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Scripts R e conjuntos de dados da disciplina MAE0006 MODELOS DE REGRESSAO.
Raw
gujarati.txt
val_agregado insu_trab insu_capital
38372840 424471 2689076
1805427 19895 57997
23736129 206893 2308272
26981983 304055 1376235
217546032 1809756 13554116
19462751 180366 1790751
28972772 224267 1210229
14313157 54455 421064
159921 2029 7188
47289846 471211 2761281
63015125 659379 3540475
1809052 17528 146371
10511786 75414 848220
105324866 963156 5870409
90120459 835083 5832503
39079550 336159 1795976
22826760 246144 1595118
38686340 384484 2503693
69910555 216149 4726625
7856947 82021 415131
21352966 174855 1729116
46044292 355701 2706065
92335528 943298 5294356
48304274 456553 2833525
17207903 267806 1212281
47340157 439427 2404122
2644567 24167 334008
14650080 163637 627806
7290360 59737 522335
9188322 96106 507488
51298516 407076 3295056
20401410 43079 404749
87756129 727177 4260353
101268432 820013 4086558
3556025 34723 184700
124986166 1174540 6301421
20451196 201284 1327353
34808109 257820 1456683
104858322 944998 5896392
6541356 68987 297618
37668126 400317 2500071
4988905 56524 311251
62828100 582241 4126465
172960157 1120382 11588283
15702637 150030 762671
5418786 48134 276293
49166991 425346 2731669
46164427 313279 1945860
9185967 89639 685587
66964978 694628 3902823
2979475 15221 361536
Raw
mod_saturado.R
# dados ficticios
x2 <- c(2, 3, 4)
y <- c(3, 5, 6)
plot(x2, y, xlim = c(1.5, 4.5), ylim = c(2, 7), pch = 19)
# modelo nulo (null)
mod2 <- lm(y ~ 1); mod2
abline(mod2, col = "red", lty = 2, lwd = 2)
plot(function(x) dnorm(x, mean(y), sd(y)), 0, 8,
xlab = "y", ylab = "Densidade")
abline(v = mean(y), col = "red", lty = 2, lwd = 2)
points(y, c(0.002, 0.002, 0.002), pch = 19)
# modelo saturado (full ou saturated)
x3 <- c(0, 0, 1)
mod1 <- lm(y ~ x2 + x3); mod1
plot(x, y, xlim = c(1.5, 4.5), ylim = c(2, 7), pch = 19)
abline(mod2, col = "red", lty = 2, lwd = 2) # null model
segments(0, -1 + 2*0, 3, -1 + 2*3, lty = 2, lwd = 2)
segments(3, -2 + 2*3, 6, -2 + 2*6, lty = 2, lwd = 2)
# modelo intermediario
mod3 <- lm(y ~ x2); mod3
abline(mod3, col = "blue", lty = 2, lwd = 2)
Raw
pesca.txt
frota ano trimestre latitude longitude diaspesca captura cpue
Santos 1995 3 23.25 41.75 8.0 1000.0000 125.00000
Santos 1996 1 23.25 41.75 4.0 1000.0000 250.00000
Santos 1999 1 23.25 41.75 5.0 1750.0000 350.00000
Santos 1998 2 23.75 41.25 9.0 1800.0000 200.00000
Ubatuba 1995 1 24.25 44.25 8.0 420.0000 52.50000
Ubatuba 1995 1 24.25 44.25 7.0 315.0000 45.00000
Ubatuba 1995 1 24.25 44.25 8.0 350.0000 43.75000
Ubatuba 1998 2 24.25 45.25 10.0 3500.0000 350.00000
Ubatuba 1998 2 24.25 45.25 7.0 950.0000 135.71429
Ubatuba 1998 2 24.25 45.25 8.0 1000.0000 125.00000
Ubatuba 1998 2 24.25 45.25 7.0 780.0000 111.42857
Ubatuba 1998 3 24.25 45.25 4.0 600.0000 150.00000
Ubatuba 1999 2 24.25 44.25 10.0 820.0000 82.00000
Ubatuba 1999 4 24.25 45.25 10.0 880.0000 88.00000
Santos 1999 1 24.25 44.75 5.0 1750.0000 350.00000
Santos 1998 1 24.75 44.25 12.0 2300.0000 191.66667
Santos 1999 1 24.75 46.25 5.0 2250.0000 450.00000
Santos 1999 2 24.75 46.25 9.0 750.0000 78.94737
Santos 1999 2 24.75 45.75 2.0 106.0000 53.00000
Santos 1999 3 24.75 45.75 4.0 910.0000 227.50000
Santos 1999 4 24.75 46.25 5.5 350.0000 63.63636
Ubatuba 1996 3 25.25 46.25 8.0 1000.0000 125.00000
Ubatuba 1996 3 25.25 46.25 10.0 1000.0000 100.00000
Ubatuba 1996 3 25.25 46.25 9.0 650.0000 72.22222
Ubatuba 1996 3 25.25 46.25 8.0 500.0000 62.50000
Ubatuba 1997 2 25.25 46.25 12.0 1700.0000 141.66667
Ubatuba 1997 2 25.25 46.25 10.0 1000.0000 100.00000
Ubatuba 1997 3 25.25 46.25 12.0 3500.0000 291.66667
Ubatuba 1997 3 25.25 46.25 10.0 2800.0000 280.00000
Ubatuba 1997 3 25.25 46.25 10.0 2500.0000 250.00000
Ubatuba 1997 3 25.25 46.25 10.0 2000.0000 200.00000
Ubatuba 1999 1 25.25 46.25 9.0 400.0000 44.44444
Ubatuba 1999 2 25.25 46.25 10.0 2100.0000 210.00000
Ubatuba 1999 2 25.25 46.25 8.0 420.0000 52.50000
Ubatuba 1999 3 25.25 46.25 10.0 1700.0000 170.00000
Ubatuba 1999 3 25.25 46.25 10.0 1200.0000 120.00000
Ubatuba 1999 4 25.25 46.25 8.0 1000.0000 125.00000
Ubatuba 1999 4 25.25 46.25 10.0 1200.0000 120.00000
Santos 1995 4 25.25 45.75 15.0 1000.0000 66.66667
Santos 1996 1 25.25 46.25 10.0 3000.0000 300.00000
Santos 1996 3 25.25 46.25 3.3 266.6667 80.00000
Santos 1998 1 25.25 46.25 10.0 2200.0000 220.00000
Santos 1998 1 25.25 45.25 14.0 3000.0000 214.28571
Santos 1998 1 25.25 45.25 14.0 2000.0000 142.85714
Santos 1999 1 25.25 45.25 12.0 2700.0000 225.00000
Santos 1999 1 25.25 45.25 12.0 1000.0000 83.33333
Santos 1999 2 25.25 45.25 2.0 106.0000 53.00000
Santos 1999 3 25.25 46.25 1.5 350.0000 233.33333
Santos 1999 3 25.25 44.75 4.0 910.0000 227.50000
Santos 1999 4 25.25 46.25 9.0 1949.0000 216.55556
Santos 1999 4 25.25 44.75 6.0 1000.0000 166.66667
Ubatuba 1996 2 25.75 46.25 6.0 1500.0000 250.00000
