Talk:Errors and residuals

message: : The text says: "The σ appears in both the numerator and the denominator in those calculations and cancels. That is fortunate because in practice one would not know the value of σ2" -- but it is pretty unclear what calculations are being referred to since in the above equations this is not the case.  --Richard Clegg 18:10, 24 July 2006 (UTC)
replies: text: {\overline{X}_n - \mu \over S_n/\sqrt{n}}. 
The numerator has a normal distribution with standard deviation σ.  The denominator is distributed as σ times a chi-distributed random variable with n − 1 degrees of freedom.  So the standard deviation σ cancels, and the probability distribution of the expression above does not depend on σ. Michael Hardy 21:39, 24 July 2006 (UTC)

text: Here, \overline{X}_n and S_n represent the sample mean and the sample standard deviation for a sample of size n, respectively. --Ziggystar (talk) 13:02, 13 December 2012 (UTC)
thread_title:  Variance cancelling 

message: The formula
{\overline{X}_n - \mu \over S_n/\sqrt{n}}.
introduces two new symbols which are not defined anywhere in the article: \overline{X}_n and S_n.  Can someone please clarify what is meant by these symbols? --Dbmercer (talk) 14:46, 3 February 2010 (UTC)
replies: text: Here, \overline{X}_n and S_n represent the sample mean and the sample standard deviation for a sample of size n, respectively. --Ziggystar (talk) 13:02, 13 December 2012 (UTC)
thread_title:  Explanation of Symbols Used? 

message: I see on the article itself that it is tagged for cleanup, but I don't see any tags here.  Nor, frankly, do I see what needs cleaning (the article looks good to me).  I am new here, what am I missing?Plf515 11:46, 24 November 2006 (UTC)
replies: text: Shouldn't the article begin with sentences defining what the terms mean? At present, it begins with sentences saying that the terms are confused with each other and that one is a misnomer. Tomgally 01:43, 20 January 2007 (UTC)
thread_title: Cleanup?

message: Is the following correct?:
:In mathematics, a residual is the error in a result. If we wish to find x such that f(x)=0, given an approximation, y of x, the residual is 0−f(y) and can be computed. The error is x−y; because x is unknown, the error cannot easily be computed.
As the article stands, it doesn't include residual outside of statistics (such as in approximation). If the above concise definition is correct, I'd like to add it near the top of this article. —Ben FrantzDale 21:31, 30 November 2006 (UTC)
replies: text: It it's outside of statistics, it doesn't belong in an article with this title.  And it doesn't look as if you're talking about the same concept. Michael Hardy 01:15, 21 January 2007 (UTC)
thread_title:  Simple Explanation 

message: I think, section 1 needs to be more precise in explaining what n and N depict. maye 18:58, 8 March 2007 (UTC)
replies: text: Maybe you meant more explicit?  For now, it's just standard notation, known to everyone (except people who are neither statisticians nor probabilists) and no attempt is made to explain it, so such explanations cannot be made more precise. Michael Hardy 23:08, 8 March 2007 (UTC)
thread_title:  More precise 

message: In my opinion, we still don't have a satisfactory answer to this question: how can we justify the concept that the statistical error is in the observation, rather than in the expected value? The explanation in the 2nd paragraph of the introduction does not convince me. I think everybody agrees that an error is something we subtract from the "wrong" value in order to obtain the "correct" value. For instance, I would say that a "fitting error" is the opposite of a residual (see previous section). Residual means "what we add to the predicted value to get the correct value or perfect fit", while "fitting error" means "what we shoud subtract from the predicted value to obtain the perfect fit"). A statistical error is properly an error only if an estimate based on a mathematical model (including linear regression) is supposed to be perfect. But any mathematical model is known to be imperfect, by definition! Why should our terminology imply that an estimate is more correct than the true value?
We do know that some statisticians describe the residual as an error (see references in previous section). Is there a good rationale? Is it just an improper (but standard) use of the word "error" in statistics, conflicting with the meaning of the word in all other contexts, including current language? Is this questionable terminological convention accepted by all statisticians? 
Notice that, even in statistics, "error of the mean" is a proper use of the word "error" (something we subtract from the sample mean in order to get the population mean)... Paolo.dL (talk) 21:00, 27 December 2007 (UTC)
thread_title:  An error is something we subtract to get the correct value 

message: Good article. Thanks to the authors. --landroni (talk) 18:44, 25 March 2009 (UTC)
thread_title:  Quality 

message: In Econometrics I often come accross the terms disturbances or discrepancies. I've created a redirect from Disturbance (statistics) to here, but I am not positively sure whether 'disturbances' point to errors or to residuals. According to a book I have, "disturbances u's are unobservable, so I would assume that it points to errors; it'd be better, however, for someone more informed that I am to do the editing (say, errors (also known as disturbances). --landroni (talk) 17:59, 14 April 2009 (UTC)
thread_title:  Disturbances 

message: I see that someone recently added a "fact" tag.  I think this can probably be found in the writings of Carl Gauss.  I will look for it. Michael Hardy (talk) 19:41, 25 January 2010 (UTC)
thread_title:  "fact" tag 

message: respectfully, the intro is way to complex; ok for later but words like univariate; almost by definition, such a word should not be used in a general encyclopedia  — Preceding unsigned comment added by 68.236.121.54 (talk) 20:50, 21 September 2012 (UTC)
thread_title: way to complex intro