23 files changed, 397 insertions, 24 deletions
diff --git a/.Rbuildignore b/.Rbuildignore
index f84e599..7fdd16c 100644
--- a/.Rbuildignore
+++ b/.Rbuildignore
@@ -11,3 +11,5 @@ experimental
 test.log$
 ^codecov\.yml$
 ^\.github$
+^.*\.Rproj$
+^\.Rproj\.user$
diff --git a/.gitignore b/.gitignore
index b752ef4..1bee8d8 100644
--- a/.gitignore
+++ b/.gitignore
@@ -1,3 +1,6 @@
 chemCal.Rcheck
 chemCal_*.tar.gz
 experimental
+.Rproj.user
+.Rhistory
+*.Rproj
diff --git a/DESCRIPTION b/DESCRIPTION
index 2b680b9..d8a9779 100644
--- a/DESCRIPTION
+++ b/DESCRIPTION
@@ -1,10 +1,14 @@
 Package: chemCal
 Version: 0.2.3.9000
-Date: 2024-11-17
+Date: 2025-01-25
 Title: Calibration Functions for Analytical Chemistry
-Authors@R: c(person("Johannes", "Ranke", role = c("aut", "cre", "cph"), 
-                    email = "johannes.ranke@jrwb.de",
-                    comment = c(ORCID = "0000-0003-4371-6538")))
+Authors@R: c(
+  person(c("Anıl", "A."), "Tellbüscher", role = "aut",
+    comment = "Linearity tests"),
+  person("Johannes", "Ranke", role = c("aut", "cre", "cph"), 
+    email = "johannes.ranke@jrwb.de",
+    comment = c(ORCID = "0000-0003-4371-6538")))
+Depends: R (>= 3.5.0)
 Suggests: MASS, knitr, testthat, investr, covr, rmarkdown
 Description: Simple functions for plotting linear
 	calibration functions and estimating standard errors for measurements
diff --git a/NAMESPACE b/NAMESPACE
index 5f98a2a..95e274b 100644
--- a/NAMESPACE
+++ b/NAMESPACE
@@ -11,12 +11,16 @@ S3method(loq,default)
 S3method(loq,lm)
 export(calplot)
 export(inverse.predict)
+export(linearity)
 export(lod)
 export(loq)
+importFrom(graphics,abline)
 importFrom(graphics,legend)
+importFrom(graphics,lines)
 importFrom(graphics,matlines)
 importFrom(graphics,plot)
 importFrom(graphics,points)
+importFrom(stats,median)
 importFrom(stats,optimize)
 importFrom(stats,predict)
 importFrom(stats,qt)
diff --git a/NEWS.md b/NEWS.md
index 5e86e24..a680498 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -1,3 +1,7 @@
+# chemCal 0.2.3.9000
+
+- 'R/linearity.R', 'data/din38402*.rda': Add linearity tests and data from DIN 38402 using a pull request by Anil Axel Tellbüscher
+
 # chemCal 0.2.3
 
 - Make the use of the 'investr' package conditional in testthat tests, update maintainer e-mail address
diff --git a/R/chemCal-package.R b/R/chemCal-package.R
index 8cc8c76..54ab190 100644
--- a/R/chemCal-package.R
+++ b/R/chemCal-package.R
@@ -54,7 +54,7 @@
 #' # LQ = 3.04 * LC (Currie 1999, p. 120)
 #' 3.04 * lod(m, alpha = 0.01, beta = 0.5)$x
 #' 
-NULL
+"din32645"
 
 
 
@@ -72,7 +72,7 @@ NULL
 #' Lewi, P.J., Smeyers-Verbeke, J. (1997) Handbook of Chemometrics and
 #' Qualimetrics: Part A, Chapter 8.
 #' @keywords datasets
-NULL
+"massart97ex1"
 
 
 
@@ -128,7 +128,7 @@ NULL
 #' # of 15, but the graphical procedure of Massart (p. 201) to derive the 
 #' # variances on which the weights are based is quite inaccurate anyway. 
 #' 
-NULL
+"massart97ex3"
 
 
 
@@ -147,7 +147,7 @@ NULL
 #' @source Rocke, David M. und Lorenzato, Stefan (1995) A two-component model
 #' for measurement error in analytical chemistry. Technometrics 37(2), 176-184.
 #' @keywords datasets
-NULL
+"rl95_cadmium"
 