Ubatuba 1996 2 25.75 46.25 6.0 850.0000 141.66667
Ubatuba 1996 2 25.75 46.25 12.0 680.0000 56.66667
Ubatuba 1996 2 25.75 46.25 13.0 650.0000 50.00000
Santos 1995 3 25.75 45.75 8.0 2000.0000 250.00000
Santos 1995 3 25.75 46.25 1.0 50.0000 50.00000
Santos 1995 4 25.75 46.25 15.0 2000.0000 133.33333
Santos 1996 3 25.75 46.25 3.3 266.6667 80.00000
Santos 1997 4 25.75 45.75 12.0 3000.0000 250.00000
Santos 1997 4 25.75 46.25 4.0 300.0000 75.00000
Santos 1998 1 25.75 46.25 9.0 1200.0000 133.33333
Santos 1998 4 25.75 46.25 12.0 2000.0000 166.66667
Santos 1999 2 25.75 46.25 9.5 750.0000 78.94737
Ubatuba 1996 2 26.25 46.25 12.0 565.0000 47.08333
Ubatuba 1996 4 26.25 47.25 10.0 1300.0000 130.00000
Ubatuba 1996 4 26.25 47.25 10.0 700.0000 70.00000
Ubatuba 1999 2 26.25 46.25 12.0 3500.0000 291.66667
Ubatuba 1999 2 26.25 46.25 12.0 2800.0000 233.33333
Ubatuba 1999 2 26.25 46.25 10.0 1500.0000 150.00000
Ubatuba 1999 2 26.25 46.25 12.0 1730.0000 144.16667
Santos 1995 2 26.25 46.75 5.0 2000.0000 400.00000
Santos 1995 3 26.25 46.75 13.0 700.0000 53.84615
Santos 1996 3 26.25 46.25 3.3 266.6667 80.00000
Santos 1996 4 26.25 46.25 10.0 2000.0000 200.00000
Santos 1996 4 26.25 46.75 9.0 1000.0000 111.11111
Santos 1997 3 26.25 45.75 12.0 6000.0000 500.00000
Santos 1997 4 26.25 45.75 7.5 1650.0000 220.00000
Santos 1997 4 26.25 46.25 7.5 1650.0000 220.00000
Santos 1997 4 26.25 46.25 4.0 300.0000 75.00000
Santos 1998 2 26.25 46.25 12.0 1800.0000 150.00000
Santos 1998 3 26.25 46.75 5.0 700.0000 140.00000
Santos 1998 4 26.25 46.25 2.0 1200.0000 600.00000
Santos 1999 1 26.25 46.25 5.0 2250.0000 450.00000
Santos 1999 1 26.25 46.25 10.0 3000.0000 300.00000
Santos 1999 1 26.25 46.25 15.0 3000.0000 200.00000
Santos 1999 1 26.25 46.25 18.0 3500.0000 194.44444
Santos 1999 2 26.25 46.25 8.0 3876.0000 484.50000
Santos 1999 2 26.25 46.25 8.0 1351.0000 168.87500
Santos 1999 2 26.25 47.75 6.0 900.0000 150.00000
Santos 1999 2 26.25 47.75 7.5 1000.0000 133.33333
Santos 1999 2 26.25 46.25 2.0 106.0000 53.00000
Ubatuba 1996 4 26.75 47.25 10.0 480.0000 48.00000
Santos 1995 1 26.75 46.25 3.0 1000.0000 333.33333
Santos 1995 1 26.75 47.75 3.0 150.0000 50.00000
Santos 1995 2 26.75 47.25 2.0 400.0000 200.00000
Santos 1995 3 26.75 46.25 10.0 1000.0000 100.00000
Santos 1995 4 26.75 46.25 5.0 1500.0000 300.00000
Santos 1997 2 26.75 47.25 15.0 4000.0000 266.66667
Santos 1997 3 26.75 46.25 12.0 3000.0000 250.00000
Santos 1997 3 26.75 46.25 2.0 400.0000 200.00000
Santos 1997 3 26.75 46.25 5.0 900.0000 180.00000
Santos 1997 3 26.75 46.25 10.0 1500.0000 150.00000
Santos 1997 3 26.75 46.75 14.0 2000.0000 142.85714
Santos 1998 2 26.75 46.75 12.0 2900.0000 241.66667
Santos 1998 3 26.75 47.25 8.0 1000.0000 125.00000
Santos 1998 3 26.75 46.25 7.0 600.0000 85.71429
Santos 1999 1 26.75 46.75 15.0 2300.0000 153.33333
Santos 1999 2 26.75 46.75 8.0 2385.0000 298.12500
Santos 1999 4 26.75 46.75 5.5 1750.0000 318.18182
Santos 1999 4 26.75 46.75 8.0 1900.0000 237.50000
Santos 1999 4 26.75 46.25 5.0 1050.0000 210.00000
Santos 1999 4 26.75 46.75 5.0 1050.0000 210.00000
Santos 1999 4 26.75 46.25 6.0 1000.0000 166.66667
Santos 1999 4 26.75 46.75 7.0 1000.0000 142.85714
Santos 1999 4 26.75 47.25 5.0 700.0000 140.00000
Santos 1997 2 27.25 46.75 8.0 4000.0000 500.00000
Santos 1998 1 27.25 46.75 14.0 1000.0000 71.42857
Santos 1998 2 27.25 47.25 3.0 1000.0000 333.33333
Santos 1998 3 27.25 46.75 13.0 2160.0000 166.15385
Santos 1998 3 27.25 46.75 13.0 1700.0000 130.76923
Santos 1998 4 27.25 46.75 2.0 700.0000 350.00000
Santos 1998 4 27.25 46.75 4.0 1000.0000 250.00000
Santos 1998 4 27.25 47.25 4.0 700.0000 175.00000
Santos 1998 4 27.25 46.75 10.0 1500.0000 150.00000
Santos 1998 4 27.25 46.75 11.0 1500.0000 136.36364
Santos 1998 4 27.25 46.75 8.0 800.0000 100.00000
Santos 1999 2 27.25 47.25 6.0 900.0000 150.00000
Santos 1999 2 27.25 47.25 7.5 1000.0000 133.33333
Santos 1999 3 27.25 48.25 5.5 1340.0000 243.63636
Santos 1999 4 27.25 46.75 12.0 2500.0000 208.33333
Santos 1999 4 27.25 46.75 10.0 2000.0000 200.00000
Santos 1999 4 27.25 46.75 5.0 700.0000 140.00000
Santos 1997 4 27.75 47.25 5.0 1342.0000 268.40000
Santos 1995 2 28.25 47.25 10.0 1500.0000 150.00000
Santos 1995 3 28.25 47.25 10.0 4000.0000 400.00000
Santos 1995 3 28.25 47.25 12.0 2000.0000 166.66667
Santos 1995 4 28.25 47.75 8.0 4500.0000 562.50000
Santos 1995 4 28.25 47.25 4.0 1500.0000 375.00000
Santos 1995 4 28.25 47.25 10.0 3500.0000 350.00000
Santos 1995 4 28.25 47.25 12.0 3500.0000 291.66667
Santos 1996 1 28.25 47.25 9.0 4000.0000 444.44444
Santos 1997 1 28.25 47.25 10.0 1300.0000 130.00000
Santos 1997 2 28.25 47.25 8.0 4500.0000 562.50000
Santos 1997 4 28.25 47.25 12.0 5700.0000 475.00000
Santos 1998 1 28.25 47.25 10.0 4500.0000 450.00000
Santos 1998 3 28.25 47.25 16.0 6500.0000 406.25000
Santos 1998 3 28.25 47.25 12.0 3000.0000 250.00000
Santos 1998 3 28.25 47.25 5.0 500.0000 100.00000
