Matlab fitting image is inconsistent with the parametric equation

I used the Curve Fitting Toolbox to make a polynomial (degree 3) . But Matlab fitting image is inconsistent with the parametric equation.

My data

year=[1750 1800 1850 1900 1950 1990 2000 2009];

population(millions)=[791 980 1260 1650 2520 5270 6060 6800];

cftool(year,population);

I want to forecast population in 1987.

then I made image by Curve Fitting Toolbox.

if I find the point by image

the population is 4458

But if I used the results from the Curve Fitting Toolbox

f(x) = p1*x^3 + p2*x^2 + p3*x + p4

p1 = 0.001021

p2 = -5.604

p3 = 1.026e+04

p4 = -6.254e+06

when x=1980, f(x)=16281

as you can see 16281 is much bigger than 4458

I want to know why and how can I change it

THANK YOU!!!!!!!!!

Answer 1

[Star Strider]

Try this —

year=[1750 1800 1850 1900 1950 1990 2000 2009];
% population(millions)=[791 980 1260 1650 2520 5270 6060 6800];
population = [791 980 1260 1650 2520 5270 6060 6800]*1E+6;
f = fit(year(:), population(:), 'poly3')

Warning: Equation is badly conditioned. Remove repeated data points or try centering and scaling.

f = 
     Linear model Poly3:
     f(x) = p1*x^3 + p2*x^2 + p3*x + p4
     Coefficients (with 95% confidence bounds):
       p1 =        1021  (491.5, 1550)
       p2 =  -5.604e+06  (-8.589e+06, -2.62e+06)
       p3 =   1.026e+10  (4.651e+09, 1.586e+10)
       p4 =  -6.254e+12  (-9.758e+12, -2.75e+12)

figure
plot(f, year, population, 'p')
grid
hl = legend;
hl.Location = 'best';
text(1980, f(1980), sprintf('1980 Population (Est) = %4.0fx10^6 \\rightarrow', f(1980)*1E-6), 'Horiz','right', 'Vert','middle')

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