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Nichtlineare Regression

> 
 restart;
> 
 with (Statistics): with (CurveFitting): with (plots):
Seed:= randomize():
Warning, the name changecoords has been redefined

Simulation der Messung einer Größe y in Abhängigkeit von x:

> 
 xWerte:= [seq (n/5, n = 0..20)]:
f:= x -> -x^2 + 4*x + 1;
yWerte:= map (x -> f(x) + (rand(90)() - 45)/70, xWerte):

> 
 ScatterPlot (xWerte, yWerte,
               color = black,
               symbol = cross,
               labels = ["x","y"]);

[Maple Plot]

Finden einer Regressionskurve mit der Methode der kleinsten Quadrate:

> 
 Punkte:= ScatterPlot (xWerte, yWerte,
                         color = black,
                         symbol = cross,
                         labels = ["x","y"]):
y:= LeastSquares (xWerte, yWerte, x, curve = a*x^2 + b*x + c):
y;

> 
 regr(x):= evalf (y, 3);
Regressionskurve:= plot (regr(x), x = 0..4,
                         color = red):
Kurve:= plot (f(x), x = 0..4,
                         color = blue,
                         linestyle = DOT):
display ([Punkte, Kurve, Regressionskurve]);

 [Maple Plot]
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