Santos 1999 3 28.25 47.25 12.0 3500.0000 291.66667
Santos 1999 3 28.25 47.25 1.5 350.0000 233.33333
Santos 1999 3 28.25 47.25 9.0 1900.0000 211.11111
Santos 1999 3 28.25 46.75 5.0 800.0000 160.00000
Santos 1999 3 28.25 47.25 5.0 800.0000 160.00000
Santos 1999 3 28.25 47.25 13.0 1300.0000 100.00000
Santos 1999 4 28.25 47.25 10.0 950.0000 95.00000
Raw
slides1_1.R
library(dobson)
data(chronic)
head(chronic)
# sob H0
theta <- 1.184
r <- chronic$number - theta
dots <- function(x,...){
sx <- sort(x)
sy <- unlist(lapply(table(sx),seq))
plot(sx, sy, ...)
}
dots(r[1:26], pch = 20, xlab = "Resíduos", ylab = "Frequência",
main = "Cidade") # cidade
dots(r[27:49], pch = 20, xlab = "Resíduos", ylab = "Frequência",
main = "Rural") # rural
# sob H1
theta1 <- 1.423
theta2 <- 0.913
r1 <- chronic$number[1:26] - theta1
r2 <- chronic$number[27:49] - theta2
dots(r1, pch = 20, xlab = "Resíduos", ylab = "Frequência",
main = "Cidade") # cidade
dots(r2, pch = 20, xlab = "Resíduos", ylab = "Frequência",
main = "Rural") # rural
Raw
slides1_2.R
library(dobson)
data(birthweight)
head(birthweight)
plot(birthweight$`boys gestational age`, birthweight$`boys weight`,
xlab = "Idade (semanas)", ylab = "Peso (gramas)",
xlim = c(35, 42), ylim = c(2350, 3500), pch = 20, col = 1)
points(birthweight$`girls gestational age`, birthweight$`girls weight`,
pch = 20, col = 2)
legend("topleft", c("meninos", "meninas"), pch = 20, col = 1:2, bty = "n")
# sob H0 ------------------------------------------------------------------
b <- 120.894
a1 <- -1610.283
a2 <- -1773.322
# residuos
mu1 <- a1 + b*birthweight$`boys gestational age`
mu2 <- a2 + b*birthweight$`girls gestational age`
res1 <- birthweight$`boys weight` - mu1
res2 <- birthweight$`girls weight` - mu2
respad1 <- res1/sd(c(res1, res2))
respad2 <- res2/sd(c(res1, res2))
plot(mu1, respad1, xlab = "Valores ajustados (gramas)",
ylab = "Resíduos padronizados", xlim = c(2500, 3475),
ylim = c(-2, 2), pch = 20, col = 1)
points(mu2, respad2, pch = 20, col = 2)
abline(h = 0, lty = 2)
legend("topright", c("meninos", "meninas"), pch = 20, col = 1:2)#, bty = "n")
plot(birthweight$`boys gestational age`, respad1,
xlab = "Idade (semanas)", ylab = "Resíduos padronizados",
xlim = c(35, 43), ylim = c(-2, 2), pch = 20, col = 1)
points(birthweight$`girls gestational age`, respad2, pch = 20, col = 2)
abline(h = 0, lty = 2)
legend("topright", c("meninos", "meninas"), pch = 20, col = 1:2)#, bty = "n")
plot(qnorm(ppoints(24)), sort(c(respad1, respad2)), ylim = c(-2, 2),
pch = 20, xlab = "Quantis normal", ylab = "Resíduos padronizados")
abline(a = 0, b = 1, lty = 2)
# sob H1 ------------------------------------------------------------------
b1 <- 111.983
b2 <- 130.400
a1 <- -1268.672
a2 <- -2141.667
# residuos
mu1 <- a1 + b1*birthweight$`boys gestational age`
mu2 <- a2 + b2*birthweight$`girls gestational age`
res1 <- birthweight$`boys weight` - mu1
res2 <- birthweight$`girls weight` - mu2
respad1 <- res1/sd(c(res1, res2))
respad2 <- res2/sd(c(res1, res2))
plot(mu1, respad1, xlab = "Valores ajustados (gramas)",
ylab = "Resíduos padronizados", xlim = c(2500, 3475),
ylim = c(-2, 2), pch = 20, col = 1)
points(mu2, respad2, pch = 20, col = 2)
abline(h = 0, lty = 2)
legend("topright", c("meninos", "meninas"), pch = 20, col = 1:2)#, bty = "n")
plot(birthweight$`boys gestational age`, respad1,
xlab = "Idade (semanas)", ylab = "Resíduos padronizados",
xlim = c(35, 43), ylim = c(-2, 2), pch = 20, col = 1)
points(birthweight$`girls gestational age`, respad2, pch = 20, col = 2)
abline(h = 0, lty = 2)
legend("topright", c("meninos", "meninas"), pch = 20, col = 1:2)#, bty = "n")
plot(qnorm(ppoints(24)), sort(c(respad1, respad2)), ylim = c(-2, 2),
pch = 20, xlab = "Quantis normal", ylab = "Resíduos padronizados")
abline(a = 0, b = 1, lty = 2)
Raw
slides1_3.R
library(dobson)
data(failure)
failure
hist(failure$lifetimes, xlab = "Tempo até a falha (horas)",
ylab = "Frequência", main = "")
library(animation)
ani.options(interval = 2, nmax = 50)
# exemplo
newton.method(interact = TRUE)
# funcao score
newton.method(FUN = function(theta) -49*2/theta + (2/(theta^3))*4794902949,
interact = TRUE, rg = c(5E3, 14E3), ylim = c(-0.005, 0.05),
ylab = expression(U(theta)), xlab = expression(theta),
main = "Newton-Raphson", tol = 1E-5)
y <- failure$lifetimes
N <- length(failure$lifetimes)
# metodo score de Fisher
old.the <- 1000 # chute inicial
new.the <- old.the/2 + sum(y^2)/(2*N*old.the); new.the
while(abs(new.the - old.the) > 0.01) {
old.the <- new.the
new.the <- old.the/2 + sum(y^2)/(2*N*old.the)
print(new.the)
}
sqrt(sum(y^2)/N) # EMV pela expressao explicita
IF <- 4*N/new.the^2; IF # informacao
EP <- 1/sqrt(IF); EP # erro padrao
# IC 95%
new.the + c(-1, 1)*1.96*EP
logvero <- function(the){
sum(log(y)) + N*log(2) - 2*N*log(the) - sum(y^2)/the^2
}
plot(function(x) logvero(x), 7000, 13000,
