On Wednesday, July 15, 2015 at 6:46:48 AM UTC-7, Centexbel wrote:

Hello,

not a specially Maple question but I have some 20000 (X, Y)
values starting as follow :

172.013964 1.5688
172.013965 1.5600
172.013968 1.5568
172.013969 1.5557
172.013978 1.5541
172.013990 1.5762
172.013994 1.5629
172.014001 1.5719
172.014002 1.5629
172.014004 1.5566
172.014005 1.5606
172.014016 1.5441
172.014026 1.5610
172.014036 1.5672
172.014054 1.5655
172.014054 1.5643
172.014060 1.5629
172.014072 1.5579
172.014073 1.5602
172.014089 1.5590
172.014093 1.5608
172.014106 1.5502
172.014130 1.5593
172.014144 1.5624
172.014148 1.5630
172.014151 1.5581
172.014172 1.5754
172.014181 1.5726
172.014203 1.5589
172.014213 1.5607
172.014231 1.5699
172.014234 1.5574
172.014238 1.5482
172.014250 1.5650
172.014263 1.5594
172.014263 1.5656
172.014288 1.5716
172.014289 1.5618

How can I find an estimated value of Y for any X value ?

Regards,

Philippe Lemaire

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You can do a least-squares fit manually. If, for example, you want a linear fit of the form y = a + b*x, a least-squares fit is obtained from the minimization of S = sum_{i=1..N} (a + b*x[i]-y[i])^2. You can either use the standard, well-known formulas
for the "best" a and b, or you can let Maple set the derivatives diff(S,a) and diff(S,b) to zero, and solve the linear equations using "solve" or "fsolve".

If, instead, you want a quadratic, then minimize S = S(a,b,c) =sum_{i=1..N}(a + b(x[i]+c*x[i]^2)^2.

In general, to fit a function of the form y = f(x,a1,a2,a3,...) involving some unknown parameters a1,a2,a3,..., you want to minimize S(a1,a2,a3,...) = sum_i (f(x[i],a1,a2,a3, ...) - y[i])^2, which you might be able to do by numerical equation-solving,
etc.

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