# Diese Funktion plottet Polynomregressions zu den Stammzelldaten mit verschiedenem Grad
Plot.degrees = function(data.set, degree, graphicspath){
# Parameter, beta und sigma, bestimmen
nobs = length(data.set)
time=0:(nobs-1)/(nobs-1)
time.2=time^2
time.3=time^3
time.4=time^4
time.5=time^5
time.6=time^6
Y.gls.4 <- gls(data.set ~ time+I(time^2)+I(time^3)+I(time^4), correlation=corAR1())
Y.gls.5 <- gls(data.set ~ time+I(time^2)+I(time^3)+I(time^4)+I(time^5), correlation=corAR1())
Y.gls.6 <- gls(data.set ~ time+I(time^2)+I(time^3)+I(time^4)+I(time^5)+I(time^6), correlation=corAR1())
######################################
# Graphik erzeugen
pdf(graphicspath, width = 10, height = 8)
time=1:144/144
par(mar=c(5.1,5.1,4.1,2.1))
plot(time, data.set, type="l", xlab="relative Zeit", ylab="relatives Wachstum", cex=2, lwd=3,
cex.axis=2, cex.lab=2)
curve(Y.gls.4$coefficients[1]+Y.gls.4$coefficients[2]*x+Y.gls.4$coefficients[3]*x^2+
Y.gls.4$coefficients[4]*x^3+Y.gls.4$coefficients[5]*x^4, add=T, lty="solid", cex=2, lwd=3)
curve(Y.gls.5$coefficients[1]+Y.gls.5$coefficients[2]*x+Y.gls.5$coefficients[3]*x^2+
Y.gls.5$coefficients[4]*x^3+Y.gls.5$coefficients[5]*x^4+Y.gls.5$coefficients[6]*x^5,
add=T, cex=2, lwd=3, lty="dotted")
curve(Y.gls.6$coefficients[1]+Y.gls.6$coefficients[2]*x+Y.gls.6$coefficients[3]*x^2+
Y.gls.6$coefficients[4]*x^3+Y.gls.6$coefficients[5]*x^4+Y.gls.6$coefficients[6]*x^5+
Y.gls.6$coefficients[7]*x^6, add=T,
cex=2, lwd=3, lty="dashed")
legend(x="topleft", legend=c("Grad 4", "Grad 5", "Grad 6"),
col=c("black", "black", "black"),cex=2, lty=c("solid", "dotted", "dashed"), lwd = 3)
dev.off()
}
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