xlab = expression(theta), ylab = "log-verossimilhança")
abline(v = new.the, lty = 2)
Raw
slides1_4.R
library(dobson)
data("poisson")
poisson
old.b <- c(1, 2) #valores iniciais
X <- model.matrix(~ poisson$x)
W <- diag(1/(old.b[1] + old.b[2]*poisson$x))
z <- poisson$y
t(X)%*%W%*%X
t(X)%*%W%*%z
new.b <- solve(t(X)%*%W%*%X)%*%t(X)%*%W%*%z; new.b
while(sqrt(sum((new.b - old.b)^2)) > 0.01) {
old.b <- new.b
W <- diag(1/(old.b[1] + old.b[2]*poisson$x))
new.b <- solve(t(X)%*%W%*%X)%*%t(X)%*%W%*%z
print(new.b)
}
# covariancia de beta
solve(t(X)%*%W%*%X)
# ajuste pela funcao 'glm'
mod <- glm(y ~ x, family = poisson(link = "identity"), data = poisson)
summary(mod)
Raw
slides1_5.R
library(dobson)
data("birthweight") # dados pesos
#-
idade <- c(birthweight$`boys gestational age`, birthweight$`girls gestational age`)
peso <- c(birthweight$`boys weight`, birthweight$`girls weight`)
sexo <- c(rep(0, 12), rep(1, 12))
dados.birth <- data.frame(idade, peso, sexo)
mod <- glm(peso ~ idade + sexo, family = gaussian(link = "identity"),
data = dados.birth)
summary(mod)
plot(birthweight$`boys gestational age`, birthweight$`boys weight`,
xlab = "Idade (semanas)", ylab = "Peso (gramas)",
xlim = c(35, 42), ylim = c(2350, 3500), pch = 20, col = 1)
points(birthweight$`girls gestational age`, birthweight$`girls weight`,
pch = 20, col = 2)
legend("topleft", c("meninos", "meninas"), pch = 20, col = 1:2, bty = "n")
abline(a = mod$coef[1], b = mod$coef[2], lty = 2)
abline(a = mod$coef[1] + mod$coef[3], b = mod$coef[2], lty = 2, col = "red")
#-
data("poisson")
mod <- glm(y ~ x, family = poisson(link = "identity"), data = poisson)
summary(mod)
Raw
slides2_1.R
#- gráfico 3 funcoes de ligacao
plot(function(x) exp(x)/(1 + exp(x)), -4, 4, ylim = c(0, 1), lty = 2,
lwd = 2, ylab = expression(pi[i]), xlab = "Componente linear")
plot(function(x) pnorm(x), -4, 4, lty = 2, col = "blue", lwd = 2,
add = TRUE)
plot(function(x) 1 - exp(-exp(x)), -4, 4, lty = 2, col = "red", lwd = 2,
add = TRUE)
legend("topleft", c("logito", "probito", "c-loglog"), lty = 2, lwd = 2,
col = c(1, 4, 2), bty = "n")
#- dados besouros
y <- c(6, 13, 18, 28, 52, 53, 61, 60)
n <- c(59, 60, 62, 56, 63, 59, 62, 60)
x <- c(1.6907, 1.7242, 1.7552, 1.7842, 1.8113, 1.8369, 1.8610, 1.8839)
plot(x, y/n, xlab = "Dose", ylab = "Proporção mortos", pch = 20)
#- ligacao logito
besouro <- cbind(y, n - y)
mod1 <- glm(besouro ~ x, family = binomial(link = "logit"))
summary(mod1)
pchisq(mod1$deviance, mod1$df.residual, lower.tail = FALSE) # p-valor para o desvio
b <- mod1$coef
plot(x, y/n, xlab = "Dose", ylab = "Proporção mortos", ylim = c(0, 1),
xlim = c(1.67, 1.90), pch = 20)
plot(function(x) exp(b[1] + b[2]*x)/(1 + exp(b[1] + b[2]*x)), 1.5, 2,
lty = 2, lwd = 2, add = TRUE)
library(MASS)
dose.p(mod1) # dose letal 50%
dose.p(mod1, p = 0.99) # dose letal 99%
# ligacao probito
mod2 <- glm(besouro ~ x, family = binomial(link = "probit"))
summary(mod2)
pchisq(mod2$deviance, mod2$df.residual, lower.tail = FALSE) # p-valor para o desvio
b <- mod2$coef
plot(function(x) pnorm(b[1] + b[2]*x), 1.5, 2, lty = 2, lwd = 2,
col = 4, add = TRUE)
# ligacao c-loglog
mod3 <- glm(besouro ~ x, family = binomial(link = "cloglog"))
summary(mod3)
pchisq(mod3$deviance, mod3$df.residual, lower.tail = FALSE) # p-valor para o desvio
b <- mod3$coef
plot(function(x) 1 - exp(-exp(b[1] + b[2]*x)), 1.5, 2, lty = 2,
lwd = 2, col = 2, add = TRUE)
dose.p(mod3) # dose letal 50%
dose.p(mod3, p = 0.99) # dose letal 99%
Raw
slides2_2.R
#- dados cupons
y <- c(30, 45, 70, 100, 137, 166, 176) # cupons usados
n <- rep(200, 7) # cupons enviados
x <- c(5, 10, 15, 20, 25, 30, 35) # desconto
plot(x, y/n, xlab = "Desconto", ylab = "Proporção cupons usados", pch = 20)
#-
cupons <- cbind(y, n - y)
mod1 <- glm(cupons ~ x, family = binomial(link = "logit"))
summary(mod1)
pchisq(mod1$deviance, mod1$df.residual, lower.tail = FALSE) # p-valor para o desvio
#-
b <- mod1$coef
plot(x, y/n, xlab = "Desconto", ylab = "Proporção cupons usados",
ylim = c(0, 1), xlim = c(0, 40), pch = 20)
plot(function(x) exp(b[1] + b[2]*x)/(1 + exp(b[1] + b[2]*x)), 0, 40,
lty = 2, lwd = 2, add = TRUE)
#-
library(MASS)
dose.p(mod1, p = 0.80)
# -------------------------------------------------------------------------
library(aplore3)
#- dados
data(chdage)
head(chdage)
View(chdage)
#-
mod2 <- glm(chd ~ age, family = binomial(), data = chdage)
summary(mod2)
pchisq(mod2$deviance, mod2$df.residual, lower.tail = FALSE) # p-valor para o desvio
#-
b <- mod2$coef
plot(function(x) exp(b[1] + b[2]*x)/(1 + exp(b[1] + b[2]*x)), 0, 80,
lty = 2, lwd = 2, ylab = expression(pi), xlab = "Idade")
#-
exp(b[2]) # RC
#-
vcov(mod2)
Var <- vcov(mod2)[2, 2]
rho <- 0.05 # 95% confianca
exp(b[2] + c(-1, 1)*qnorm(1 - rho/2)*sqrt(Var)) # IC para RC
Raw
slides2_3.R
library(dobson)
data("doctors")
doctors
doctors2 <- cbind(doctors, agecat = rep(1:5, 2))