 
 
@@ -167,7 +167,7 @@ NULL
 #' @source Rocke, David M. und Lorenzato, Stefan (1995) A two-component model
 #' for measurement error in analytical chemistry. Technometrics 37(2), 176-184.
 #' @keywords datasets
-NULL
+"rl95_toluene"
 
 
 
@@ -188,7 +188,81 @@ NULL
 #' Toronto.
 #' \url{https://sites.chem.utoronto.ca/chemistry/coursenotes/analsci/stats/index.html}
 #' @keywords datasets
-NULL
+"utstats14"
 
 
 
+
+
+#' Nitrite calibration data
+#' 
+#' Example dataset B.1 from DIN 38402 with concentrations in µg/L and the extinction
+#' as response measured using continuous flow analysis (CFA) according to 
+#' ISO 13395.
+#' 
+#' @name din38402b1
+#' @docType data
+#' @format A tibble containing 12 concentration levels with the respective 
+#' instrument response values.
+#' @references DIN 38402-51:2017-05, Beuth Verlag, Berlin. 
+#' https://dx.doi.org/10.31030/2657448
+#' @keywords datasets
+"din38402b1"
+
+
+
+
+
+#' Copper calibration data
+#' 
+#' Example dataset B.3 from DIN 38402. Cu was measured according to ISO 11885,
+#' using ICP-OES. The concentration are reported in mg/L and the response as 
+#' counts/s, describing the count of photons that are detected by the 
+#' photomultiplier detector of the device.
+#' 
+#' @name din38402b3
+#' @docType data
+#' @format A tibble containing 13 concentration levels and the respective 
+#' instrument response values.
+#' @references DIN 38402-51:2017-05, Beuth Verlag, Berlin. 
+#' https://dx.doi.org/10.31030/2657448
+#' @keywords datasets
+"din38402b3"
+
+
+
+
+
+#' Carbamazepin calibration data
+#' 
+#' Example dataset B.6 from DIN 38402 measured using LC-MS/MS. The 
+#' concentrations are reported in in µg/L and the response in arbitrary
+#' units (AU).
+#' 
+#' @name din38402b6
+#' @docType data
+#' @format A tibble containing 12 concentration levels and the respective 
+#' instrument response values.
+#' @references DIN 38402-51:2017-05, Beuth Verlag, Berlin. 
+#' https://dx.doi.org/10.31030/2657448
+#' @keywords datasets
+"din38402b6"
+
+
+
+
+
+#' Iron calibration data
+#' 
+#' Example dataset C.3 from DIN 38402 determined by ion chromatography.
+#' Concentrations are reported in mg/L and the extinction as response.
+#' 
+#' @name din38402c3
+#' @docType data
+#' @format A tibble containing 10 concentration levels and the respective 
+#' response values.
+#' @references DIN 38402-51:2017-05, Beuth Verlag, Berlin. 
+#' https://dx.doi.org/10.31030/2657448
+#' @keywords datasets
+"din38402c3"
+
diff --git a/R/linearity.R b/R/linearity.R
new file mode 100644
index 0000000..8a4f09b
--- /dev/null
+++ b/R/linearity.R
@@ -0,0 +1,107 @@
+#' Assess the linearity of a calibration curve
+#' 
+#' A function to create diagnostic plots for the assessment of the linearity of 
+#' calibration data based on their point-to-point slope or the curvature. 
+#' The underlying methods follow ISO 84 66-1:2021 and DIN 32 402-51:2017 
+#' (German Industrial Norm).
+#' 
+#' The point-to-point slope method is based on the assumption that the slope 
+#' between two points should not vary greatly within the linear range. 
+#' 
+#' The curvature method is similar to the point-to-point slope method. Here, 
+#' the ratio between the instrument signal and the concentration of the 
+#' calibration standard is assumed not to vary greatly within the linear range.
+#' 
+#' The use of the Mandel test is discouraged due to its limitations in the 
+#' identification of non-linear behaviour of calibration curves (Andrade and 
+#' Gomes-Carracedo, 2013). 
+#' 
+#' @param x numeric vector of independent values (usually concentrations).
+#' @param y numeric vector of dependent values (usually the signal of the 
+#' analytical device).
+#' @param method character string. Supported methods are "slope" and 
+#' "curvature".
+#' @param tolerance numeric value between 0 and 1, describing the acceptable
+#' deviation from the median of the slopes or the signal-to-concentration
+#' ratio. The default tolerance is 10%.
+#' @return returns a diagnostic plot 
