Quadratic fit without linear algebra (32SII)  NOT only for statistics lovers  LONG Message #1 Posted by Tizedes Csaba [Hungary] on 25 June 2004, 7:01 a.m.
Hello,
I want to fit quadratic equation curves to pumps' characteristics, but I dont want to use linear equation solver, and I want to use only my 32SII. And I dont want to store the points' coordinates.
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# What do you think about this method??? #
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Let y=A*x^2+B*x+C, the derivative is:
y'=2*A*x+B == m*x+b, so A=m/2, and B=b.
And if we minimize the sum of calculated and given y's
differece's square, we give C=AVER(y)A*AVER(x^2)B*AVER(x).
AVER() is average function.
Here is the 32SII version:
LBL S #First start
CLSum
INPUT X
STO I
STO U
x^2
STO K
INPUT Y
STO J
STO V
LBL I #Input more points
INPUT X
ENTER
STO+I
x^2
STO+K
Roll Down
RCLU
INPUT Y
STO+J
RCLV
/
1/x #End of numerical differentiation
RCL X
RCL+U
2
/
Sum+
RCL X
STO U
RCL Y
STO V
n
1
+
STO N
VIEW N
GTO I
LBL C #Calculating A, B and C
m
2
/
STO A
VIEW A
b
STO B
VIEW B
RCL J
RCL A
RCL*K

RCL B
RCL*I

RCL/N
STO C
VIEW C
RTN
LBL S: CK=BE1E 15.0
LBL I: CK=D9ED 42.0
LBL C: CK=C868 30.0
Variables:
A, B, C: Coefficients
X, Y: New point coordinates
U, V: Old point coordinates
I: SumX
J: SumY
K: SumX^2
N: Number of datapoints
And statistic registers
Usage:
1., Sort the datapoints in increasing order of X
2., Start program with XEQ S
3., Enter the datapoints (No correction available!)
4., If you entered the last data, and you see N=... screen
start the coefficientcalculator routine: XEQ C
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An example:

MEASURED CALCULATED
Q H H_Excel H_HP32SII Delta%_HP32SII
(flow) (head)
[m3/h] [m] [m] [m] [%]

0 90.0 90.0 90.0 0
30 90.2 90.2 90.2 0.02
60 86.4 86.5 86.5 +0.13
90 79.0 79.0 79.0 0.01
120 67.7 67.6 67.6 0.12
150 52.4 52.4 52.4 0

And the coefficients:
Excel HP32SII
A 2.133E3 2.139E3
B +6.956E2 +7.017E2
C +9.000E+1 +9.000E+1
Enjoy! :D
Csaba
Edited: 28 June 2004, 3:26 a.m.
