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Strange results for simple calculations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg109511] Strange results for simple calculations
  • From: koringkriek <astronerma at gmail.com>
  • Date: Mon, 3 May 2010 06:10:03 -0400 (EDT)

Hi All,
I have a data which I fit with the polynomial of 4th order and then I
want to find the mean of the differences between the data and the
model:

(* my data, 21 points *)
data = {{47.5, 0.01484}, {48.5, 0.01603}, {49.5, 0.017195}, {50.5,
0.0240}, {51.5, 0.033409}, {52.5, 0.0467}, {53.5, 0.05748},
{54.5,0.063885}, {55.5, 0.071935}, {56.5, 0.0748}, {57.5, 0.07639},
{58.5, 0.07639}, {59.5, 0.0748}, {60.5, 0.069635}, {61.5, 0.0609},
{62.5, 0.05578}, {63.5, 0.05167}, {64.5, 0.0450}, {65.5, 0.0406},
{66.5, 0.0381}, {67.5, 0.03641}};

(* polynomial fit *)
f = Fit[data, {1, x, x^2, x^3, x^4}, x]

(* differences between the data an model *)
var = Table[data[[i, 2]] - f /. x -> data[[i, 1]], {i, 1,
Length[data]}]

(* calculate mean *)
Mean[var]

My result is: -3.65422*10^-14 which I find "a bit" underestimated.
Same goes wrong if I just want to do Sum[var].
Now compare the two loops where the difference is only in the upper
limit of the sum 20 or 21:

(* loop 1 *)
i = 1;
a = 0;
While[i <= 21,
 a = a + var[[i]];
 i = i + 1;
 ]
a

(* loop 2 *)
i = 1;
a = 0;
While[i <= 20,
 a = a + var[[i]];
 i = i + 1;
 ]
a

First loop returns -7.67386*10^-13 the second 0.00251855. So, is there
something wrong with the last point in my table var? How about I
change the initial value of i and let it count till 21,

(* loop 3 *)
i = 2;
a = 0;
While[i <= 21,
 a = a + var[[i]];
 i = i + 1;
 ]
a

And the result is: -0.000761973! I am completely lost here. Could
someone please explain me what I am doing wrong?

Cheers
Anna




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