doctors2
dim(doctors2) # 10 x 5
plot(doctors2$agecat, 1E5*doctors2$deaths/doctors2$`person-years`,
col = rep(c(2, 1), each = 5), pch = 20, xlab = "Idade (categoria)",
ylab = "Mortes por 100000")
legend("topleft", c("não fumante", "fumante"), pch = 20, col = 1:2, bty = "n")
mod1 <- glm(deaths ~ agecat + smoking, offset = log(`person-years`/1E5),
family = poisson(link = "log"), data = doctors2)
summary(mod1)
pchisq(mod1$deviance, mod1$df.residual, lower.tail = FALSE) # nao faz sentido neste caso
b <- mod1$coef
plot(function(x) exp(b[1] + b[2]*x), 0, 5, lty = 2, add = TRUE)
plot(function(x) exp(b[1] + b[2]*x + b[3]), 0, 5, lty = 2, col = "red", add = TRUE)
exp(b[3]) # risco relativo fumante
Raw
slides2_4.R
nbacter <- c(175, 108, 95, 82, 71, 50, 49, 31, 28, 17, 16, 11)
texpo <- 1:12
plot(texpo, nbacter, xlab = "Tempo de exposição", ylab = "Número bactérias",
pch = 20)
mod1 <- lm(nbacter ~ texpo)
mod1 <- glm(nbacter ~ texpo, family = gaussian())
summary(mod1)
b <- mod1$coefficients
plot(function(x) b[1] + b[2]*x, 0, 12, lty = 2, lwd = 2, col = "red",
add = TRUE)
mod2 <- glm(nbacter ~ texpo, family = poisson(link = "identity"))
summary(mod2)
b <- mod2$coefficients
plot(function(x) b[1] + b[2]*x, 0, 12, lty = 2, lwd = 2,
col = "green", add = TRUE)
mod3 <- glm(nbacter ~ texpo, family = poisson())
summary(mod3)
b <- mod3$coefficients
plot(function(x) exp(b[1] + b[2]*x), 0, 12, lty = 2, lwd = 2,
col = "blue", add = TRUE)
legend("topright", c("Normal/identidade", "Poisson/identidade",
"Poisson/log"), lty = 2, lwd = 2,
col = c("red", "green", "blue"), bty = "n")
exp(b[2])
# -------------------------------------------------------------------------
store <- read.csv("~/caminho/para/o/arquivo/store.txt", sep = "")
head(store)
dim(store)
mod1 <- glm(nclientes ~ I(domic/1E3) + I(renda/1E3) + idade + distconc
+ distloja, family = poisson(), data = store)
summary(mod1)
b <- mod1$coefficients
exp(b)
round(100*(exp(b) - 1), 2)
round(100*(exp(5*b[4]) - 1), 2) # covariavel idade domicilio
Raw
slides3_1.R
plot(function(x) dnorm(x, 5, 1), 0, 15, ylab = "")
mu <- 5; phi <- 4
plot(function(x) dgamma(x, shape = phi, rate = phi/mu), 0, 15,
add = TRUE, col = "blue")
turbina <- read.csv("~/caminho/para/o/arquivo/turbina.txt", sep = "")
head(turbina)
dim(turbina)
mean(turbina$tempo); sd(turbina$tempo)
plot(density(turbina$tempo), xlab = "Tempo", ylab = "Densidade", main = "")
hist(turbina$tempo, prob = TRUE, xlab = "Tempo", ylab = "Densidade", main = "")
mod1 <- glm(tempo ~ 1, family = Gamma(link = "identity"), data = turbina)
summary(mod1)
library(MASS)
phi <- gamma.shape(mod1); phi # phi
2/sqrt(phi$alpha) # assimetria
aggregate(tempo ~ tipo, turbina, mean)
aggregate(tempo ~ tipo, turbina, sd)
aggregate(tempo ~ tipo, turbina, sd)/aggregate(tempo ~ tipo, turbina, mean)
boxplot(split(turbina$tempo, turbina$tipo), xlab = "Tipo", ylab = "Tempo")
cdplot(as.factor(turbina$tipo) ~ turbina$tempo, xlab = "Duração",
ylab = "Tipo")
turbina$tipo <- factor(turbina$tipo)
mod2 <- update(mod1, . ~ tipo)
summary(mod2)
phi <- gamma.shape(mod2); phi # phi
2/sqrt(phi$alpha) # assimetria
turbina <- data.frame(turbina, tipo2 = turbina$tipo)
levels(turbina$tipo2)
levels(turbina$tipo2) <- c("1", "2", "1", "1", "5")
mod3 <- update(mod2, . ~ tipo2, data = turbina)
summary(mod3)
phi <- gamma.shape(mod3); phi # phi
2/sqrt(phi$alpha) # assimetria
Raw
slides3_2.R
pesca <- read.csv("~/caminho/para/o/arquivo/pesca.txt", sep = "")
head(pesca)
dim(pesca)
plot(density(pesca$cpue), xlab = "CPUE (kg/dias pesca)", ylab = "Densidade", main = "")
aggregate(cpue ~ frota, pesca, mean)
aggregate(cpue ~ frota, pesca, sd)
aggregate(cpue ~ frota, pesca, length)
aggregate(cpue ~ frota, pesca, sd)/aggregate(cpue ~ frota, pesca, mean)
boxplot(split(pesca$cpue, pesca$frota), xlab = "Frota", ylab = "CPUE")
cdplot(as.factor(pesca$frota) ~ pesca$cpue, xlab = "CPUE",
ylab = "Frota")
aggregate(cpue ~ ano, pesca, mean)
aggregate(cpue ~ ano, pesca, sd)
aggregate(cpue ~ ano, pesca, length)
aggregate(cpue ~ ano, pesca, sd)/aggregate(cpue ~ ano, pesca, mean)
boxplot(split(pesca$cpue, pesca$ano), xlab = "Ano", ylab = "CPUE")
aggregate(cpue ~ trimestre, pesca, mean)
aggregate(cpue ~ trimestre, pesca, sd)
aggregate(cpue ~ trimestre, pesca, length)
aggregate(cpue ~ trimestre, pesca, sd)/aggregate(cpue ~ trimestre, pesca, mean)
boxplot(split(pesca$cpue, pesca$trimestre), xlab = "Trimestre", ylab = "CPUE")
cdplot(as.factor(pesca$trimestre) ~ pesca$cpue, xlab = "CPUE",
ylab = "Trimestre")
pairs(~ cpue + latitude + longitude, data = pesca, pch = 20,
panel = panel.smooth, lty = 2)
panel.hist <- function(x, ...) {
usr <- par("usr"); on.exit(par(usr))
par(usr = c(usr[1:2], 0, 1.5) )
h <- hist(x, plot = FALSE)
breaks <- h$breaks; nB <- length(breaks)
y <- h$counts; y <- y/max(y)
rect(breaks[-nB], 0, breaks[-1], y, col = "grey", ...)
