\name{stepback}
\alias{stepback}

\title{Fitting a linear model by backward-stepwise regression }
\description{
   \code{stepback} fits a linear regression model applying a backward-stepwise strategy.
}
\usage{
stepback(y = y, d = d, alfa = 0.05)
}

\arguments{
  \item{y}{ dependent variable }
  \item{d}{ data frame containing by columns the set of variables that could be in the selected model }
  \item{alfa}{ significance level to decide if a variable stays or not in the model}
}
\details{
  The strategy begins analysing a model with all the variables included in d. 
  If all variables are statistically significant (all variables have a p-value less than alfa)
  this model will be the result. If not, the less statistically significant variable will be 
  removed and the model is re-calculated. The process is repeated up to find a model with all 
  the variables statistically significant.
       
}
\value{
     \code{stepback} returns an object of the class \code{\link{lm}}, where the model uses 
     \code{y} as dependent variable and all the selected variables from \code{d} as independent variables. 
             
     The function \code{\link{summary}} are used to obtain a summary and analysis of variance table of the results. 
     The generic accessor functions \code{\link{coefficients}}, \code{\link{effects}},
     \code{\link{fitted.values}} and \code{\link{residuals}} extract various useful features of the value returned by \code{\link{lm}}.
}
\references{Conesa, A., Nueda M.J., Alberto Ferrer, A., Talon, T. 2005.
maSigPro: a Method to Identify Significant Differential Expression Profiles in Time-Course Microarray Experiments.
 }
\author{ Ana Conesa, aconesa@ivia.es; Maria Jose Nueda, mj.nueda@ua.es}
\seealso{ \code{\link{lm}}, \code{\link{step}}, \code{\link{stepfor}}, \code{\link{two.ways.stepback}}, \code{\link{two.ways.stepfor}}}
\examples{

## create design matrix
Time <- rep(c(rep(c(1:3), each = 3)), 4)
Replicates <- rep(c(1:12), each = 3)
Control <- c(rep(1, 9), rep(0, 27))
Treat1 <- c(rep(0, 9), rep(1, 9), rep(0, 18))
Treat2 <- c(rep(0, 18), rep(1, 9), rep(0,9))
Treat3 <- c(rep(0, 27), rep(1, 9))
edesign <- cbind(Time, Replicates, Control, Treat1, Treat2, Treat3)
rownames(edesign) <- paste("Array", c(1:36), sep = "")
dise <- make.design.matrix(edesign)
dis <- as.data.frame(dise$dis)


## expression vector
y <- c(0.082, 0.021, 0.010, 0.113, 0.013, 0.077, 0.068, 0.042, -0.056, -0.232, -0.014, -0.040, 
-0.055, 0.150, -0.027, 0.064, -0.108, -0.220, 0.275, -0.130, 0.130, 1.018, 1.005, 0.931,
 -1.009, -1.101, -1.014, -0.045, -0.110, -0.128, -0.643, -0.785, -1.077, -1.187, -1.249, -1.463)

s.fit <- stepback(y = y, d = dis)
summary(s.fit)


}
\keyword{regression}