+#' 
+#' @author Anıl Axel Tellbüscher
+#' 
+#' @importFrom graphics abline
+#' @importFrom graphics lines
+#' @importFrom stats median
+#' 
+#' @examples
+#' # Continuous Flow Analysis (CFA) data
+#' data(din38402b1)
+#' 
+#' # Point-to-point slope plot
+#' linearity(din38402b1$conc, din38402b1$ext, method = "slope")
+#' 
+#' # Curvature plot
+#' linearity(din38402b1$conc, din38402b1$ext, method = "curvature")
+#' 
+#' @references ISO 8466-1:2021. Water quality — Calibration and evaluation of 
+#' analytical methods — Part 1: Linear calibration function
+#' 
+#' J. M. Andrade and M. P. Gomez-Carracedo (2013) Notes on the use of 
+#' Mandel's test to check for nonlinearity in laboratory calibrations. 
+#' Analytical Methods 5(5), 1145 - 1149.
+#' 
+#' @export
+# Function to assess linearity of data using either slope or curvature method
+linearity <- function(x, y, method = c("slope", "curvature"), tolerance = 0.1) {
+  
+  # Check data integrity
+  # Ensure that x and y vectors have the same length
+  stopifnot("x and y must have the same length!" = length(x) == length(y))
+  
+  method <- match.arg(method)
+  
+  # Calculate the 'result' based on the chosen method
+  if (method == "slope") {
+    # For the 'slope' method, calculate the difference between consecutive points
+    x_diff = diff(x)        # Difference in x values
+    y_diff = diff(y)        # Difference in y values
+    result = y_diff / x_diff # Point-to-point slope (rate of change)
+  } else if (method == "curvature") {
+    # For the 'curvature' method, calculate the signal-to-concentration ratio
+    result = y / x # Element-wise division of y by x
+  }
+  
+  # Calculate the median of the results for tolerance check
+  result_median <- median(result)
+  
+  # Define upper and lower tolerance boundaries
+  upper_tolerance <- result_median + tolerance * result_median
+  lower_tolerance <- result_median - tolerance * result_median
+  
+  # Create a data frame to store the result and corresponding indices
+  df <- data.frame(result = result, index = 1:length(result))
+  
+  # Identify points that fall outside the tolerance range
+  outside_tolerance <- rbind(
+    subset(df, result > upper_tolerance), # Points above the upper tolerance
+    subset(df, result < lower_tolerance)  # Points below the lower tolerance
+  )
+  
+  # Basic scatter plot of the result against the index
+  plot(result ~ index, data = df, 
+       main = "linearity assessment", ylab = method, 
+       pch = 16)
+  
+  # Draw a line connecting all the points to visualize the trend
+  lines(df$index, df$result, col = "blue") # Blue line connecting points
+  
+  # Highlight points that are outside the tolerance range in red
+  points(x = outside_tolerance$index, y = outside_tolerance$result, 
+         pch = 16, col = "red")
+  
+  # Add a horizontal line at the median value of the result
+  abline(h = result_median, col = "red")
+  
+  # Add dashed horizontal lines at the upper and lower tolerance limits
+  abline(h = upper_tolerance, col = "red", lty = 3) # Upper tolerance
+  abline(h = lower_tolerance, col = "red", lty = 3) # Lower tolerance
+}
diff --git a/check.log b/check.log
index 60e9e39..fdc71ef 100644
--- a/check.log
+++ b/check.log
@@ -1,18 +1,19 @@
 * using log directory ‘/home/jranke/git/chemCal/chemCal.Rcheck’
-* using R version 4.1.3 (2022-03-10)
-* using platform: x86_64-pc-linux-gnu (64-bit)
+* using R version 4.4.2 (2024-10-31)
+* using platform: x86_64-pc-linux-gnu
+* R was compiled by
+    gcc (Debian 12.2.0-14) 12.2.0
+    GNU Fortran (Debian 12.2.0-14) 12.2.0
+* running under: Debian GNU/Linux 12 (bookworm)
 * using session charset: UTF-8
 * using option ‘--as-cran’
 * checking for file ‘chemCal/DESCRIPTION’ ... OK
-* this is package ‘chemCal’ version ‘0.2.3’
+* this is package ‘chemCal’ version ‘0.2.3.9000’
 * package encoding: UTF-8
-* checking CRAN incoming feasibility ... NOTE
+* checking CRAN incoming feasibility ... [3s/15s] NOTE
 Maintainer: ‘Johannes Ranke <johannes.ranke@jrwb.de>’
 
