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-\name{inverse.predict}
-\alias{inverse.predict}
-\alias{inverse.predict.lm}
-\alias{inverse.predict.rlm}
-\alias{inverse.predict.default}
-\title{Predict x from y for a linear calibration}
-\usage{inverse.predict(object, newdata, \dots,
- ws, alpha=0.05, var.s = "auto")
-}
-\arguments{
- \item{object}{
- A univariate model object of class \code{\link{lm}} or
- \code{\link[MASS:rlm]{rlm}}
- with model formula \code{y ~ x} or \code{y ~ x - 1}.
- }
- \item{newdata}{
- A vector of observed y values for one sample.
- }
- \item{\dots}{
- Placeholder for further arguments that might be needed by
- future implementations.
- }
- \item{ws}{
- The weight attributed to the sample. This argument is obligatory
- if \code{object} has weights.
- }
- \item{alpha}{
- The error tolerance level for the confidence interval to be reported.
- }
- \item{var.s}{
- The estimated variance of the sample measurements. The default is to take
- the residual standard error from the calibration and to adjust it
- using \code{ws}, if applicable. This means that \code{var.s}
- overrides \code{ws}.
- }
-}
-\value{
- A list containing the predicted x value, its standard error and a
- confidence interval.
-}
-\description{
- This function predicts x values using a univariate linear model that has been
- generated for the purpose of calibrating a measurement method. Prediction
- intervals are given at the specified confidence level.
- The calculation method was taken from Massart et al. (1997). In particular,
- Equations 8.26 and 8.28 were combined in order to yield a general treatment
- of inverse prediction for univariate linear models, taking into account
- weights that have been used to create the linear model, and at the same
- time providing the possibility to specify a precision in sample measurements
- differing from the precision in standard samples used for the calibration.
- This is elaborated in the package vignette.
-}
-\note{
- The function was validated with examples 7 and 8 from Massart et al. (1997).
-}
-\references{
- 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,
- p. 200
-}
-\examples{
-# This is example 7 from Chapter 8 in Massart et al. (1997)
-data(massart97ex1)
-m <- lm(y ~ x, data = massart97ex1)
-inverse.predict(m, 15) # 6.1 +- 4.9
-inverse.predict(m, 90) # 43.9 +- 4.9
-inverse.predict(m, rep(90,5)) # 43.9 +- 3.2
-}
-\keyword{manip}

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