Actually, is there a relationship in regression when changing values?

[Soley101]

Hello, I've just started learning about regression. While working on some problems I noticed that one problem set had exactly the x,y values swapped. And as you know when you switch the points that's normally an inverse, but the regression doesn't show that pattern as the regression values are not inverses. I expected them to be the inverses but they are not. How do I explain that..maybe I don't fully understand what regression is.

For instance (I don't have my calc on me but I assure you I know how to do the regression) but I am mean let's say there are 3 coordinates 2,2 3,4 6,6 then the reverse would be 2,2 4,3 6,6. But the regressions are not identical. so is there a pattern or relationship? lol i go crazy at this hour.

 

[statdad]

There is no simple relationship between the coefficients obtained in the two regressions. Look at the formula for slope when you regress $$y$$ on $$x$$. Switching the roles of the two variables gives the formula for the ''slope'' when you regress $$x$$ on $$y$$.