-New maintainer:
-  Johannes Ranke <johannes.ranke@jrwb.de>
-Old maintainer(s):
-  Johannes Ranke <jranke@uni-bremen.de>
+Version contains large components (0.2.3.9000)
 * checking package namespace information ... OK
 * checking package dependencies ... OK
 * checking if this is a source package ... OK
@@ -21,18 +22,18 @@ Old maintainer(s):
 * checking for hidden files and directories ... OK
 * checking for portable file names ... OK
 * checking for sufficient/correct file permissions ... OK
-* checking serialization versions ... OK
 * checking whether package ‘chemCal’ can be installed ... OK
 * checking installed package size ... OK
 * checking package directory ... OK
-* checking for future file timestamps ... OK
+* checking for future file timestamps ... NOTE
+unable to verify current time
 * checking ‘build’ directory ... OK
 * checking DESCRIPTION meta-information ... OK
 * checking top-level files ... OK
 * checking for left-over files ... OK
 * checking index information ... OK
 * checking package subdirectories ... OK
-* checking R files for non-ASCII characters ... OK
+* checking code files for non-ASCII characters ... OK
 * checking R files for syntax errors ... OK
 * checking whether the package can be loaded ... OK
 * checking whether the package can be loaded with stated dependencies ... OK
@@ -67,16 +68,16 @@ Old maintainer(s):
   Running ‘testthat.R’
  OK
 * checking for unstated dependencies in vignettes ... OK
-* checking package vignettes in ‘inst/doc’ ... OK
+* checking package vignettes ... OK
 * checking re-building of vignette outputs ... OK
 * checking PDF version of manual ... OK
+* checking HTML version of manual ... OK
 * checking for non-standard things in the check directory ... OK
 * checking for detritus in the temp directory ... OK
 * DONE
 
-Status: 1 NOTE
+Status: 2 NOTEs
 See
   ‘/home/jranke/git/chemCal/chemCal.Rcheck/00check.log’
 for details.
 
