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re:[apstat] why does the regression line always pass through x bar y bar?
Posted:
Sep 30, 2010 12:05 AM


An excellent question and in a rather confusing lesson I attempted with my students I think we discussed a very reasonable answer.
Imagine you have a bunch of data points that you would represent as ordered pairs: (x1,y1) (x2,y2) so on and so forth. We want to standardize these points and therefore take the zscore of each coordinate and then replot these zscores. (Zx1,Zy1) (Zx2,Zy2) so on and so forth.
Our new plot is now "centered" on the coordinate plane. More importantly (xbar,ybar) is now (0,0), this comes naturally from the definition of a zscore. Z=(xxbar)/s If x=xbar naturally our zscore becomes 0.
Now, I'm an AP Statistics n00b and I would personally stop here and say the leastsquared line of zscores always passes through the origin but that may seem a little like "handwaving" to your students so you can continue.
The equation for a linear model is given by yhat=bnot+b1x
bnot=(ybar)(b1)(xbar) where b1 is the slope. TADA!!! with our standardized scatterplot both xbar and ybar are 0 and therefore the yintercept of our standardized regression line is 0. Therefore, our regression line must pass through (0,0) AKA (xbar,ybar).
Please forgive the notation. bnot = "b subzero"
I really hopes this help a bit. I'm using BVD 3rd and the two equations I use near the end are derived in the text but once again... *shudders* Frequently asked questions (FAQ: http://www.mrderksen.com/faq.htm List Archives from 1994: http://mathforum.org/kb/forum.jspa?forumID=67  To search the list archives for previous posts go to http://lyris.collegeboard.com/read/?forum=apstat To unsubscribe click here: http://lyris.collegeboard.com/read/my_forums/ To change your subscription address or other settings click here: http://lyris.collegeboard.com/read/my_account/edit



