# Which one is the regression line of x on y?

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?

– Dave
Mar 1, 2021 at 19:14
• @Dave this is simple linear regression Mar 1, 2021 at 19:25
• Okay...so the first one is the regression equation for some data set. What is the other equation?
– Dave
Mar 1, 2021 at 19:28
• @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 Mar 1, 2021 at 19:31
• 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.
– whuber
Mar 1, 2021 at 20:43

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.