-
diff --git a/data/din38402b1.rda b/data/din38402b1.rda
new file mode 100644
index 0000000..ccaf554
--- /dev/null
+++ b/data/din38402b1.rda
diff --git a/data/din38402b3.rda b/data/din38402b3.rda
new file mode 100644
index 0000000..80e80e3
--- /dev/null
+++ b/data/din38402b3.rda
diff --git a/data/din38402b6.rda b/data/din38402b6.rda
new file mode 100644
index 0000000..def8f0e
--- /dev/null
+++ b/data/din38402b6.rda
diff --git a/data/din38402c3.rda b/data/din38402c3.rda
new file mode 100644
index 0000000..c4688ef
--- /dev/null
+++ b/data/din38402c3.rda
diff --git a/man/din32645.Rd b/man/din32645.Rd
index a8e6a31..5b9603f 100644
--- a/man/din32645.Rd
+++ b/man/din32645.Rd
@@ -7,6 +7,9 @@
 \format{
 A dataframe containing 10 rows of x and y values.
 }
+\usage{
+din32645
+}
 \description{
 Sample dataset to test the package.
 }
diff --git a/man/din38402b1.Rd b/man/din38402b1.Rd
new file mode 100644
index 0000000..2c538b8
--- /dev/null
+++ b/man/din38402b1.Rd
@@ -0,0 +1,23 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/chemCal-package.R
+\docType{data}
+\name{din38402b1}
+\alias{din38402b1}
+\title{Nitrite calibration data}
+\format{
+A tibble containing 12 concentration levels with the respective
+instrument response values.
+}
+\usage{
+din38402b1
+}
+\description{
+Example dataset B.1 from DIN 38402 with concentrations in µg/L and the extinction
+as response measured using continuous flow analysis (CFA) according to
+ISO 13395.
+}
+\references{
+DIN 38402-51:2017-05, Beuth Verlag, Berlin.
+https://dx.doi.org/10.31030/2657448
+}
+\keyword{datasets}
diff --git a/man/din38402b3.Rd b/man/din38402b3.Rd
new file mode 100644
index 0000000..83abd0f
--- /dev/null
+++ b/man/din38402b3.Rd
@@ -0,0 +1,24 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/chemCal-package.R
+\docType{data}
+\name{din38402b3}
+\alias{din38402b3}
+\title{Copper calibration data}
+\format{
+A tibble containing 13 concentration levels and the respective
+instrument response values.
+}
+\usage{
+din38402b3
+}
+\description{
+Example dataset B.3 from DIN 38402. Cu was measured according to ISO 11885,
+using ICP-OES. The concentration are reported in mg/L and the response as
+counts/s, describing the count of photons that are detected by the
+photomultiplier detector of the device.
+}
+\references{
+DIN 38402-51:2017-05, Beuth Verlag, Berlin.
+https://dx.doi.org/10.31030/2657448
+}
+\keyword{datasets}
diff --git a/man/din38402b6.Rd b/man/din38402b6.Rd
new file mode 100644
index 0000000..289ee41
--- /dev/null
+++ b/man/din38402b6.Rd
@@ -0,0 +1,23 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/chemCal-package.R
+\docType{data}
+\name{din38402b6}
+\alias{din38402b6}
+\title{Carbamazepin calibration data}
+\format{
+A tibble containing 12 concentration levels and the respective
+instrument response values.
+}
+\usage{
+din38402b6
+}
+\description{
+Example dataset B.6 from DIN 38402 measured using LC-MS/MS. The
+concentrations are reported in in µg/L and the response in arbitrary
+units (AU).
+}
+\references{
+DIN 38402-51:2017-05, Beuth Verlag, Berlin.
+https://dx.doi.org/10.31030/2657448
+}
+\keyword{datasets}
diff --git a/man/din38402c3.Rd b/man/din38402c3.Rd
new file mode 100644
index 0000000..e9ac83e
--- /dev/null
+++ b/man/din38402c3.Rd
@@ -0,0 +1,22 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/chemCal-package.R
+\docType{data}
+\name{din38402c3}
+\alias{din38402c3}
+\title{Iron calibration data}
+\format{
+A tibble containing 10 concentration levels and the respective
+response values.
+}
+\usage{
+din38402c3
+}
+\description{
+Example dataset C.3 from DIN 38402 determined by ion chromatography.
+Concentrations are reported in mg/L and the extinction as response.
+}
+\references{
+DIN 38402-51:2017-05, Beuth Verlag, Berlin.
+https://dx.doi.org/10.31030/2657448
+}
+\keyword{datasets}
diff --git a/man/linearity.Rd b/man/linearity.Rd
new file mode 100644
index 0000000..52c2423
--- /dev/null
+++ b/man/linearity.Rd
@@ -0,0 +1,64 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/linearity.R
+\name{linearity}
+\alias{linearity}
+\title{Assess the linearity of a calibration curve}
+\usage{
+linearity(x, y, method = c("slope", "curvature"), tolerance = 0.1)
