## Idg.pl

Package ‘NRAIA'
Title Data sets from Nonlinear Regression Analysis and Its Applications''
Maintainer Douglas Bates <

[email protected]>
Author R port by Douglas Bates <

[email protected]>
Description Datasets from Bates and Watts (1988) Nonlinear Regression
Analysis and Its Applications'' with sample code.

Depends lattice, stats
License GPL (>= 2)
Date/Publication 2011-04-09 07:48:41
R topics documented:
Biochemical Oxygen Demand
The BOD2 data frame has 8 rows and 2 columns giving the biochemical oxygen demand versus timein an evaluation of water quality.

This data frame contains the following columns:
Time A numeric vector giving the time of the measurement (days).

demand A numeric vector giving the biochemical oxygen demand (mg/l).

Bates and Watts (1998), Nonlinear Regression Analysis and Its Applications, Wiley, (AppendixA4.1).

Originally from Marske (1967), M.Sc. Thesis, University of Wisconsin - Madison.

# simplest form of fitting a first-order model to these data
(fm1 <- nls(demand A*(1-exp(-exp(lrc)*Time)), data = BOD2,
start = c(A = 2.2, lrc = log(0.25))))
# using the plinear algorithm
(fm2 <- nls(demand (1-exp(-exp(lrc)*Time)), data = BOD2,
start = c(lrc = log(0.25)), algorithm = "plinear", trace = TRUE))
# using a self-starting model
(fm3 <- nls(demand SSasympOrig(Time, A, lrc), data = BOD2))
plotfit(fm3, xlab = "Time (days)",
ylab = "Biochemical Oxygen Demand")
Chloride ion concentrations
The Chloride data frame has 54 rows and 2 columns representing measurements of the chlorideion concentration in blood cells suspended in a salt solution.

This data frame contains the following columns:
conc A numeric vector giving the chloride ion concentration (%).

Time A numeric vector giving the time of the concentration measurement (min).

There is a noticeable serial correlation in the residuals from a fit of a simple asymptotic regressionmodel to these data, as described in section 3.8 of Bates and Watts (Wiley, 1988). We can eitheruse a modified model with nls, as described in the reference, or model it directly with the gnlsfunction.

Bates and Watts (1998), Nonlinear Regression Analysis and Its Applications, Wiley (AppendixA4.1).

Originally from Sredni (1970), Ph.D. Thesis, University of Wisconsin - Madison.

## Fit nonlinear regression model
(fm1 <- nls(conc Asym*(1 - prop*exp(-exp(lrc)*Time)), data = Chloride,
start = c(Asym = 50, prop = 0.6, lrc = log(0.25)), trace = TRUE))
plotfit(fm1, xlab = "Time (min)", ylab = "Chloride ion concentration (%)")
# plot shows patterns in the residuals
xlab = "Least squares fitted values",
ylab = "Least squares residuals",
main = "Residuals from least squares fit")
abline(h = 0, lty = 2, lwd = 0)
xlab = "Least squares residual",
ylab = "Lagged least squares residual",
main = "Lag plot of least squares residuals")
abline(h = 0, lty = 2, lwd = 0)
abline(v = 0, lty = 2, lwd = 0)
## Use conditional linearity in another formulation of the model
(fm2 <- nls(conc cbind(1, exp(-exp(lrc)*Time)), data = Chloride,
start = c(lrc = log(0.25)), algorithm = "plinear", trace = TRUE))
## Using a self-Starting model in yet another formulation
(fm3 <- nls(conc SSasympOff(Time, Asym, c0, lrc), data = Chloride))
Coal liquefaction data
The Coal data frame has 23 rows and 20 columns of data on a coal liquefaction process.

