s = 5493.68334077 t = -2422.15013853 u = 425.883370029
So, to find x when y = 1.5, with a relative error of 1E-8, the function call looks like this:
fipoly(fclist,fglist,1.5,1E-8,"rel") which returns x = 2.6627...
Using the same test cases as in tip [11.5], the table below shows the execution times and errors in x
for various maximum y error limits, for both the relative and absolute error conditions.
1.831.775.84 E-105.84 E-101 E-12
1.451.415.84 E-106.67 E-101 E-11
1.431.386.67 E-106.67 E-101 E-10
1.331.306.67 E-106.67 E-101 E-9
1.321.271.35 E-81.35 E-81 E-8
1.301.233.21 E-72.82 E-61 E-7
1.201.163.19 E-63.19 E-61 E-6
1.151.121.74 E-51.74 E-51 E-5
0.990.956.96 E-46.96 E-41 E-4
0.920.906.56 E-36.56 E-31 E-3
0.710.703.03 E-23.03 E-21 E-2
0.720.703.03 E-23.03 E-21 E-1
"rel" mean
execution time,
sec
"abs" mean
execution time,
sec"rel" max x-error"abs" max x-erroryemax
There is little point to setting the error tolerance to less than 1E-12, since the 89/92+ only use 14
significant digits for floating point numbers and calculations. For this function, we don't gain much by
setting the error limit to less than 1E-9.
Note that this program is much faster than using nsolve(): compare these execution times of about 1.3
seconds, to those of about 4 seconds in tip [11.5].
The code is straightforward. The variable nm is the maximum number of iterations that fipoly() will
execute to try to find a solution. It is set to 30, but this is higher than needed in almost all cases. If
Newton's method can find an answer at all, it can find it very quickly. However, I set nm to 30 so that it
will be more likely to return a solution if a poor estimating function is used.
I use separate loops to handle the relative and absolute error cases, because this runs a little faster
than using a single loop and testing for the type of error each loop pass.
[6.13] Find coefficients of determination for all regression equations
The 89/92+ can fit 10 regression equations, but do not find the coeffcient of determination r
2
for all the
equations. However, r
2
is defined for any regression equation, and these two functions calculate it:
r2coef(lx,ly)
func
©Find coefficient of determination r^2, no adjustment for DOF
©lx is list of x-data points
©ly is list of y-data points
©24 nov 99/dburkett@infinet.com
1-sum((regeq(lx)-ly)^2)/sum((ly-mean(ly))^2)
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