modelos de volume

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rls<- read.table(file="C:/Users/Igor/Documents/metodos estatisticos/rv2131.txt",header=T)
rls
#criando variaveis
d2<- (rls$d)^2
d2
d2h<- (rls$d^2*rls$h)
d2h
dh<- (rls$d*rls$h)
dh
vdd2<- (rls$v/(rls$d^2))
vdd2
vd2<- (rls$v*(rls$d^2))
vd2
invh<- (1/rls$h)
invh
lnv<- log(rls$v)
lnv
lnd<- log(rls$d)
lnd
lnh<- log(rls$h)
lnh
#modelo1
md1<- lm(rls$v~d2+d2h+rls$h)
md1
summary(md1)
erro1<- residuals(md1)
erro1
md1est<- fitted.values(md1)
md1est
ep<- (erro1/rls$v)*100
ep
mdep<- mean(ep)
mdep
#erro do desvio
summary(md1)
r1<-0.9926
r1ajust<-0.9923
syx<- 0.008473
syxporc<- (syx/mean(rls$v))*100
syxporc
#modelo2
md2<- lm(rls$v~rls$d+d2+dh+d2h)
md2
erro2<- residuals(md2)
erro2
md2est<- fitted.values(md2)
md2est
ep2<- (erro2/rls$v)*100
ep2
mdep2<- mean(ep2)
mdep2
#erro padrao
summary(md2)
r2<- 0.9929
r2ajust<-0.9926
syx2<- 0.008341
syx2
syx2porc<- (syx2/mean(rls$v))*100
syx2porc
#modelo3
md3<- lm(vdd2~rls$h)
md3
residuals(md3)
fitted.values(md3)
md3est<- d2*(fitted.values(md3))
md3est
erro3<- (rls$v-md3est)
erro3
ep3<- (erro3/rls$v)*100
ep3
mdep3<- mean(ep3)
mdep3
#erro padrao e coeficiente de determinaçao
n1<- 95-1
c<- (sum(rls$v))^2/95
c
sqtotal<- (sum(rls$v^2))-c
sqtotal
sqres3<- sum(erro3^2)
sqres3
glres3<- 95-2
glres3
syx3<- sqrt(sqres3/glres3)
syx3
syx3porc<- (syx3/mean(rls$v))*100 
syx3porc
r3<- 1-(sqres3/sqtotal)
r3
r3ajust<- 1-((1-r3)*(n1/glres3))
r3ajust
#modelo4
md4<- lm(vd2~invh)
md4
summary(md4)
residuals(md4)
fitted.values(md4)
md4est<- (fitted.values(md4))/d2
md4est
erro4<- (rls$v-md4est)
erro4
ep4<- (erro4/rls$v)*100
ep4
mdep4<- mean(ep4)
mdep4
#erro padrao e coeficiente de determinação
sqres4<- sum(erro4^2)
sqres4
glres4<- 95-2
glres4
syx4<- sqrt(sqres4/glres4)
syx4
syx4porc<-(syx4/mean(rls$v))*100
syx4porc
r4<- 1-(sqres4/sqtotal)
r4
r4ajust<- 1-((1-r4)*(n1/glres4))
r4ajust
#modelo5
md5<- lm(rls$v~d2h)
md5
erro5<- residuals(md5)
erro5
md5est<- fitted.values(md5)
md5est
ep5<- (erro5/rls$v)*100
ep5
mdep5<- mean(ep5)
mdep5
#erro padrao e coeficiente de determinaçao
summary(md5)
r5<- 0.9919
r5ajust<- 0.9918
syx5<- 0.008734
syx5porc<- (syx5/mean(rls$v))*100
syx5porc
#modelo6
md6<- lm(lnv~lnd+lnh)
md6
residuals(md6)
fitted.values(md6)
md6est<- exp(fitted.values(md6))
md6est
erro6<- (rls$v-md6est)
erro6
ep6<- (erro6/rls$v)*100
ep6
mdep6<- mean(ep6)
mdep6
#erro padrao e coeficiente de determinaçao
sqres6<- sum(erro6^2)
sqres6
glres6<- 95-3
glres6
syx6<- sqrt(sqres6/glres6)
syx6
syx6porc<- (syx6/mean(rls$v))*100
syx6porc
r6<- 1-(sqres6/sqtotal)
r6
r6ajust<- 1-((1-r6)*(n1-glres6))
r6ajust
