I have the two regression lines $6x+y=30$ and $3x+2y=25$. How do I identify which one is which? It is given that the first one is the regression line of x on y. How is that? Any ideas?
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$\begingroup$ Context, please. It is unclear what you're asking. $\endgroup$– DaveMar 1, 2021 at 19:14
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$\begingroup$ @Dave this is simple linear regression $\endgroup$– thedumbkidMar 1, 2021 at 19:25
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$\begingroup$ Okay...so the first one is the regression equation for some data set. What is the other equation? $\endgroup$– DaveMar 1, 2021 at 19:28
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$\begingroup$ @Dave okay so for the same dataset, we can have two regression lines. One which will minimise the squared distances of the points along the x axis and another which will minimise the squared distances of the points along the y axis $\endgroup$– thedumbkidMar 1, 2021 at 19:31
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3$\begingroup$ See stats.stackexchange.com/questions/22718. It implies that when you plot both lines on x,y axes, the one with steeper slope will be for the regression of x as a function of y, so just draw a picture. $\endgroup$– whuber ♦Mar 1, 2021 at 20:43
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Take any one of the lines to be the regression line of $x$ on $y$. Find the regression coefficient of $y$ on $x$ and of $x$ and $y$ from the given lines. Call them $b_{yx}$ and $b_{xy}$ respectively. Then we know that $b_{yx}\cdot b_{xy}=r^2$. If this is less than or equal to $1$, your choice was correct; otherwise not.
answered Mar 1, 2021 at 19:31