[(X-u)^3] = E[X^3] -3uE[X^2] + 3u^2E[X] - u^3}.$$ I am not sure where to go from here, any suggestions? Is there a better way to go about proving this? $H_0(X,A) = 0 \iff A \cap X_i \neq \emptyset \forall $ path-components $X_i$ I've been doing some more exercises in , in particular the following:  Show that $H_0(X,A) = 0$ iff $A$ meets each path-component of $X$.  "$\Leftarrow$": Let $x_i \in A \cap X_i \neq \emptyset \forall $ path-components $X_i$. Then for any $x \in X_i$ there is a path $\gamma$ from $x_i$ to $x$. They therefore differ by a boundary: $\partial \gamma = x - x_i$ and therefore $\{&#160;x \} = \{ x_i \}$ in $H_0(X,A) $. Therefore $H_0(X,A) = 0$.  "$\Rightarrow$" Now for this direction I'm not so sure and I'd be glad if you could give me a hint. Let $H_0(X,A) = 0$. By definition, the relative homology group is calculated from the following sequence of chain groups:  $$ 0 \rightarrow C_0(A) \rightarrow C_0(X) \xrightarrow{\partial_1} C_0(X) / C_0(A) \xrightarrow{\partial_0} 0$$  Then $H_0(X, A) = H_0(C_0(X) / C_0(A)) = ker \partial_0 / im \partial_0 = (C_0(X) / C_0(A) ) / im \partial_1 = 0$.  There are two cases where this equality holds:  (i) $C_0(X) / C_0(A) = 0$  (ii) $im \partial_1 = C_0(X) / C_0(A)$  In case (i), $A \cap X_i \neq \emptyset$ for all $X_i$.  In case (ii) I'm not sure how to proceed. Can you give me a hint? Many thanks for your help!  Edit Or maybe I could do the second direction like this:  $$0 = H_0(X,A) = \oplus_i H_0(X_i, A) \implies  H_0(X_i, A) = 0 \forall i$$  $$ \implies A \cap X_i \neq \emptyset \forall i$$? how to read xml file from url using php Behavior of $\sum a_n x^n$ given $\sum |a_n - a_{n-1}| < \infty$ Let $(a_n)_{n=0}^{\infty}$  be a sequence of real numbers satisfying $\sum_{1}^{\infty} |a_n - a_{n-1}| &lt; \infty$   Which of the following conclusions must then be true?  The series $\sum a_nx^n$ converges   Nowhere on $ \mathbb{R}$ Everywhere on $  \mathbb{R}$ On some interval containing $(-1,1)$ Only on $(-1,1)$   What I have tried is Make an inequality with $|a -b| \leq |a| +|b|$ .. but i cant proceed further .. Any sort of help will be deeply appreciable . How to find files that contain one criterion but exclude a different criterion How to disable grub menu at boot time in Ubuntu 20.04? Hidden features of Python In low-cost mass-produced items I often run into black blobs of what looks like resin applied directly on top of something on the PCB. What are these things exactly? I suspect this is some kind of custom IC that is layed out directly on the PCB to save on the plastic  housing/connector pins. Is this correct? If so, what is this technique called?    This is a photograph of the inside of a cheap digital multimeter. The black blob is the only non-basic piece of circuitry present, along with an op-amp (top) and a single bipolar junction transistor. Integral ${\frac{1}{\pi^2}} \int_{0}^{\infty}\frac{{(\ln{x}})^2}{\sqrt{x}{(1-x)^2}} \mathrm d x$ How do you get to the Secret Room in the Tavern? My friend and I noticed that there seems to be an inaccessible room in the Tavern with something behind it. We saw that there was a Treasure Chest seemingly floating somewhere off the map.     In addition, if you walk up to the second floor of the Tavern and position your camera through the wall just right, you can highlight something called the Defender's Forge.   Confirmation of the speculation was confirmed in the notes for the 7.07 patch, which had a note that said the following:     Moved bonus-item crates back into the main section of the Halloween Tavern, out from the Secret Room.   What is this Secret Room? How do I get there? Do I need to beat the campaign first or something else? The Royal Order of Adverbs I know that the pattern manner-place-time shouldn't be taken too seriously if one wants to speak natural English.   In real life, people rarely use a string of adverbs. Speakers will easily break the pattern for emphatic or stylistic reasons (usually placing the adverb at the beginning of the sentence). Other factors such as length and specificity will also override the arrangement.  But I'm constructing illustrative sentences that highlight (and stick to) the Royal Order of Adverbs.   