#graficos
#diametro ~ erro %
par(mfrow=c(3,2))
plot(rls$d,ep,xlim=c(0,25),ylim=c(-50,100),main="mod1",xlab="DAP",ylab="erro1 %")
abline(h=0)
plot(rls$d,ep2,xlim=c(0,25),ylim=c(-50,100),main="mod2",xlab="DAP",ylab="erro2 %")
abline(h=0)
plot(rls$d,ep3,xlim=c(0,25),ylim=c(-50,100),main="mod3",xlab="DAP",ylab="erro3 %")
abline(h=0)
plot(rls$d,ep4,xlim=c(0,25),ylim=c(-50,100),main="mod4",xlab="DAP",ylab="erro4 %")
abline(h=0)
plot(rls$d,ep5,xlim=c(0,25),ylim=c(-50,100),main="mod5",xlab="DAP",ylab="erro5 %")
abline(h=0)
plot(rls$d,ep6,xlim=c(0,25),ylim=c(-50,100),main="mod6",xlab="DAP",ylab="erro6 %")
abline(h=0)
# volume estimado ~ erro em metros
par(mfrow=c(3,2))
plot(md1est,erro1,xlim=c(0,1),ylim=c(-1,1),main="mod1",xlab="volume estimado1",ylab="erro1 (m)")
abline(h=0)
plot(md2est,erro2,xlim=c(0,1),ylim=c(-1,1),main="mod2",xlab="volume estimado2",ylab="erro2 (m)")
abline(h=0)
plot(md3est,erro3,xlim=c(0,1),ylim=c(-1,1),main="mod3",xlab="volume estimado3",ylab="erro3 (m)")
abline(h=0)
plot(md4est,erro4,xlim=c(0,1),ylim=c(-1,1),main="mod4",xlab="volume estimado4",ylab="erro4 (m)")
abline(h=0)
plot(md5est,erro5,xlim=c(0,1),ylim=c(-1,1),main="mod5",xlab="volume estimado5",ylab="erro5 (m)")
abline(h=0)
plot(md6est,erro6,xlim=c(0,1),ylim=c(-1,1),main="mod6",xlab="volume estimado6",ylab="erro6 (m)")
abline(h=0)
#modelos nao lineares volumetricos#
#v1=b1*d^b2*h^b3+E#
nlvest1<- nls(rls$v~b1*rls$d^b2*rls$h^b3,data=rls, start=list(b1=0.1, b2=0.1, b3=0.1))
nlvest1
nlvest2<- nls(rls$v~b1*rls$d^b2*rls$h^b3,data=rls, start=list(b1=3.452e-05, b2=1.868e+00, b3=1.124e+00))
nlvest2
v1<- (3.452e-05*rls$d^1.868e+00*rls$h^1.124e+00)
v1
errov1<- (rls$v-v1)
errov1
pcerrov1<- (errov1/rls$v)*100
pcerrov1
mderrov1<- mean(pcerrov1)
mderrov1
#erro padrao e coeficientes de determinação#
sqresv1<- sum(errov1^2)
sqresv1
glresv1<- 95-3
glresv1
r2v1<- 1-(sqresv1/sqtotal)
r2v1
r2v1ajust<- 1-((1-r2v1)*(n1/glresv1))
r2v1ajust
syxv1<- sqrt(sqresv1/glresv1)
syxv1
syxv1pc<- (syxv1/mean(rls$v))*100
syxv1pc
#v2+b1*d^b2+E#
nlv2est1<- nls(rls$v~b1*rls$d^b2,data=rls, start=list(b1=0.1, b2=0.1))
nlv2est1
nlv2est2<-nls(rls$v~b1*rls$d^b2,data=rls, start=list(b1=0.0001775, b2=2.5038713))
nlv2est2
v2<- (0.0001775*rls$d^2.5038713)
v2
errov2<- (rls$v-v2)
errov2
pcerrov2<- (errov2/rls$v)*100
pcerrov2
mderro2<- mean(pcerrov2)
mderro2
#erro padrao e coeficiente de determinação
sqresv2<- sum(errov2^2)
sqresv2
glresv2<- 95-2
glresv2
r2v2<- 1-(sqresv2/sqtotal)
r2v2
r2v2ajust<- 1-((1-r2v2)*(n1/glresv2))
r2v2ajust
syxv2<- sqrt(sqresv2/glresv2)
syxv2
syxv2pc<- (syxv2/mean(rls$v))*100
syxv2pc
summary(nlv2est2)