Mma Fit function

• To: mathgroup at yoda.physics.unc.edu
• Subject: Mma Fit function
• From: herrmann at siam.math.tamu.edu (joe herrmann)
• Date: Fri, 20 Nov 1992 15:36:18 -0600

```Hello Math Group,
Why does the fit function lose accuracy as I go from a polynomial of degree 8 to a
polynomial of degree 9 in the following:

Mathematica 2.0 for NeXT
-- NeXT graphics initialized --

In[1]:= D1={{0, 19.6}, {0.92, 16.87}, {1.84, 15.06}, {2.94, 11.15},

{3.87, 16.31}, {4.97, 12.65}, {5.90, 13.80}, {7.00, 12.95},

{7.92, 14.70}, {10.95, 27.04}, {12.03, 28.63}, {12.95, 27.13},

{13.87, 23.34}, {14.98, 24.11}, {15.90, 22.59},{16.82, 21.35},

{17.93, 21.35}, {19.03, 22.59}, {19.95, 22.10},{23.88, 19.57},
{24.98, 17.18}}

Out[1]= {{0, 19.6}, {0.92, 16.87}, {1.84, 15.06}, {2.94, 11.15},

>    {3.87, 16.31}, {4.97, 12.65}, {5.9, 13.8}, {7., 12.95}, {7.92, 14.7},

>    {10.95, 27.04}, {12.03, 28.63}, {12.95, 27.13}, {13.87, 23.34},

>    {14.98, 24.11}, {15.9, 22.59}, {16.82, 21.35}, {17.93, 21.35},

>    {19.03, 22.59}, {19.95, 22.1}, {23.88, 19.57}, {24.98, 17.18}}

In[2]:= Fit[D1,Table[x^i,{i,0,8}],x]

2            3             4
Out[2]= 19.8808 - 7.54938 x + 4.91733 x  - 1.68623 x  + 0.297257 x  -

5               6                 7             -7  8
>    0.0276971 x  + 0.00138897 x  - 0.0000355021 x  + 3.63124 10   x

In[4]:= Fit[D1,Table[x^i,{i,0,9}],x]

2             3             4
Out[4]= 0.101922 + 0.275108 x + 0.641608 x  + 0.885697 x  - 0.415304 x  +

5              6                7             -6  8
>    0.0721119 x  - 0.0063344 x  + 0.000300326 x  - 7.33029 10   x  +

-8  9
>    7.22822 10   x

Thanks for your help.  I encountered this problem while teaching a mathematics modeling
class.

Joe Herrmann

herrmann at math.tamu.edu

```

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