This data frame contains the following columns:
Time the time of the observation, measured from the beginning of the run (min).

temp the temperature of the run (K).

pressure the pressure at which the run was performed (MPa).

fe2o3 iron oxide? (Fe2 O3) concentration in the run (wt% maf).

tr transfer rate of the feed (wt% maf).

x1 inlet composition of unconverted coal (wt %).

x2 inlet composition of thermal residuals (wt %).

x3 inlet composition of C4-822K (wt %).

x4 inlet composition of C1-C3 gases (wt %).

x5 inlet composition of byproduct gases (wt %).

x6 inlet composition of water (wt %).

x7 inlet composition of hydrogen (wt %).

x8 inlet composition of Coal (wt %).

y1 outlet composition of unconverted coal (wt %).

y2 outlet composition of thermal residuals (wt %).

y3 outlet composition of C4-822K (wt %).

y4 outlet composition of C1-C3 gases (wt %).

y5 outlet composition of byproduct gases (wt %).

y6 outlet composition of water (wt %).

y7 outlet composition of hydrogen (wt %).

Bates and Watts (1998), Nonlinear Regression Analysis and Its Applications, Wiley (AppendixA4.7).

Originally from Lythgoe (1986), M.Sc. Thesis, Queen's University at Kingston.

x8s <- with(Coal, equal.count(x8))
xyplot( y1 x1 x8s * Time, Coal, type = c("g","p"))xyplot( y2 x2 x8s * Time, Coal, type = c("g","p"))xyplot( y3 x3 x8s * Time, Coal, type = c("g","p"))xyplot( y4 x4 x8s * Time, Coal, type = c("g","p"))xyplot( y5 x5 x8s * Time, Coal, type = c("g","p"))xyplot( y6 x6 x8s * Time, Coal, type = c("g","p"))xyplot( y7 x7 x8s * Time, Coal, type = c("g","p"))
Ethyl Acrylate data
The Ethyl data frame has 12 rows and 3 columns of ethyl acrylate concentrations in exhalate of arat.

This data frame contains the following columns:
start start of collection period, measured from the start of the experiment (hr).

length duration of the collection period (hr).

CO2 exhaled radioactively tagged CO2 (g).

Bates and Watts (1998), Nonlinear Regression Analysis and Its Applications, Wiley (AppendixA1.10).

Originally from Watts, deBethizy, and Stiratelli (1986), Technical Report, Rohm and Haas Co.

xyplot(cumsum(CO2) I(start + length), # compare to Figure 3.10, page 97
data = Ethyl, type = c("g","S"), scales=list(x=list(log =2)),
xlab = "Time (hr)",
ylab = expression(plain("Normalized cumulative CO")[2]*(g)))
Isomerization data
The Isom data frame has 24 rows and 4 columns from an isomerization experiment.

This data frame contains the following columns:
hyd partial pressure of hydrogen (psia).

n.pent partial pressure of n-pentane (psia).

iso.pen partial pressure of isopentane (psia).

rate reaction rate for isomerization of n-pentane to isopentane (1/hr).

These are data on the reaction rate of catalytic isomerization of n-pentane to isopentane.

Bates and Watts (1998), Nonlinear Regression Analysis and Its Applications, Wiley (AppendixA1.5).

Originally from Carr (1960), Industrial and Engineering Chemistry, 52, pp. 391-396.

splom(Isom, main = "Isom data")
xyplot(rate hyd, data = Isom, type = c("g", "p"),
xlab = "Hydrogen partial pressure (psia)",
ylab = expression(plain("Reaction rate (hr") {-1}*plain(")")))
xyplot(rate n.pent, data = Isom, type = c("g", "p"),
xlab = "n-pentane partial pressure (psia)",
ylab = expression(plain("Reaction rate (hr") {-1}*plain(")")))
xyplot(rate iso.pen, data = Isom, type = c("g", "p"),
xlab = "iso-pentane partial pressure (psia)",
ylab = expression(plain("Reaction rate (hr") {-1}*plain(")")))
## Note - the model is mis-stated on page 272, x2 and x3 are reversed
nls(rate b3*(n.pent - iso.pen/1.632)/(1+b2*hyd+b3*n.pent+b4*iso.pen),
data = Isom, start = c(b2 = 0.1, b3 = 0.1, b4 = 0.1),
algorithm = "plinear", trace = TRUE)
# compare to Table 2.2, page 56
The Leaves data frame has 15 rows and 2 columns of leaf length over time.

