+- HP Forums (https://archived.hpcalc.org/museumforum) +-- Forum: HP Museum Forums (https://archived.hpcalc.org/museumforum/forum-1.html) +--- Forum: Old HP Forum Archives (https://archived.hpcalc.org/museumforum/forum-2.html) +--- Thread: Quadratic fit without linear algebra (32SII) - NOT only for statistics lovers - LONG (/thread-59242.html) Quadratic fit without linear algebra (32SII) - NOT only for statistics lovers - LONG - Tizedes Csaba [Hungary] - 06-25-2004 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. ```############################################ # # # What do you think about this method??? # # # ############################################ 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 RCL-U INPUT Y STO+J RCL-V / 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 coefficient-calculator routine: XEQ C ===================================================== 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 -2.133E-3 -2.139E-3 B +6.956E-2 +7.017E-2 C +9.000E+1 +9.000E+1 ``` Enjoy! :D Csaba Edited: 28 June 2004, 3:26 a.m.