To comment on the following update, log in, then open the issue:
http://www.openoffice.org/issues/show_bug.cgi?id=78250
------- Additional comments from [EMAIL PROTECTED] Thu Jun 14 19:09:32 +0000
2007 -------
The 2nd spreadsheet contains the calculations using a stable algorithm. You can
test this algorithm for RSQ() and see how it behaves comparatively to the
default implementation of RSQ().
Basically, the algorithm goes like this:
1.) N*sum(Xi^2) - (sum(Xi))^2 is replaced by:
N * sum(Xi - Xm)^2, where Xm = the MEAN of X
the N will cancel later, so I did NOT multiply with N
2.) N*sum(Xi*Yi) - (sum(Xi))*(sum(Yi)) is equivalent to:
N*sum[(Xi-Xm)*(Yi-Ym)]
3.) dividing the previous 2 quantities and canceling N gives:
b = sum[(Xi-Xm)*(Yi-Ym)]/sum(Xi-Xm)^2
4.) Ycalc-i = a + b * Xi
adding every Ycalc gives:
sum(Yc-i) = sum(a) + b*sum(Xi)
however sum(Yc-i) = sum(Yi) = N*Ym, therefore
N*Ym = N*a + N*b*Xm => canceling N
Ym = a + b * Xm =>
a = Ym - b * Xm
[I actually could mathematically show that *this is indeed TRUE*.]
5.) and final step, calculating R^2
first calculate:
Yfirst = Yi - Ym
Ysecond = Yi - Ycalc, then
Yfirst - Ysecond, and
Yfirst + Ysecond
and finally:
R^2 = (Yf - Ys)*(Yf + Ys)/((Yi - Ym)^2
As you can see, this algorithm works even for the very difficult test case I
provided.
---------------------------------------------------------------------
Please do not reply to this automatically generated notification from
Issue Tracker. Please log onto the website and enter your comments.
http://qa.openoffice.org/issue_handling/project_issues.html#notification
---------------------------------------------------------------------
To unsubscribe, e-mail: [EMAIL PROTECTED]
For additional commands, e-mail: [EMAIL PROTECTED]
---------------------------------------------------------------------
To unsubscribe, e-mail: [EMAIL PROTECTED]
For additional commands, e-mail: [EMAIL PROTECTED]
