Simple Linear Regression. You regress $Y \sim X$, and You know $\beta_{y,x}$.
Now, if you regress $X \sim Y$, what can you say about $\beta_{x,y}$, what about its range?
$\beta_{x,y} = \beta_{y,x}\frac{s_{x,x}}{s_{y,y}}$.
How can I infer the range?
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1$\begingroup$ What do you mean by "range" in this context? There isn't any fixed range for regression coefficients, it's a function of the units of the data. $\endgroup$– gung - Reinstate MonicaCommented Nov 12, 2020 at 23:08
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$\begingroup$ $\beta_{y,x} = 3.0$, the question is, can you give numerical value about the range of $\beta_{x,y}?$ $\endgroup$– kukuCommented Nov 12, 2020 at 23:22
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1$\begingroup$ Does this answer your question? Effect of switching response and explanatory variable in simple linear regression $\endgroup$– Sextus EmpiricusCommented Nov 12, 2020 at 23:46
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$\begingroup$ Other related stats.stackexchange.com/questions/458928 and stats.stackexchange.com/questions/385812 $\endgroup$– Sextus EmpiricusCommented Nov 12, 2020 at 23:47
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$\begingroup$ @kuku, what do you mean, "the question is"? Is this a question from a course or a textbook? Also, I'm still not sure what you mean by "range" here. Are you asking if there is some maximum (minimum) number that $\hat{\beta}_{x,y}$ can take? $\endgroup$– gung - Reinstate MonicaCommented Nov 13, 2020 at 1:45
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