This data frame contains the following columns:
Time time from initial emergence (days).

Length leaf length (cm).

Bates and Watts (1998), Nonlinear Regression Analysis and Its Applications, Wiley (AppendixA4.5).

Originally from Heyes and Brown (1956) in F.L. Milthorpe (ed), The Growth of Leaves, London:Butterworth.

options(show.signif.stars = FALSE)
## first fit a logistic model
fm1 <- nls(Length SSlogis(Time, Asym, xmid, scal), data = Leaves)
plotfit(fm1, xlab = "Time from initial emergence (days)",
ylab = "Leaf length (cm)", main = "Logistic growth model")
## compare with Richards growth model
fm2 <- nls(Length Asym/(1+exp(-(Time - xmid)/scal)) exp(-lpow), Leaves,
c(coef(fm1),c(lpow = 0)))
plotfit(fm2, xlab = "Time from initial emergence (days)",
ylab = "Leaf length (cm)", main = "Richards growth model")
pm1 <- profile(fm1)
plot(pm1, aspect = 'xy', layout = c(3,1))
plot(pm1, absVal = FALSE, aspect = 'xy', layout = c(3,1))
pm2 <- profile(fm2, alpha = 0.05)
plot(pm2, aspect = 'xy', layout = c(4,1))
plot(pm2, absVal = FALSE, aspect = 'xy', layout = c(4,1))
The Lipo data frame has 12 rows and 2 columns of lipoprotein concentrations over time.

This data frame contains the following columns:
time a numeric vector giving the time of the concentration measurement (hr)
conc a numeric vector of concentrations.

Bates and Watts (1998), Nonlinear Regression Analysis and Its Applications, Wiley (AppendixA4.1).

plot(conc time, data = Lipo,
xlab = "Time since drug administration (hr)",
ylab = "Lipoprotein concentration",
main = "Lipo data and fitted curve", las = 1)
fm1 <- nls(conc SSbiexp(time, A1, lrc1, A2, lrc2), data = Lipo)
usr <- par("usr")
xx <- seq(usr[1], usr[2], len = 51)
lines(xx, predict(fm1, list(time = xx)))
title(sub = deparse(fm1$call$formula))
Viscosity of lubricants
The Lubricant data frame has 53 rows and 3 columns on the viscosity of a lubricant at differentpressures and temperatures.

This data frame contains the following columns:
pressure a numeric vector of pressures (stokes).

viscos a numeric vector of observed log(kinematic viscosity).

tempC a numeric vector of temperatures (degrees Celsius).

Bates and Watts (1998), Nonlinear Regression Analysis and Its Applications, Wiley (AppendixA1.5).

tempf <- as.factor(Lubricant$tempC)
xyplot(viscos pressure, Lubricant, groups = tempf,
xlab = "Pressure (atm)", type = c("g", "p"),
ylab = "kinematic viscosity (stokes)",
scales = list(y = list(log = 2)),
auto.key = list(space = "top", columns = 4))
Nitrendipene data
The Nitren data frame has 26 rows and 5 columns from an experiment in cardiology.

This data frame contains the following columns:
log.NIF a numeric vector giving the log of the NIF concentration
tiss1 a numeric vector giving the reaction in tissue 1.

tiss2 a numeric vector giving the reaction in tissue 2.

tiss3 a a numeric vector giving the reaction in tissue 3.

tiss4 a numeric vector giving the reaction in tissue 4.

