I got a formula: $$ s(b_1) = \sqrt{\frac{1}{n-2}·\frac{\sum{(y_i-\hat{y}_i)^2}}{\sum{(x_i-\bar{x})^2}}} $$ , is this correct? and how can I calculate the standard error of the intercept?  I am leanring R, When I execute the command "summary(lrfit)",it will give result as follow. I am interested how these values calculated...  Coefficients:             Estimate Std. Error t value Pr(&gt;|t|)     (Intercept) 2.341231   1.096730   2.135 0.044170 *   X0          1.615907   0.170735   9.464 3.25e-09 *** X1          0.014385   0.003613   3.981 0.000631 ***
For my own understanding, I am interested in manually replicating the calculation of the standard errors of estimated coefficients as, for example, come with the output of the lm() function in R, but haven't been able to pin it down. What is the formula / implementation used?
Can sweetened condensed milk be substituted for whole milk and sugar? I am making a fudge recipe that calls for 1cup whole milk and 5 cups sugar. It also uses 2 sticks of butter and 25 marshmallows. I'm wondering if I can omit the milk and cut back on the sugar by using sweetened condensed milk. Why does blowing on someone who is wet feel colder than on someone who is dry? How to make a domain receiving email behind cloudflare? We've just been learning about complex numbers in class, and I don't really see why they're called numbers.  Originally, a number used to be a means of counting (natural numbers).  Then we extend these numbers to instances of owing other people money for instance (integers).  After that, we consider fractions when we need to split things like 2 pizzas between three people.  We then (skipping the algebraic numbers for the purposes of practicality), we use the real numbers to describe any length; e.g. the length of a diagonal of a unit square.  But this is when our original definition of a number fails to make sense- when we consider complex numbers, which brings me to my main question: what is a rigorous definition of 'number'?  Wikipedia claims that "A number is a mathematical object used to count, label, and measure", but this definition fails to make sense after we extend $\mathbb{R}$.     Does anyone know of any definition of number that can be generalised to complex numbers as well (and even higher order number systems like the quaternions)? Better Information On Defense Damage Clash of Clans The way that Clash of Clans chooses to convey information about how much damage defense buildings output is bad. The current method of telling the user that a mortar does X dmg a second is pretty worthless since they fire much slower than once a second.  Where can I find a break down / what is the damage break down for how much damage these buildings do per shot rather than per second?  Sure, information on each level of the buildings would be nice but if that is too much I think simply providing the data for level one of each building would also work. Why are my PHP sessions dying? And why can't I restore them? I have an app using PHP and the PayPal API. The basic way it works to get a payment is that you do a web service call to PayPal to get a token and then do a browser redirect to PayPal with that token for the user to pay. After the payment details have been confirmed, PayPal redirects back to the URL you originally set in the service call.  This all works, millions of people use it every day, et cetera.  Strange thing is, when PayPal redirects back, the PHP session is gone. It's a .  First question: why is this happening? Both pages are on the same domain, both use HTTPS. The session works for all requests up until the PayPal redirect back.  The linked forum thread suggests a workaround, to persist the session ID in the PayPal request and then to retrieve it later and restore the session. Great, except it doesn't seem to work.  I can add some log statements:  log(session_id());   before and after the various redirects. When coming back from PayPal, I log some more.  log("session id is " . session_id()); $session_id = get_session_id_from_paypal(); log("setting it back to " . $session_id); session_id($session_id); session_start(); log("session id is now " . session_id());   The result is not at all what I'd expect:     session_id is fc8f459a186a3f4695ff9ac71b563825   setting it back to 82460dcf8c8ddd538466e7cb89712e72   session_id is now 360ba3fd99d233e0735397278d2b2e55     Second question: why is the session id not at all what I set it to? What am I doing wrong? Or, at least, why do none of the session variables come back? Mint 18 will boot only to a black screen Multiple vs single field capture for phone number form input Working on a form dealing with phone numbers, I've seen two methods to capture user input .   In past practices example 2 (image below) has proved effective in controlling phone number lengths on forms.   However with responsive in mind it would seem example 1 is considered a more popular pattern on forms. I've researched both patterns with the findings below.     Example 1  Pros   1 input = less taps on mobile device 1 input = less coding   Cons   could be difficult to control phone number format (1-555-555-5555, +22444455555, and etc)   Example 2  Pros   easier to control phone format reduced user error   Cons   3 inputs = more taps on mobile device more inputs = more coding   Both inputs have pros and cons and I'm not such which method would provide the best user experience for responsive environments. Can anyone share some insight or provide a better way to use phone number inputs? Use Listing in newenvironment I am trying to do a new environment or command (i tried both) where i can put in the name, description and code of a Method in c++ and it gives me a new section with the MethodName, the code listed and the description below. But i am not able to use the listings environment in a new command or new environment.. Consider my MWE   \documentclass[a4paper,11pt]{article} \usepackage{listings}  \newcommand{\method}[3] { \section{#1}\label{#1} \begin{lstlisting} #2 \end{lstlisting} #3 }   \begin{document}  \method{MethodName}{Method Void MethodName()}{Description of the Method blablabla}  \end{document}   How can I fix this?   I would prefer to do it using a macro since I don't need an ending. Install java Runtime Environment Create SOAP envelope of XML and send it as HttpWebRequest to WebService Where did dedicated.abac.net. come from in my rDNS and PTR records? So I followed this guide to the letter:   I did so for 3 domains.  When I "test" the records and enter: host 64.150.176.81 on my linux machine, it shows me 81.172.150.64.in-addr.arpa domain name pointer 64-150-172-81.dedicated.abac.net.  when it should be showing me 81.176.150.64.in-addr.arpa domain name pointer 64-150-172-81.example.com.  Has anybody encountered a similar problem?  I am hosting with codero, not abac.net btw. Why this :$\sum\limits_{n=1}^\infty\frac1{n\sin n}$ is not harmonic series and is convergent? I'm confused how this series :$$\displaystyle \sum_{n=1}^\infty\frac1{n\sin n}$$ is a convergent series as wolfram show  and it's not harmonic series in the same time .  My question here is:  Why this :$$\displaystyle \sum_{n=1}^\infty\frac1{n\sin n}$$ is not harmonic series and is convergent ? What is so special about speed of light in vacuum? I need this desperately but can't find it. Am I doing something wrong? I have a large table that is already partitioned by an identifier (CustomerId). I have created new customers, and want to add new partitions to the table, and want to confirm the correct way to do this. My predecessor set this up and is no longer available so I cannot confirm.  There are currently partitions for 60 distinct CustomerIds (let's say 1-60), and a filegroup and file for each. I have created new filegroups and files for the new customers (61-68) and need to partition the existing data already in this table. So, the data that's already in the table, with customerId 61-68 needs to be moved into separate partitions.   I tried to use the partition wizard, but couldn't find an option for what I wanted. As far as I can tell, I need to run something like:  ALTER PARTITION SCHEME PS_Details  NEXT USED Filegroup61 ALTER PARTITION FUNCTION PF_Details ()  SPLIT RANGE (61)   I'm looking for someone to point me in the right direction as to best practice for this sort of thing. Do I take the data out of the table, into a new table stored in the Filegroup61 then switch the partition in? Not really sure how to approach this. What are all the marriages and child relationships following the final chapter? In the last chapter of Naruto, some characters got married, and some of them had kids. What is the entire husband-wife-kids set? UnboundLocalError: local variable 'url_request' referenced before assignment System settings won't open on Ubuntu 20.04 LTS after adding System76/pop PPA "ping: unknown host google.com" but IPs works fine