There is "a general phenomenon known as  (Berkson, 1946), whereby observations on a common consequence of two independent causes render those causes dependent. For example, the outcomes of two independent coins are rendered dependent by the testimony that at least one of them is a tail" ().  $$ y = \beta_0 + \beta_1x_1 + \beta_2x_2 + \epsilon $$  If (a) we make a linear regression model as above in which $x_2$ is a common consequence of independent causes $y$ and $x_1$ and (b) these latter two are rendered dependent by observations on $x_2$:   Is $\hat\beta_1 \ne 0$? Why?  "Yes, because that is what Pearl must mean by "rendered dependent."  Is the true value of $\beta_1 = 0$? Why?  "Yes, because that is what Pearl must mean by "independent causes."    *Or, do we not have enough information?  *Or, is Berkson's paradox not applicable (e.g., to a linear regression model with a continuous $y$)?  Berkson, J. (1946). Limitations of the application of fourfold table analysis to hospital data. Biometrics Bulletin 2, 47–53.
If granted omniscience and we know that $\beta_1$ in a multiple linear regression model is truly 0, what does that mean in words (and math notation)?  The model is: $Y = \beta_0 + \beta_1X_1 + \beta_2X_2 + \epsilon$  Does $\beta_1 = 0$ mean:   Empirically: "If we make infinite, perfect measurements of our data, $\hat\beta_1$ approaches 0 at the limit?" [Math: ??] Formally: "In the true, finite population of our data, $X_1$ has 0 association with $Y$ and their vectors of values are perfectly linearly independent, uncorrelated, and orthogonal?" [Math: ??]   What does $\beta_1 = 0$ mean, precisely?
"Within" and "in" when referring to time I know that both can mean "inside" but what I don't have clear is whether both mean the same when talking about time. For example:   The party is in two days = The party is within two days ??   According to this link  within means a limit that can be exceeded, so I'm wondering too if say "the party is within two days max" is correct or redundant. In the United States we have a saying, "your mileage may vary", which means "your experience may be different".  In English-speaking countries that don't use Imperial miles, is there an equivalent expression? When computing the covariance matrix of a sample, is one then guaranteed to get a symmetric and positive-definite matrix?  Currently my problem has a sample of 4600 observation vectors and 24 dimensions. 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Also, talking more about black holes, as far as I understand the term "temperature", it is defined by the amount of kinetic energy of the particles of a body and from what I have read, there are no particles inside a black hole, I know that you can find the temperature of a black hole by analyzing its Hawking radiation but I cant really understand how the term "temperature" can be applied to a black hole. Does it mean that whatever is that it is inside a black hole has kinetic energy? Have physicist already experienced the death of any regular black hole (by regular I mean space-sized black holes not micro ones created in labs)? Also, where is the Hawking radiation form? Because if it is released by the black hole I bet it must have formed outside the event horizon, but how exactly? Is there a need to set Objects to Nothing I always read that it is recommended to set objects to nothing, once I am done with them. But I normally use them only in functions inside forms.  Isn't the reference lost and memory released when the function scope is left, regardless of setting objects to Nothing?   i.e. is it really necessary to do:  Set db = Nothing Set record_set = Nothing Comaximal ideals in a commutative ring When using the xhtml1-transitional.dtd doctype, collecting a credit card number with the following HTML  &lt;input type="text" id="cardNumber" name="cardNumber" autocomplete='off'/&gt;   will flag a warning on the W3C validator:     there is no attribute "autocomplete".   Is there a W3C / standards way to disable browser auto-complete on sensitive fields in a form? Following an online tutorial that uses an object named "icosahedron" from Add > Mesh > Regular Solids > Archimedean > Icosahedron. This object is not available in my version of Blender (2.74). Presenter asks me to include an add-on named "Add Mesh: Regular Solids", which again is not listed in my User Preferences dialog. What can I do about it? If I said, &quot;I will run, not if it is snowing, if I my shoes are comfortable.&quot; Does the &quot;if my shoes are comfortable&quot; modify the &quot;I will run&quot; clause? I agree the sentence would be clearer with the addition of &quot;and&quot; in place of the comma. However, without the &quot;and&quot; is it still clear that the &quot;if my shoes are comfortable&quot; clause modifies the &quot;I will run&quot; clause? How to use a variable for a key in a JavaScript object literal? How to avoid ArrayIndexOutOfBoundsException or IndexOutOfBoundsException? I am trying to get an Epson WF-2760 scanner that is network-connected working. I'm using Ubuntu 16.04.2 64-bit and the printer works a treat. I have installed the Epson drivers from their site, including the plugins. I have edited /etc/sane.d/dll.conf to enable epson, epson2, and epsonds. I have edited each of the respective .conf files to include the network address of the device (IPV4: 192.168.128.11).   The scanner is not detected in any software that I have tried (including Image Scan and Simple Scan).  Any help is appreciated! How to write conditional equations with one-sided curly brackets I want to write a conditional expression such as the following.    What is the best way to express such conditional expressions in Latex? Wrong user when logging into Data Explorer I think I'm having the same issue as reported in this question:    When I log into SEDE with the same OpenID account I use for SE, a different user comes up ("James Wiseman" on Stack Exchange and "adsense" in Data Explorer).  Is there anything I can do personally to rectify this, or must I rely on the admins? I have an ArrayList&lt;String&gt; that I'd like to return a copy of.  ArrayList has a clone method which has the following signature:  public Object clone()   After I call this method, how do I cast the returned Object back to ArrayList&lt;String&gt;? Way to go from recursion to iteration I've used recursion quite a lot on my many years of programming to solve simple problems, but I'm fully aware that sometimes you need iteration due to memory/speed problems.  So, sometime in the very far past I went to try and find if there existed any "pattern" or text-book way of transforming a common recursion approach to iteration and found nothing. Or at least nothing that I can remember it would help.   Are there general rules? Is there a "pattern"? incoming mail just sits in the drop folder OS X computer name not matching what shows on terminal My computer name in System Preferences &gt; Sharing is set to &quot;archos&quot;, but is showing as &quot;iphone&quot; on Terminal. It just started doing this after I loaded Xcode for doing iPhone development: Last login: Mon Nov  7 14:46:55 on ttys001 iphone:~ travis$   Any ideas what could be causing this?