Bates and Watts (1998), Nonlinear Regression Analysis and Its Applications, Wiley (AppendixA1.5).

matplot(Nitren[, 1], Nitren[, -1], las = 1,
xlab = "log(NIF concentration)",
ylab = "reaction level",
main = paste("Nitren data and fitted curves,",
"omitting zero concentration data"))
## without the data at NIF concentration of zero
options(na.action = na.omit)
fm1 <- nls(tiss1 SSfpl(log.NIF, A, B, xmid, scal), Nitren)
fm2 <- nls(tiss2 SSfpl(log.NIF, A, B, xmid, scal), Nitren)
fm3 <- nls(tiss3 SSfpl(log.NIF, A, B, xmid, scal), Nitren)
fm4 <- nls(tiss4 SSfpl(log.NIF, A, B, xmid, scal), Nitren)
usr <- par("usr")
xx <- seq(usr[1], usr[2], len = 50)
lines(xx, predict(fm1, list(log.NIF = xx)), col = 1, lty = 2)
lines(xx, predict(fm2, list(log.NIF = xx)), col = 2, lty = 2)
lines(xx, predict(fm3, list(log.NIF = xx)), col = 3, lty = 2)
lines(xx, predict(fm4, list(log.NIF = xx)), col = 4, lty = 2)
title(sub = deparse(fm1$call$formula))
## replacing the data at NIF concentration of zero by a very small value
log.NIF <- Nitren[, 1]
log.NIF[ is.na(log.NIF) ] <- -18
Nitren[, 1] <- log.NIF
matplot(Nitren[, 1], Nitren[, -1], las = 1,
xlab = "log(NIF concentration)",
ylab = "reaction level",
main = paste("Nitren data and fitted curves",
"- zero concentration recoded as -18"))
fm1 <- nls(tiss1 SSfpl(log.NIF, A, B, xmid, scal), Nitren)
fm2 <- nls(tiss2 SSfpl(log.NIF, A, B, xmid, scal), Nitren)
fm3 <- nls(tiss3 SSfpl(log.NIF, A, B, xmid, scal), Nitren)
fm4 <- nls(tiss4 SSfpl(log.NIF, A, B, xmid, scal), Nitren)
usr <- par("usr")
xx <- seq(usr[1], usr[2], len = 50)
lines(xx, predict(fm1, list(log.NIF = xx)), col = 1, lty = 2)
lines(xx, predict(fm2, list(log.NIF = xx)), col = 2, lty = 2)
lines(xx, predict(fm3, list(log.NIF = xx)), col = 3, lty = 2)
lines(xx, predict(fm4, list(log.NIF = xx)), col = 4, lty = 2)
title(sub = deparse(fm1$call$formula))
Nitrite utilization by bean leaves
The Nitrite data frame has 48 rows and 3 columns giving nitrite utilization by bean leaves underdifferent light conditions on two different days.

This data frame contains the following columns:
light a numeric vector of light intensities.

utilization a numeric vector of nitrite utilizations.

day a factor with levels 1 2
Bates and Watts (1998), Nonlinear Regression Analysis and Its Applications, Wiley (AppendixA1.10).

xyplot(utilization light, Nitrite, groups = day,
xlab = "Light intensity", type = c("a", "g", "p"),
ylab = "Nitrite utilization",
auto.key = list(space = "top", columns = 2))
O-xylene reaction data
The O.xylene data frame has 57 rows and 4 columns of data on a chemical engineering experi-ment.

This data frame contains the following columns:
oxygen a numeric vector giving the oxygen partial pressure.

o.xyl a numeric vector giving the O.xylene partial pressure.

temp a numeric vector giving the temperature (Kelvins).

rate a numeric vector giving the rate of reaction.

