(35S) Linearized S-Curve (Logistic Curve) Regression

[gerry_in_polo]

HP-35s Program - Linearized S-Curve (Logistic Curve) Regression (Gerardo V. Lozada, M.S., P.E.E., HP-35s, 2018-03-10)

Linearizes the Logistic Function (S-Curve) so that linear regression may be performed on historical data.

S = F/(1+b*e^(-c*T))

Program S accepts and stores into F the projected ultimate value or upper limit of the variable to be forecasted and then the given pairs of historical data in the sequence of S (dependent) and then T (independent, i.e. Time), storing them into statistical pair memory via the Σ+ key.

Program F then displays F, calculates and displays the values of r, r^2, ln(b), b and c using the 35s' built-in linear regression variables and then uses these values to compute S from given values of T. The program listings below have been cleansed of typographical errors noticed by Dieter (thanks) that resulted from my long-hand transcription of the program listing on my 35s (no USB on the 35s to automatically transfer a program). This program has been tested several times on my 35s before I uploaded the listing here.

Historical Data Input Routine
S001 LBL S
S002 CLΣ
S003 INPUT F
S004 INPUT S
S005 RCL F
S006 x<>y
S007 ÷
S008 1
S009 -
S010 LN
S011 INPUT T
S012 Σ+
S013 STOP
S014 GTO S004

Regression and Forecasting Routine
F001 LBL F
F002 VIEW F
F003 r
F004 STO R
F005 VIEW R
F006 x^2
F007 STO R
F008 VIEW R
F009 m
F010 +/-
F011 STO C
F012 VIEW C
F013 b
F014 STO B
F015 VIEW B
F016 e^x
F017 STO B
F018 VIEW B
F019 INPUT T
F020 RCL C
F021 x
F022 +/-
F023 e^x
F024 RCL B
F025 x
F026 1
F027 +
F028 RCL F
F029 x<>y
F030 ÷
F031 STO S
F032 VIEW S
GTO F019