+}
+\arguments{
+\item{x}{numeric vector of independent values (usually concentrations).}
+
+\item{y}{numeric vector of dependent values (usually the signal of the
+analytical device).}
+
+\item{method}{character string. Supported methods are "slope" and
+"curvature".}
+
+\item{tolerance}{numeric value between 0 and 1, describing the acceptable
+deviation from the median of the slopes or the signal-to-concentration
+ratio. The default tolerance is 10\%.}
+}
+\value{
+returns a diagnostic plot
+}
+\description{
+A function to create diagnostic plots for the assessment of the linearity of
+calibration data based on their point-to-point slope or the curvature.
+The underlying methods follow ISO 84 66-1:2021 and DIN 32 402-51:2017
+(German Industrial Norm).
+}
+\details{
+The point-to-point slope method is based on the assumption that the slope
+between two points should not vary greatly within the linear range.
+
+The curvature method is similar to the point-to-point slope method. Here,
+the ratio between the instrument signal and the concentration of the
+calibration standard is assumed not to vary greatly within the linear range.
+
+The use of the Mandel test is discouraged due to its limitations in the
+identification of non-linear behaviour of calibration curves (Andrade and
+Gomes-Carracedo, 2013).
+}
+\examples{
+# Continuous Flow Analysis (CFA) data
+data(din38402b1)
+
+# Point-to-point slope plot
+linearity(din38402b1$conc, din38402b1$ext, method = "slope")
+
+# Curvature plot
+linearity(din38402b1$conc, din38402b1$ext, method = "curvature")
+
+}
+\references{
+ISO 8466-1:2021. Water quality — Calibration and evaluation of
+analytical methods — Part 1: Linear calibration function
+
+J. M. Andrade and M. P. Gomez-Carracedo (2013) Notes on the use of
+Mandel's test to check for nonlinearity in laboratory calibrations.
+Analytical Methods 5(5), 1145 - 1149.
+}
+\author{
+Anıl Axel Tellbüscher
+}
diff --git a/man/massart97ex1.Rd b/man/massart97ex1.Rd
index d154a9c..c49f416 100644
--- a/man/massart97ex1.Rd
+++ b/man/massart97ex1.Rd
@@ -12,6 +12,9 @@ Massart, L.M, Vandenginste, B.G.M., Buydens, L.M.C., De Jong, S.,
 Lewi, P.J., Smeyers-Verbeke, J. (1997) Handbook of Chemometrics and
 Qualimetrics: Part A, Chapter 8.
 }
+\usage{
+massart97ex1
+}
 \description{
 Sample dataset from p. 175 to test the package.
 }
diff --git a/man/massart97ex3.Rd b/man/massart97ex3.Rd
index 284a435..82d3191 100644
--- a/man/massart97ex3.Rd
+++ b/man/massart97ex3.Rd
@@ -13,6 +13,9 @@ Massart, L.M, Vandenginste, B.G.M., Buydens, L.M.C., De Jong, S.,
 Lewi, P.J., Smeyers-Verbeke, J. (1997) Handbook of Chemometrics and
 Qualimetrics: Part A, Chapter 8.
 }
+\usage{
+massart97ex3
+}
 \description{
 Sample dataset from p. 188 to test the package.
 }
diff --git a/man/rl95_cadmium.Rd b/man/rl95_cadmium.Rd
index 8e0b02c..db6a841 100644
--- a/man/rl95_cadmium.Rd
+++ b/man/rl95_cadmium.Rd
@@ -13,6 +13,9 @@ six calibration standards.
 Rocke, David M. und Lorenzato, Stefan (1995) A two-component model
 for measurement error in analytical chemistry. Technometrics 37(2), 176-184.
 }
+\usage{
+rl95_cadmium
+}
 \description{
 Dataset reproduced from Table 1 in Rocke and Lorenzato (1995).
 }
diff --git a/man/rl95_toluene.Rd b/man/rl95_toluene.Rd
index 1f8836a..2e0f3a5 100644
--- a/man/rl95_toluene.Rd
+++ b/man/rl95_toluene.Rd
@@ -12,6 +12,9 @@ six calibration standards.
 Rocke, David M. und Lorenzato, Stefan (1995) A two-component model
 for measurement error in analytical chemistry. Technometrics 37(2), 176-184.
 }
+\usage{
+rl95_toluene
+}
 \description{
 Dataset reproduced from Table 4 in Rocke and Lorenzato (1995). The toluene
 amount in the calibration samples is given in picograms per 100 µL.
diff --git a/man/utstats14.Rd b/man/utstats14.Rd
index 1b739d4..bb952ff 100644
--- a/man/utstats14.Rd
+++ b/man/utstats14.Rd
@@ -14,6 +14,9 @@ Tutorial website maintained by the Departments of Chemistry, University of
 Toronto.
 \url{https://sites.chem.utoronto.ca/chemistry/coursenotes/analsci/stats/index.html}
 }
+\usage{
+utstats14
+}
 \description{
 Dataset read into R from
 \url{https://sites.chem.utoronto.ca/chemistry/coursenotes/analsci/stats/files/example14.xls}.