Bates and Watts (1998), Nonlinear Regression Analysis and Its Applications, Wiley (AppendixA1.6).

tempf <- with(O.xylene, ordered(temp))
levels(tempf) <- paste(levels(tempf), "K")
Oxygen <- with(O.xylene, equal.count(oxygen))
O.xyl <- with(O.xylene, equal.count(o.xyl))
xyplot(rate o.xyl Oxygen * tempf, O.xylene,
type = c("g", "p"), aspect = 'xy',
xlab = "O.xylene partial pressure",
ylab = "Reaction rate")
xyplot(rate o.xyl Oxygen, O.xylene, groups = tempf,
type = c("g", "p"), aspect = 2.5,
xlab = "O.xylene partial pressure",
ylab = "Reaction rate",
auto.key = list(space = "right"))
xyplot(rate oxygen O.xyl, O.xylene, groups = tempf,
type = c("g", "p"), aspect = 2.5,
xlab = "Oxygen partial pressure",
ylab = "Reaction rate",
auto.key = list(space = "right"))
Pyrolysis of Oil Shale
The Oilshale data frame has 64 rows and 4 columns from an experiment on the pyrolysis of oilshale.

This data frame contains the following columns:
time a numeric vector giving the time since the beginning of the experiment.

bitumen a numeric vector giving the proportion of bitumen.

oil a numeric vector giving the proportion of oil.

temp a numeric vector giving the temperature of the run.

Bates and Watts (1998), Nonlinear Regression Analysis and Its Applications, Wiley (AppendixA1.5).

PCB concentrations in Lake Cayuga fish
The PCB data frame has 28 rows and 2 columns giving the concentration of polychlorinated biphenyls(PCB's) in fish caught in Lake Cayuga in northern New York state. The fish had been tagged asyearlings so their ages could be accurately determined.

This data frame contains the following columns:
age a numeric vector giving the age of the fish in years.

conc a numeric vector giving the concentration of PCB's in the fish.

Bates and Watts (1998), Nonlinear Regression Analysis and Its Applications, Wiley (AppendixA1.1).

# compare to Figure 1.1 (p. xxx)
xyplot(conc age, PCB, aspect = 'xy',
type = c("g", "p"), xlab = "Age of fish (yr)",
ylab = "PCB concentration")
# compare to Figure 1.2 (p. xxx)
xyplot(conc age, PCB, scales = list(y = list(log = 2)),
aspect = 'xy', type = c("g", "p", "smooth"),
xlab = "Age of fish (yr)",
ylab = "PCB concentration")
# linear model in cube root of age
summary(fm1 <- lm(log(conc) I(age (1/3)), data = PCB))
xyplot(log(conc) I(age (1/3)), data = PCB, aspect = 'xy',
xlab = "Cube root of age (yr)", type = c("g", "p", "r"),
ylab = "log(PCB concentration)",
main = "Transformed PCB data and fitted line",
sub = deparse(fm1$call$formula))
# diagnostic plots
opar <- par(mfrow = c(2, 2))
plot(fm1, which = 1:4, las = 1)
Alpha-pinene and by-products
The Pinene data frame has 8 rows and 6 columns giving the proportion of alpha-pinene and fourof its by-products over time.

This data frame contains the following columns:
time a numeric vector giving the time at which the observation is made. (hours)
a.pin a numeric vector giving the alpha-pinene proportion. (%)
dipen a numeric vector giving the dipene proportion. (%)
alloo a numeric vector giving the allo-ocimene proportion. (%)
pyron a numeric vector giving the pyronene proportion. (%)
dimer a numeric vector giving the dimer proportion. (%)
Bates and Watts (1998), Nonlinear Regression Analysis and Its Applications, Wiley (AppendixA1.6).

xyplot(a.pin + dipen + alloo + pyron + dimer time, Pinene,
type = c("b", "g"), aspect = 'xy',
xlab = "Time (hr)", ylab = "Proportion (%)",
auto.key = list(space = "right", lines = TRUE))
Alpha-pinene and by-products
The Pinene data frame has 8 rows and 6 columns giving the proportion of alpha-pinene and fourof its by-products over time from a second experiment.

