Timeline for Independent variable = Random variable?
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| Nov 15, 2016 at 23:24 | comment | added | l7ll7 | that random variable takes on specific values -i.e. becomes a constant from the mathematical point of view- but I', unsure for the moment and would wish that a pure mathematician who know stats could explain them. Maybe some are on this site ?) | |
| Nov 15, 2016 at 23:23 | comment | added | l7ll7 | (I would even go so far as to say that some mathematician -specifically those that don't have to do much with physics- are rendered incapable of understanding concept in a fuzzy manner: Either they understand them completely in all rigour or not at all) But I'm not going (yet) going to accept your (or the other) answers, because I need to sort this problem out with mathematical precision. (I seem to have the impression, that this confusion arises from the fact the in statistics random variables are sometimes conflated with constants that come from on specific instance of a trial where [...] | |
| Nov 15, 2016 at 23:23 | comment | added | l7ll7 | Ok, that's is good to know what kind of answers I can expect/is the standard at econometrics/statistics departments and I appreciate that feedback very much (I would upvote again, but I can't since I already did). The problem with mathematics is "once you go black you never go back": Yearlong training in mathematical precision will induce a feeling of uneasiness if something is not crystal-clear fleshed out until one achieves claritiy [...] | |
| Nov 15, 2016 at 16:10 | comment | added | Statsanalyst | e.g. the dependent variable in a model for voting trends in UK politics might be the number of votes received by the Conservative candidate in each constituency (Riding to Canadians, District to Americans), and the independent variable might be average house prices (a proxy for wealth/income in the UK). Neither of these is a "random" variable as I understand it, but this would be a perfectly reasonable thing to model. | |
| Nov 15, 2016 at 16:03 | comment | added | Statsanalyst | It sounds as though you have a much greater understanding of maths than me. I'm just giving you the standard university undergraduate econometrics/statistics answer. I wonder if perhaps you might be overthinking it a bit, at least from the perspective of practical analysis. Regarding the quote from that book, my interpretation of that is that the specific x and y to which he is referring are random - but that doesn't mean that any x or any y are random. | |
| Nov 15, 2016 at 14:37 | comment | added | l7ll7 | P.S. I want to add that there is no such thing as a "variable" in mathematics when you look at it as a "standalone" objects (my background is maths). Variables in mathematics are just parts of standalone objects (e.g. arguments of function), but have no standalone meaning. If I would just write "x" in mathematics, it could mean the function $x\mapsto x$, or it could be a specific number, if $x$ was assigned a values previously, but we don't have just $x$. And since log. regression is a mathematical model, I'm interested in the mathematical meaning of $X$. | |
| Nov 15, 2016 at 14:25 | comment | added | l7ll7 | Ok, but what is it, if it is not a random variable ? Just a (therefore deterministic) function ? I'm confused regarding the mathematical nature of the object "$X$". Actually, I found in the meantime a textbook, Probability and Statistics by Papoulis, where on page 149 he says "given two random variables $X$ and $Y$ [...]" and then goes on to explain how to regress $X$ on $Y$. So he seems to understand $X$ as a random variable ? | |
| Nov 15, 2016 at 12:55 | history | answered | Statsanalyst | CC BY-SA 3.0 |