bsp_6_1ff.m

% Beispiel für Kap 6.1 - 6.3
%% Beispiel Zugversuch
n = 10;
[xi, yi] = erzeugeZugversuchDaten(n);
% gerundetes Ergebnis, i.F. verwendet:
xi = [0.0601 0.1437 0.2399 0.3468 0.4407 0.5386 0.6188 0.7471 ...
      0.8235 0.9344]';
yi = [9.68 11.92 28.61 32.42 44.63 51.47 60.91 75.12 79.79 93.80]';

xq = mean(xi);
yq = mean(yi);
B = ((xi - xq)'*(yi - yq))/((xi - xq)'*(xi - xq))
A = yq - B*xq
sYX = sqrt(1/(n-2)*sum((yi - A - B*xi).^2))

%% Varianzen
VA = (sYX^2/n)*sum(xi.^2)/sum((xi - xq).^2);
VB = sYX^2/sum((xi - xq).^2);
sigA = sqrt(VA)
sigB = sqrt(VB)
% relativ
sigrelA = sigA/A
sigrelB = sigB/B

%% Konfidenzintervalle
p = 0.05;
t = tinv(1 - p/2, n - 2)
GAu = A - t*sYX*sqrt(sum(xi.^2)/(n*sum((xi - xq).^2)))
GAo = A + t*sYX*sqrt(sum(xi.^2)/(n*sum((xi - xq).^2)))
GBu = B - t*sYX/sqrt(sum((xi - xq).^2))
GBo = B + t*sYX/sqrt(sum((xi - xq).^2))
chiu = chi2inv(p/2, n-2)
chio = chi2inv(1 - p/2, n-2)
GSu = (n-2)/chio*sYX^2
GSo = (n-2)/chiu*sYX^2
Gsigu = sqrt(GSu)
Gsigo = sqrt(GSo)

%% Test
b0 = 90;
p = 0.01;
c = tinv(1-p, n-2)
T = (B - b0)/sYX*sqrt(sum((xi - xq).^2))
pWert = 1 - tcdf(T, n-2)

%% Bestimmtheitsmaß
yhati = A + B*xi;
SQT = sum((yi - yq).^2)
SQE = sum((yhati - yq).^2)
SQR = sum((yhati - yi).^2)
R2 = SQE/SQT