This data frame contains the following columns:
time a numeric vector giving the time at which the observation is made. (hr)
a.pin a numeric vector giving the alpha-pinene proportion. (%)
dipen a numeric vector giving the dipene proportion. (%)
alloo a numeric vector giving the allo-ocimene proportion. (%)
pyron a numeric vector giving the pyronene proportion. (%)
dimer a numeric vector giving the dimer proportion. (%)
Bates and Watts (1998), Nonlinear Regression Analysis and Its Applications, Wiley (AppendixA1.6).

xyplot(a.pin + dipen + alloo + pyron + dimer time, Pinene2,
type = c("b", "g"), aspect = 'xy',
xlab = "Time (hr)", ylab = "Proportion (%)",
auto.key = list(space = "right", lines = TRUE))
Plot x-y data and a fitted model
Extract the original data from a fitted model and plot these data along with a smooth curve of thefitted model function. The fitted model must be for one covariate only.

## S3 method for class 'nls'
A fitted model object, typically a nls fitted model.

Arguments to be passed to or
A lattice object.

fm1 <- nls(rate conc/(K + conc), Puromycin, c(K = 0.05),
subset = state == "treated", alg = "plinear")
plotfit(fm1, from = 0)
Count Rumford's cooling data
The Rumford data frame has 13 rows and 2 columns from an experiment by Count Rumford onthe rate of cooling.

This data frame contains the following columns:
time a numeric vector giving the time since the beginning of the experiment (hr).

temp a numeric vector giving the temperature (degrees Fahrenheit) of the cannon.

Bates and Watts (1998), Nonlinear Regression Analysis and Its Applications, Wiley (AppendixA1.5).

plot(temp time, Rumford, las = 1,
xlab = "Time since beginning of experiment (hr)",
ylab = "Temperature of cannon (degrees F)",
main = "Rumford data and fitted curve")
fm1 <- nls(temp 60 + 70 * exp(tc * time), data = Rumford,
start = c(tc = -0.01))
usr <- par("usr")
xx <- seq(usr[1], usr[2], len = 50)
lines(xx, predict(fm1, list(time = xx)))
Pharmacokinetics of saccharin
The Sacch2 data frame has 10 rows and 2 columns from an experiment on the pharmacokineticsof saccharin.

This data frame contains the following columns:
time a numeric vector giving the time since drug administration (min).

conc a numeric vector giving the observed concentration of saccharin.

Bates and Watts (1998), Nonlinear Regression Analysis and Its Applications, Wiley (AppendixA1.5).

xyplot(conc time, Sacch2, type = c("g", "b"),
xlab = "Time since drug administration (min)",
ylab = "Saccharin concentration", aspect = "xy")
xyplot(conc time, data = Sacch2, type = c("g", "b"),
scales = list(y = list(log = 2)), aspect = 'xy',
xlab = "Time since drug administration (min)",
ylab = "Saccharin concentration")
fm1 <- nls(conc SSfol(1.0, time, lKe, lKa, lCl), data = Sacch2)
xpred <- seq(0, 140, len = 51)
ypred <- predict(fm1, list(time = xpred, Dose = rep(1.0, length(xpred))))
lines(xpred, ypred)
Elimination of saccharin
The Saccharin data frame has 9 rows and 3 columns from an experiment on the elimination ofsaccharin.

This data frame contains the following columns:
start start of collection period, measured from the start of the experiment (hr).

length duration of the collection period (hr).

sacch exhaled radioactively tagged CO2 (g).

Bates and Watts (1998), Nonlinear Regression Analysis and Its Applications, Wiley (AppendixA1.5).

xyplot(cumsum(sacch) I(start + length), Saccharin,
type = c("g", "S"), scales = list(x = list(log = 2)),
xlab = "Time (hr)", ylab = "Cumulative saccharin")
The sPMMA data frame has 23 rows and 3 columns from an experiment on the dielectric responseof a sample of syndiotactic poly-methyl-methacrylate (sPMMA).

