NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Peter Fogg
Date: 2010 Dec 1, 19:29 +1100
- The HP41 Series - and certainly TI ones - as well as (almost) all other HP series have automatic ad IMMEDIATE statistics computation through punching the single function "Sigma+" key, which immediately gives you for a (x,y) pair the "cumulated values of all previous x" , i.e "Sigma x" and the "cumulated value of all previous y", i.e. "Sigma y", as well as a few other items such as (at least) "Sigma xy", "Sigma x**2" and "Sigma y**2", + Number of single data entries (i.e. the "n" number) to the best of my recollection. From these data it is fairly easy to derive both : slope of the best fit linear regression - which you can then very easily compare to the "predicted slope", as well as correlation coefficient which - if close to 1 or -1 - will indicate NO outlier, and if below @ 0.75 in absolute value will indicate one or more outlier(s). In other words, no need to tediously add up "all those figures and divide by the number of observations", it is all automatic : just hit the "Mean" key.
Linear regression is a function of the data points. They could be very good data points, as yours are in the example, and then the slope will approximate the actual slope. Or not, and then the derived slope may not approximate the actual slope at all. In other words, there is a danger that outliers can significantly skew the derived slope provided by linear regression. This has been pointed out by David Burch, together with an example, here:
http://www.starpath.com/resources2/sight_average.pdf
