Nichtlineare Regression
> restart;
with(stats): with(statplots): with(fit): with(plots):
Seed:= randomize():
interface(displayprecision = 3):
opts:= 'font = [Courier, 12],
size = [350, 300]':
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):
yWerte:= map(x -> f(x) + (rand(90)() - 45)/70, xWerte):
> scatterplot (xWerte, yWerte, opts,
color = black,
symbol = cross,
labels = ["x", "y"]);
symbol = cross,
labels = ["x", "y"]);
Finden einer Regressionskurve mit der Methode der kleinsten Quadrate:
> Punkte:= scatterplot(xWerte, yWerte,
color = black,
symbol = cross,
labels = ["x", "y"]):
lsq:= leastsquare[[x,y], y = a*x^2 + b*x + c,
{a, b, c}]([xWerte, yWerte]):
y:= rhs(lsq);
symbol = cross,
labels = ["x", "y"]):
lsq:= leastsquare[[x,y], y = a*x^2 + b*x + c,
{a, b, c}]([xWerte, yWerte]):
y:= rhs(lsq);
> regr(x):= evalf(y, 3);
Regressionskurve:= plot(regr(x), x = 0..4,
opts,
color = red):
Kurve:= plot(f(x), x = 0..4,
color = blue,
linestyle = DOT):
display([Punkte, Kurve, Regressionskurve]);
opts,
color = red):
Kurve:= plot(f(x), x = 0..4,
color = blue,
linestyle = DOT):
display([Punkte, Kurve, Regressionskurve]);
