__matlab of logistic curve model based on population forecast model Matlab

Data:

Year	Time Variable t= year-1970	Population y	Year	Time Variable t= year-1970	Population y
1971	1	33815	1986	16	34520
1972	2	33981	1987	17	34507
1973	3	34004	1988	18	34509
1974	4	34165	1989	19	34521
1975	5	34212	1990	20	34513
1976	6	34217	1991	21st	34515
1977	7	34344	1992	22	34517
1978	8	34458	1993	23	34519
1979	9	34498	1994	24	34519
1980	10	34476	1995	25	34521
1981	11	34483	1996	26	34521
1982	12	34488	1997	27	34523
1983	13	34513	1998	28	34525
1984	14	34497	1999	29	34525
1985	15	34511	2000	30	34527

The basic forms of the logistic model are:

Y=1/(A+b*exp (-T))

So make y ' =1/y; X ' =exp (-t) strong curves into linear models

Y ' =a+b*x '

Matlab code to analyze and fit the calculation:

Code one: (intentionally in this way when the data is low, enter data directly into the code)

Clear
CLC
% Read population data (1971-2000)
y=[33815	33981	34004	34165	34212	34327	34344	34458	34498	34476	34483	34488	34513	34497 34511 34520 34507	34509	34521	34513	34515	34517	34519	34519 34521 34521 34523	34525	34525	34527]
% Read time variable data (t= year -1970)
t=[1	2	3	4	5	6	7	8	9 m (	20)
The linearization of
the treatment for t = 1:30, the 
   x (t) =exp (-T);
   Y (t) =1/y (t);
End
%, and output regression coefficient B, that is to calculate the value of a and B in the regression equation y ' =a+bx '
c=zeros (30,1) +1;
The x=[c,x '];% equals 30 equations that solve the values of A and B.
B=INV (X ' *x) *x ' *y '
for i=1:30,
% compute regression fitting value    
    z (i) =b (1,1) +b (2,1) *x (i);
% calculates the deviation
    s (i) =y (i)-sum (y)/30;
% calculation Error    
    W (i) =z (i)-Y (i)
; End
% calculates the deviation squared and S
s=s*s ';
% regression error squared and Q
q=w*w ';
% calculates regression squared and U
u=s-q;
% computed, and output F-test value
f=28*u/q
% to calculate the fitting value of nonlinear regression model for
j=1:30,
    Y (j) =1/(B (1,1) +b (2,1) *exp (-j));
End
% output fitting curve of nonlinear regression model (logisic curve)
plot (t,y, ' r* ')

Fitting Graphics:

Improved code (reads data from Excel when there is more data):

Clear
CLC
y=xlsread (' D:\sun1.xlsx ', 1, ' b1:b30 ');% read Data
y=y ';
T=xlsread (' D:\sun1.xlsx ', 1, ' a1:a30 ');% read Data
t=t ';
For t=1:30,
    x (t) =exp (-T);
    Y (t) =1/y (t);
End
C=zeros (30,1) +1;
X=[c,x '];
B=INV (x ' *x) *x ' *y '%b=inv (x ' *x) *x ' *y '

for i=1:30,
    z (i) =b (1,1) +b (2,1) *x (i);
    S (i) =y (i)-sum (y)/30;
    W (i) =z (i)-Y (i);
End
s=s*s ';
Q=w*w ';
U=s-q;
f=28*u/q
for j=1:30,
    Y (j) =1/(B (1,1) +b (2,1) *exp (-j));
End
Plot (t,y)

Fitting curve Graph:

Output results:

Regression coefficient b and f test value:

B =


1.0E-04 *


0.2902
0.0182




F =


47.8774