}
pairs(~ cpue + latitude + longitude, data = pesca,
pch = 20, lower.panel = NULL, upper.panel = panel.smooth,
diag.panel = panel.hist, lty = 2)
pesca$ano <- factor(pesca$ano)
pesca$trimestre <- factor(pesca$trimestre)
mod1 <- glm(cpue ~ latitude + longitude + ano + trimestre + frota,
family = Gamma(link = "log"), data = pesca)
summary(mod1)
mod2 <- glm(cpue ~ latitude + ano + trimestre + frota,
family = Gamma(link = "log"), data = pesca)
summary(mod2)
mod3 <- glm(cpue ~ latitude + frota,
family = Gamma(link = "log"), data = pesca)
summary(mod3)
library(MASS)
phi <- gamma.shape(mod3); phi # phi
2/sqrt(phi$alpha) # assimetria
# -------------------------------------------------------------------------
econo <- read.csv("~/caminho/para/o/arquivo/gujarati.txt", sep = "")
head(econo)
dim(econo)
plot(density(econo$val_agregado/1E8), xlab = "Valor agregado (10^8)", ylab = "Densidade", main = "")
hist(econo$val_agregado/1E8, prob = TRUE, xlab = "Valor agregado (10^8)", ylab = "Densidade", main = "")
mod1 <- glm(val_agregado ~ I(log(insu_trab)) + I(log(insu_capital)),
family = Gamma(link = "log"), data = econo)
summary(mod1)
library(MASS)
phi <- gamma.shape(mod1); phi # phi
2/sqrt(phi$alpha) # assimetria
betas <- coef(mod1)[2] + coef(mod1)[3]; betas
V <- vcov(mod1)
var.betas <- V[2, 2] + V[3, 3] + 2*V[2, 3]; var.betas
# IC 95%
betas + c(-1, 1)*qnorm(1 - 0.05/2)*sqrt(var.betas)
Raw
slides4_1.R
# -------------------------------------------------------------------------
# Slides 1, pg. 156
#- Dados
library(dobson)
data("birthweight")
idade <- c(birthweight$`boys gestational age`, birthweight$`girls gestational age`)
peso <- c(birthweight$`boys weight`, birthweight$`girls weight`)
sexo <- c(rep(0, 12), rep(1, 12))
dados.birth <- data.frame(idade, peso, sexo)
#- Ajuste
mod <- glm(peso ~ idade + sexo, family = gaussian(link = "identity"),
data = dados.birth)
summary(mod)
#- Diagnostico
library(glmtoolbox)
res <- residuals2(mod, standardized = TRUE) # res vs. valores ajustados
plot(res) # res vs. index
abline(h = 0, lty = 2)
acf(res) # autocorrelacao res
eta <- mod$linear.predictors # eta ajustado
plot(eta, res) # res vs. eta ajustado
abline(h = 0, lty = 2)
plot(dados.birth$idade, res) # res vs. covariavel
abline(h = 0, lty = 2)
z <- resid(mod, type = "working") + eta # z ajustado
plot(z, eta) # z vs. eta, ambos ajustados
abline(0, 1)
envelope(mod, standardized = TRUE) # QQ-plot com envelope simulado 95% com resíduo quantilico
envelope(mod, standardized = TRUE, rep = 1E3, conf = 0.99,
type = "deviance")
# outros tipos de residuos
res <- residuals2(mod, standardized = TRUE, type = "pearson")
res <- residuals2(mod, standardized = TRUE, type = "deviance")
# pontos influentes
p <- ncol(model.matrix(mod))
n <- nrow(model.matrix(mod))
cutoff <- qf(0.5, p, n - p); cutoff
cooks <- cooks.distance(mod) # distancia de Cook
plot(cooks, type = "h", ylim = c(0, max(cutoff, max(cooks))))
abline(h = cutoff, lty = 2)
# -------------------------------------------------------------------------
# Slides 2, pg. 4
#- Dados besouros
y <- c(6, 13, 18, 28, 52, 53, 61, 60)
n <- c(59, 60, 62, 56, 63, 59, 62, 60)
x <- c(1.6907, 1.7242, 1.7552, 1.7842, 1.8113, 1.8369, 1.8610, 1.8839)
plot(x, y/n, xlab = "Dose", ylab = "Proporção mortos", pch = 20)
#- Ajuste com ligacao logito
besouro <- cbind(y, n - y)
mod1 <- glm(besouro ~ x, family = binomial(link = "logit"))
summary(mod1)
# Diagnostico
res <- residuals2(mod1, standardized = TRUE)
plot(res)
abline(h = 0, lty = 2)
acf(res)
eta <- mod1$linear.predictors
plot(eta, res)
abline(h = 0, lty = 2)
plot(x, res)
abline(h = 0, lty = 2)
z <- resid(mod1, type = "working") + eta
plot(z, eta, main = "logito")
abline(0, 1)
envelope(mod1, standardized = TRUE)
p <- ncol(model.matrix(mod1))
n <- nrow(model.matrix(mod1))
cutoff <- qf(0.5, p, n - p); cutoff
cooks <- cooks.distance(mod1) # distancia de Cook
plot(cooks, type = "h", ylim = c(0, max(cutoff, max(cooks))))
abline(h = cutoff, lty = 2)
#- Ajuste com ligacao probito
mod2 <- glm(besouro ~ x, family = binomial(link = "probit"))
summary(mod2)
# Diagnostico
res <- residuals2(mod2, standardized = TRUE)
plot(res)
abline(h = 0, lty = 2)
acf(res)
eta <- mod2$linear.predictors
plot(eta, res)
abline(h = 0, lty = 2)
plot(x, res)
abline(h = 0, lty = 2)
z <- resid(mod2, type = "working") + eta
plot(z, eta, main = "probit")
abline(0, 1)
