ai = read.table(file.path(pfad, "ai.txt"))
head(ai)
pairs(ai)
ai.lm = lm(F1 ~ Kiefer + Lippe, data = ai)
summary(ai.lm)

summary(lm(F1 ~ Kiefer, data=ai))
summary(lm(F1 ~ Lippe, data=ai))
# Nicht signifikant

vokala = read.table(file.path(pfad, "vokala.txt"))
head(vokala)
v.lm = lm(F1 ~ Rms + Dauer, data = vokala)
stepAIC(v.lm)
rms.lm = lm(F1 ~ Rms, data = vokala)
summary(rms.lm)
# Prüfen, ob die Regression durchgeführt werden darf
# residuals normalverteilt?
shapiro.test(resid(rms.lm))
# OK
plot(resid(rms.lm))
# OK
acf(resid(rms.lm))
# OK

queen = read.table(file.path(pfad, "queen.txt"))
head(queen)
with(queen, plot(f0, Alter))
#
q.lm = lm(Alter ~ f0 + I(f0^2) + I(f0^3), data=queen)
summary(q.lm)
# Adjusted R-squared: 0.7653
stepAIC(q.lm)
summary(lm(Alter ~ I(f0^2) + I(f0^3), data=queen))
# Adjusted R-squared: 0.7697
summary(lm(Alter ~ f0 + I(f0^2), data=queen))
# Adjusted R-squared: 0.7655

q.lm = lm(Alter ~ I(f0^2) + I(f0^3), data=queen)
k = coef(q.lm)
curve(k[1] + k[2]*x^2 + k[3] * x^3, add=T)


shapiro.test(resid(q.lm))
# OK
plot(resid(q.lm))
# etwas fragwürdig
acf(resid(q.lm))
# fragwürdig

with(queen, plot(f0 ~ Alter))
q.lm = lm(f0 ~ Alter + I(Alter^2) + I(Alter^3), data=queen)
stepAIC(q.lm)
q.lm = lm(f0 ~ I(Alter^2) + I(Alter^3), data=queen)
k = coef(q.lm)
curve(k[1] + k[2]*x^2 + k[3] * x^3, add=T)
with(queen, plot(f0 ~ Alter, xlim = c(20, 150)))
curve(k[1] + k[2]*x^2 + k[3] * x^3, add=T)
predict(q.lm, data.frame(Alter=100))

q.lm = lm(f0 ~ log(Alter), data = queen)
with(queen, plot(f0 ~ Alter, xlim = c(20, 150), ylim=c(100, 300)))
k = coef(q.lm)
curve(k[1] + k[2] * log(x), add=T)
predict(q.lm, data.frame(Alter=100))