3D Bell
- From: "Herbert Seidenberg" <herbds7-msxls@xxxxxxxxx>
- Date: 29 May 2006 18:59:04 -0700
As discussed in the post
http://tinyurl.com/mk8dn
sci.stat.math, Nov 11, 2001, Gauss fitting,
in addittion to the center, I also need to find the height of the bell.
I created a perfect 3D bell with the equations given by Saha,
with the following parameters
Mx, My =4
Sx, Sy =1.6
Sxy =.99
To simulate sample data, I removed some x,y points and added noise.
The resulting 7 x 7 "array1" looks like this:
1 2 3 4 5 6 7
1 0.721 0.860 0.651 0.314 0.096
2 0.721 1.600 2.255 2.021 0.417 0.096
3 2.255 3.987 2.687 1.151 0.314
4 0.651 2.021 3.987 3.987 2.021 0.651
5 0.314 1.151 2.687 3.987 3.760
6 0.096 1.151 2.021 2.255 1.600 0.721
7 0.096 0.651 0.721 0.385
To find the center, I translated Chris Geyer's formulas into MS Excel:
xm ={1;2;3;4;5;6;7}
ym ={1,2,3,4,5,6,7}
xySum =SUM(array1) = 55.06
xcent =SUMPRODUCT(array1*xm)/xySum =4.00
ycent =SUMPRODUCT(array1*ym)/xySum =4.00
This gives me the correct center of the bell.
How can I find the height of the bell (about 5.00)
using only the data in the array, and a math tool
no more complex than Excel (with Data Analysis)?
.
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