library(MASS)


# dB-RMS Energie zum Mittelpunkt
avrms = dcut(vowlax.rms, .5, prop=T)

temp = vowlax.l == "a" & vowlax.spkr=="68"

dat = cbind(dcut(vowlax.fdat[temp,1], .5, prop=T), 
avrms[temp], dur(vowlax[temp,]))

colnames(dat) = c("F1", "RMS", "d")
dat = data.frame(dat)
attach(dat)
par(mfrow=c(1,2))
plot(RMS, F1)
plot(d, F1)


o = lm(F1 ~ RMS+d)
summary(o)
stepAIC(o)

# Normalverteilung pruefen
shapiro.test(resid(o))
# Konstante Varianz?
plot(resid(o))
# Autokorrelation?
acf(resid(o))
plot(o, 4)


##############
pfad = "das Verzeichnis wo queen.txt gespeichert ist"
queen  = read.table(paste(pfad, "queen.txt", sep="/"))
plot(f0, Alter)
r = lm(Alter ~ f0 + I(f0^2))
summary(r)
stepAIC(r)
k = coef(r)
curve(k[1] + k[2]*x + k[3]*x^2, add=T, col="blue", lwd=2)


pfun <- function(k, x=250)
{
k[1] + k[2]*x + k[3]*x^2
}
pfun(k, x=seq(200, to=300, by=10))

# In order to predict f0 from age, then the lm regression
# has to be done the other way round
plot(Alter, f0)
r = lm(f0 ~ Alter + I(Alter^2))
summary(r)
stepAIC(r)
k = coef(r)
curve(k[1] + k[2]*x + k[3]*x^2, add=T, col="blue", lwd=2)
pfun(k, x=100)
[1] 261.7433
# i.e. a parabola may be the wrong model