What all the online sources are doing is mixing adverbs and prepositional phrases, but I can't have the concept of prepositional phrases in my examples just yet. This means I should include only one-word or two-word adverbs (without prepositions).   So, I have these:    He sat quietly upstairs all day. She waited impatiently outside this morning. They gather noisily downtown every Saturday night.   Are the sentences above still correct, as in natural-sounding? Somehow they started sounding a bit off to me. I guess I just need to test them with a second pair of ears. Minimum bounty on a question is now 100 rep? Is it possible to take screenshots on the 3DS? In Pokemon X and Y there are specific locations in the game that allows you to save what are essentially 3D screenshots from the upper screen using a virtual camera. This made me wonder - is it possible to take screenshots, 3D or otherwise, from within the 3DS? I have a BA degree in Biochemistry.  I worked at a research lab for 5 yrs before I quit my job to be a stay at home.  Now I want to change my career and get into the field of QA.  I don't have much knowledge as to what the best way is to get into this field.  I cant afford to take online courses, so I want to self teach it to me.  Any suggestions and help would be greatly appreciated. Fold a plane. then fold again Imagine a piece of paper and you fold it in half and then fold it again. that's what I am trying to do and cant. If I use bones the influence of the bones won't allow me to because I need 2 bones to control the same area. If I try shape keys it just deforms the mesh if I try to make it in multiple steps or does the wrong animation because it draws the shortest path instead of rotating from a point like a piece of paper would. While reviewing "First Posts" on Stack Overflow, I often come across new users posting comments as answers. It seems (at least to me) they are not doing this because they are unaware of how Stack Overflow works but because they can't comment on any question they are forced to put it as answer.  I have found duplicate questions for my request like:   ,  and    but the best explanation I have found is an  to .     I think the main reason this isn't supported is there's no way to   downvote comments, which would make them attractive to spammers. If   somebody comments on the top answer in a question the only way to get   rid of it is for six people to flag it. Comment flags don't show up on   10k tools, so it needs to be six people that happen to stumble across   the spam comment, or a moderator that checks the list manually. People   can comment every 15 seconds, so that can get out of hand pretty   quickly. Comments also aren't listed on the user's profile page, so   it's hard to see at a glance if a user has been spamming   So I am suggesting allowing new users (with less than 50 reputation points) to comment only 5 times every day or only 25 times times until they reach 50 reputation points or any other variation of it. What's the typical microclimate in the aircraft passenger cabin? When preparing for a commercial jet flight it'd be nice to know how warm my clothes should be so that I don't freeze after sitting for several hours in say +16 degrees Celsius (61 degrees Fahrenheit).  What's the typical temperature in the passenger cabin? Are there air drafts? How cold and how warm can it reasonably get? How can I run a Minecraft Server on multiple CPU cores? I am working on setting up a Minecraft server on a machine I have at home. This particular machine has two quad-core CPUs running at 2.0Ghz so I would like to take advantage of the number of cores and run a server with 4 or 6 of the cores. My server of choice is CraftBukkit, the latest version of which is craftbukkit-1.4.7-R1.0 and launched with a start-up script of:  "C:\Program Files\Java\jre7\bin\java.exe" -Xms1G -Xmx8G -jar craftbukkit-1.4.7-R1.0.jar"   The  says:     Minecraft servers, as of 1.1.0, can use multiple cores, so now they will not sit idle.   but does not really expand on this.  My questions, then:   Is it possible to set the number of cores the server uses? How do I do it - via start-up options, or other methods? Is it really worth it and would it make that much of a difference with a lot of players? How do I clear command prompts in minecraft?