% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/linearReg_R2stat.R
\name{linearReg.R2stat}
\alias{linearReg.R2stat}
\title{Use R^2 statistic to compute Bayes factor for regression designs}
\usage{
linearReg.R2stat(N, p, R2, rscale = "medium", simple = FALSE)
}
\arguments{
\item{N}{number of observations}

\item{p}{number of predictors in model, excluding intercept}

\item{R2}{proportion of variance accounted for by the predictors, excluding
intercept}

\item{rscale}{numeric prior scale}

\item{simple}{if \code{TRUE}, return only the Bayes factor}
}
\value{
If \code{simple} is \code{TRUE}, returns the Bayes factor (against the
intercept-only null). If \code{FALSE}, the function returns a
vector of length 3 containing the computed log(e) Bayes factor,
along with a proportional error estimate on the Bayes factor and the method used to compute it.
}
\description{
Using the classical R^2 test statistic for (linear) regression designs, this
function computes the corresponding Bayes factor test.
}
\details{
This function can be used to compute the Bayes factor corresponding to a
multiple regression, using the classical R^2 (coefficient of determination)
statistic.  It can be used when you don't have access to the full data set
for analysis by \code{\link{lmBF}}, but you do have the test statistic.

For details about the model, see the help for \code{\link{regressionBF}},
and the references therein.

The Bayes factor is computed via Gaussian quadrature.
}
\examples{
## Use attitude data set
data(attitude)
## Scatterplot
lm1 = lm(rating~complaints,data=attitude)
plot(attitude$complaints,attitude$rating)
abline(lm1)
## Traditional analysis
## p value is highly significant
summary(lm1)

## Bayes factor
## The Bayes factor is over 400,000;
## the data strongly favor hypothesis that
## the slope is not 0.
result = linearReg.R2stat(30,1,0.6813)
exp(result[['bf']])
}
\references{
Liang, F. and Paulo, R. and Molina, G. and Clyde, M. A. and
  Berger, J. O. (2008). Mixtures of g-priors for Bayesian Variable
  Selection. Journal of the American Statistical Association, 103, pp.
  410-423

  Rouder, J. N.  and Morey, R. D. (in press, Multivariate Behavioral Research). Bayesian testing in
  regression.

  Perception and Cognition Lab (University of Missouri): Bayes factor
  calculators. \url{http://pcl.missouri.edu/bayesfactor}
}
\seealso{
\code{\link{integrate}}, \code{\link{lm}}; see
  \code{\link{lmBF}} for the intended interface to this function, using
  the full data set.
}
\author{
Richard D. Morey (\email{richarddmorey@gmail.com}) and Jeffrey N.
  Rouder (\email{rouderj@missouri.edu})
}
\keyword{htest}