envelope(mod2, standardized = TRUE)
p <- ncol(model.matrix(mod2))
n <- nrow(model.matrix(mod2))
cutoff <- qf(0.5, p, n - p); cutoff
cooks <- cooks.distance(mod2) # distancia de Cook
plot(cooks, type = "h", ylim = c(0, max(cutoff, max(cooks))))
abline(h = cutoff, lty = 2)
identify(cooks, n = 1)
mod2.omit1 <- update(mod2, subset = c(-1)) # ajuste sem a observacao 1
coef(mod2)
coef(mod2.omit1)
#- Ajuste com ligacao c-loglog
mod3 <- glm(besouro ~ x, family = binomial(link = "cloglog"))
summary(mod3)
# Diagnostico
res <- residuals2(mod3, standardized = TRUE)
plot(res)
abline(h = 0, lty = 2)
acf(res)
eta <- mod3$linear.predictors
plot(eta, res)
abline(h = 0, lty = 2)
plot(x, res)
abline(h = 0, lty = 2)
z <- resid(mod3, type = "working") + eta
plot(z, eta, main = "cloglog")
abline(0, 1)
envelope(mod3, standardized = TRUE)
p <- ncol(model.matrix(mod3))
n <- nrow(model.matrix(mod3))
cutoff <- qf(0.5, p, n - p); cutoff
cooks <- cooks.distance(mod3) # distancia de Cook
plot(cooks, type = "h", ylim = c(0, max(cutoff, max(cooks))))
abline(h = cutoff, lty = 2)
# -------------------------------------------------------------------------
# Slides 2, pg. 31
#- Dados
library(aplore3)
data(chdage)
head(chdage)
View(chdage)
#- Ajuste
mod1 <- glm(chd ~ age, family = binomial(link = "logit"), data = chdage)
summary(mod1)
#- Diagnostico
res <- residuals2(mod1, standardized = TRUE)
plot(res)
abline(h = 0, lty = 2)
acf(res)
eta <- mod1$linear.predictors
plot(eta, res)
abline(h = 0, lty = 2)
plot(chdage$age, res)
abline(h = 0, lty = 2)
z <- resid(mod1, type = "working") + eta
plot(z, eta)
abline(0, 1)
envelope(mod1, standardized = TRUE)
p <- ncol(model.matrix(mod1))
n <- nrow(model.matrix(mod1))
cutoff <- qf(0.5, p, n - p); cutoff
cooks <- cooks.distance(mod1) # distancia de Cook
plot(cooks, type = "h", ylim = c(0, max(cutoff, max(cooks))))
abline(h = cutoff, lty = 2)
# -------------------------------------------------------------------------
# Slides 2, pg. 43
#- Dados
library(dobson)
data("doctors")
head(doctors)
doctors2 <- cbind(doctors, agecat = rep(1:5, 2))
doctors2
dim(doctors2) # 10 x 5
plot(doctors2$agecat, 1E5*doctors2$deaths/doctors2$`person-years`,
col = rep(c(2, 1), each = 5), pch = 20, xlab = "Idade (categoria)",
ylab = "Mortes por 100000")
legend("topleft", c("não fumante", "fumante"), pch = 20, col = 1:2, bty = "n")
#- Ajuste
mod1 <- glm(deaths ~ agecat + smoking, offset = log(`person-years`/1E5),
family = poisson(link = "log"), data = doctors2)
summary(mod1)
#- Diagnostico
res <- residuals2(mod1, standardized = TRUE)
res <- residuals2(mod1, standardized = TRUE, identify = 4, labels = NULL)
plot(res)
abline(h = 0, lty = 2)
acf(res)
eta <- mod1$linear.predictors
plot(eta, res)
abline(h = 0, lty = 2)
z <- resid(mod1, type = "working") + eta
plot(z, eta)
abline(0, 1)
envelope(mod1, standardized = TRUE)
p <- ncol(model.matrix(mod1))
n <- nrow(model.matrix(mod1))
cutoff <- qf(0.5, p, n - p); cutoff
cooks <- cooks.distance(mod1) # distancia de Cook
plot(cooks, type = "h", ylim = c(0, max(cutoff, max(cooks))))
abline(h = cutoff, lty = 2)
identify(cooks, n = 1)
mod1.omit5 <- update(mod1, subset = c(-5))
coef(mod1)
coef(mod1.omit5)
# -------------------------------------------------------------------------
# Slides 2, pg. 58
#- Dados
store <- read.csv("~/caminho/para/o/arquivo/store.txt", sep = "")
head(store)
dim(store) # 110 x 6
#- Ajuste
mod1 <- glm(nclientes ~ I(domic/1E3) + I(renda/1E3) + idade + distconc
+ distloja, family = poisson(link = "log"), data = store)
summary(mod1)
#- Diagnostico
res <- residuals2(mod1, standardized = TRUE)
plot(res)
abline(h = 0, lty = 2)
acf(res)
eta <- mod1$linear.predictors
plot(eta, res)
abline(h = 0, lty = 2)
plot(store$domic/1E3, res)
abline(h = 0, lty = 2)
plot(store$renda/1E3, res)
abline(h = 0, lty = 2)
plot(store$idade, res)
abline(h = 0, lty = 2)
z <- resid(mod1, type = "working") + eta
plot(z, eta)
abline(0, 1)
envelope(mod1, standardized = TRUE)
p <- ncol(model.matrix(mod1))
n <- nrow(model.matrix(mod1))
cutoff <- qf(0.5, p, n - p); cutoff
cooks <- cooks.distance(mod1) # distancia de Cook
plot(cooks, type = "h", ylim = c(0, max(cutoff, max(cooks))))
abline(h = cutoff, lty = 2)
# -------------------------------------------------------------------------
# Slides 3, pg. 59
#- Dados
pesca <- read.csv("~/caminho/para/o/arquivo/pesca.txt", sep = "")
head(pesca)
dim(pesca)