This data frame contains the following columns:
freq a numeric vector giving the frequency of the driving signal (Hz).

real a numeric vector giving the real component of the dielectric response.

imag a numeric vector giving the imaginary component of the dielectric response.

Bates and Watts (1998), Nonlinear Regression Analysis and Its Applications, Wiley (AppendixA1.5).

xyplot(imag real, data = sPMMA, xlab = "Real component",
ylab = "Imaginary component", type = c("p", "g"))
xyplot(real + imag freq, data = sPMMA, xlab = "Frequency (Hz)",
ylab = "Component of dielectric response",
main = "sPMMA data", type = c("g", "p"), aspect = 'xy',
auto.key = list(space = "right"))
Richards Growth Model
This selfStart model evaluates the Richards growth model function and its gradient. It has aninitial attribute that creates initial estimates of the parameters Asym, xmid, scal and lpow.

SSRichards(input, Asym, xmid, scal, lpow)
a numeric vector of values at which to evaluate the model.

a numeric parameter representing the asymptote.

a numeric parameter representing the x value at the inflection point of the curve.

The value of SSlogis will be Asym/2 at xmid.

a numeric scale parameter on the input axis.

the natural logarithm of the inverse of the power to which the denominator israised.

a numeric vector of the same length as input. It is the value of the expression Asym*(1+exp((xmid-input)/scal)) (-exp(-lpow)). If all of the arguments Asym, xmid, scal and lpow arenames of objects, the gradient matrix with respect to these names is attached as an attribute namedgradient.

summary(fm1 <- nls(Length SSRichards(Time, Asym, xmid, scal, lpow), Leaves))
Pharmacokinetics of sulfisoxazole
The Sulfi data frame has 12 rows and 2 columns from an experiment on the pharmacokinetics ofsulfisoxazole.

This data frame contains the following columns:
time a numeric vector giving the time since drug administration (min).

conc a numeric vector giving the observed concentration of sulfisoxazole (µg/ml).

Bates and Watts (1998), Nonlinear Regression Analysis and Its Applications, Wiley (AppendixA1.5).

plot(conc time, data = Sulfi, las = 1,
xlab = "Time since drug administration (min)",
ylab = expression(plain("Sulfisoxazole concentration (")
main = "Sulfisoxazole data and fitted curve")
fm1 <- nls(conc SSbiexp(time, A1, lrc1, A2, lrc2),
usr <- par("usr")
xx <- seq(usr[1], usr[2], len = 50)
lines(xx, predict(fm1, list(time = xx)))
plot(conc time, data = Sulfi, las = 1, log = "y",
xlab = "Time since drug administration (min)",
ylab = expression(plain("Sulfisoxazole concentration (")
main = "Sulfisoxazole data (log scale)")
lines(xx, predict(fm1, list(time = xx)))
The Tetra data frame has 9 rows and 2 columns from an experiment on the pharmacokinetics oftetracycline.

This data frame contains the following columns:
time a numeric vector of time since drug administration (hr).

conc a numeric vector of tetracycline concentrations.

Bates and Watts (1998), Nonlinear Regression Analysis and Its Applications, Wiley (AppendixA1.5).

plot(conc time, data = Tetra, las = 1,
xlab = "Time since drug administration (hr)",
ylab = "concentration",
main = "Tetracycline data with fitted curve")
fm1 <- nls(conc SSfol(1.0, time, lKe, lKa, lCl), Tetra)
usr <- par("usr")
xx <- seq(usr[1], usr[2], len = 101)
lines(xx, predict(fm1, list(time = xx)))
∗Topic datasets
Nitren, Nitrite,
panel.curve, 15, 16
Pinene2, Rumford,
Sacch2, Saccharin,
∗Topic nonlinear
∗Topic regression

Source: http://www.idg.pl/mirrors/CRAN/web/packages/NRAIA/NRAIA.pdf

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