plot(density(pesca$cpue), xlab = "CPUE (kg/dias pesca)", ylab = "Densidade", main = "")
#- Ajuste
pesca$ano <- factor(pesca$ano)
pesca$trimestre <- factor(pesca$trimestre)
mod1 <- glm(cpue ~ latitude + longitude + ano + trimestre + frota,
family = Gamma(link = "log"), data = pesca)
summary(mod1)
mod2 <- glm(cpue ~ latitude + ano + trimestre + frota,
family = Gamma(link = "log"), data = pesca)
summary(mod2)
mod3 <- glm(cpue ~ latitude + frota,
family = Gamma(link = "log"), data = pesca)
summary(mod3)
#- Diagnostico
res <- residuals2(mod3, standardized = TRUE)
plot(res)
abline(h = 0, lty = 2)
acf(res)
eta <- mod3$linear.predictors
plot(eta, res)
abline(h = 0, lty = 2)
plot(pesca$latitude, res)
abline(h = 0, lty = 2)
z <- resid(mod3, type = "working") + eta
plot(z, eta)
abline(0, 1)
envelope(mod3, standardized = TRUE)
p <- ncol(model.matrix(mod3))
n <- nrow(model.matrix(mod3))
cutoff <- qf(0.5, p, n - p); cutoff
cooks <- cooks.distance(mod3) # distancia de Cook
plot(cooks, type = "h", ylim = c(0, max(cutoff, max(cooks))))
abline(h = cutoff, lty = 2)
Raw
store.txt
nclientes domic renda idade distconc distloja
9 606 41393 3 3.04 6.32
6 641 23635 18 1.95 8.89
28 505 55475 27 6.54 2.05
11 866 64646 31 1.67 5.81
4 599 31972 7 0.72 8.11
4 520 41755 23 2.24 6.81
0 354 46014 26 0.77 9.27
14 483 34626 1 3.51 7.92
16 1034 85207 13 4.23 4.40
13 456 33021 32 3.07 6.03
9 19 39198 22 2.96 6.09
14 530 38794 5 2.77 6.08
5 337 30855 1 1.33 9.86
9 586 28852 7 2.98 8.64
9 1113 120065 9 3.58 5.26
7 525 32229 3 1.27 7.56
4 377 36828 15 1.92 8.91
26 1127 90302 26 5.83 1.74
32 877 51707 27 5.19 3.66
26 1007 89860 55 5.03 2.03
11 657 60513 32 4.38 8.30
12 302 42191 54 3.41 5.21
3 603 28736 41 0.34 8.29
15 556 49129 33 4.78 3.89
12 635 29308 42 2.53 6.17
9 386 26734 14 4.99 9.70
14 1011 57862 54 4.60 3.94
10 925 70030 36 4.58 8.66
22 898 46027 44 3.03 5.60
8 731 32202 43 5.15 9.67
3 584 32871 13 1.47 8.02
11 439 29564 18 3.67 5.10
2 153 46806 21 0.84 9.18
6 1069 59805 22 2.50 9.43
11 443 42555 53 2.62 5.75
10 392 36998 7 1.03 7.74
0 828 85664 4 1.30 9.66
15 159 21238 4 2.98 8.66
9 830 47972 40 2.28 9.26
16 234 33246 26 3.95 4.61
29 1004 45927 24 4.90 2.69
6 643 58315 8 0.78 6.26
26 741 69177 9 6.61 0.87
13 306 40886 27 4.53 2.68
0 180 44588 14 0.88 9.38
8 644 47347 35 2.94 7.69
8 109 31791 9 4.37 9.31
21 809 42740 17 4.10 4.75
12 722 59175 35 2.38 5.09
26 1006 48862 48 5.04 2.21
3 786 54678 20 3.59 8.52
7 1041 59835 40 1.68 7.59
5 524 51756 39 0.57 9.10
9 725 34817 18 1.88 7.96
13 482 29942 14 3.17 6.91
28 666 68684 25 5.78 2.55
10 450 64790 3 4.35 6.03
12 667 58535 25 2.78 5.59
6 921 42919 13 2.48 7.69
11 412 40722 32 2.47 9.43
12 526 42120 30 4.29 6.15
11 523 28647 43 2.69 7.54
9 1066 61464 40 1.15 8.25
8 1001 70136 29 2.58 9.67
9 669 34595 38 4.06 8.78
8 582 30878 58 1.91 6.86
6 872 39366 52 0.73 8.67
6 758 61563 31 3.08 8.33
15 782 38412 26 2.72 6.71
15 551 41045 2 3.62 7.45
12 201 23864 43 4.80 8.74
10 730 38647 9 0.67 7.92
8 738 58387 13 2.01 6.60
3 469 37242 40 1.42 8.37
10 898 38337 32 2.63 9.56
10 780 68201 5 4.12 6.69
15 622 41066 46 4.48 4.10
6 391 40873 19 1.67 6.90
9 531 54655 40 2.32 5.69
21 566 49826 1 3.06 4.03
13 410 29013 50 2.68 7.58
8 719 78082 31 2.70 4.89
6 684 57506 51 2.13 8.31
8 865 47118 46 2.17 9.06
21 1031 72373 48 6.27 1.75
7 862 67787 1 2.10 8.63
19 758 40305 15 3.95 5.58
13 1141 50026 45 2.79 6.18
24 1289 98701 8 5.87 2.73
7 674 58195 54 4.30 6.40
3 683 47991 57 1.54 9.52
8 650 63123 15 3.17 9.46
9 406 39051 29 3.11 9.62
18 966 114633 38 6.33 2.22
12 1103 55773 44 4.58 8.68
8 312 43393 41 2.25 6.43
16 787 61765 53 5.39 3.37
5 416 33348 48 1.48 7.66
8 528 44541 31 4.91 9.67
11 919 40795 8 2.97 7.79
12 482 55972 9 2.91 5.85
14 781 33140 30 1.42 5.71
17 120 19673 21 2.65 6.25
17 693 36190 6 4.70 9.54
6 348 25768 42 1.43 7.11
15 780 53974 47 4.21 6.41
10 752 71814 1 3.13 5.47
6 817 54429 47 1.90 9.90
4 268 34022 54 1.20 9.51
6 519 52850 43 2.92 8.62
Raw
turbina.txt
tipo tempo
1 3.03
1 5.53
1 5.60
1 9.30
1 9.92
1 12.51
1 12.95
1 15.21
1 16.04
1 16.84
2 3.19
2 4.26
2 4.47
2 4.53
2 4.67
2 4.69
2 5.78
2 6.79
2 9.37
2 12.75
3 3.46
3 5.22
3 5.69
3 6.54
3 9.16
3 9.40
3 10.19
3 10.71
3 12.58
3 13.41
4 5.88
4 6.74
4 6.90
4 6.98
4 7.21
4 8.14
4 8.59
4 9.80
4 12.28
4 25.46
5 6.43
5 9.97
5 10.39
5 13.55
5 14.45
5 14.72
5 16.81
5 18.39
5 20.84
5 21.51
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