# linearReg.R2stat: Use R^2 statistic to compute Bayes factor for regression... In BayesFactor: Computation of Bayes Factors for Common Designs

## Description

Using the classical R^2 test statistic for (linear) regression designs, this function computes the corresponding Bayes factor test.

## Usage

 `1` ```linearReg.R2stat(N, p, R2, rscale = "medium", simple = FALSE) ```

## Arguments

 `N` number of observations `p` number of predictors in model, excluding intercept `R2` proportion of variance accounted for by the predictors, excluding intercept `rscale` numeric prior scale `simple` if `TRUE`, return only the Bayes factor

## 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 `lmBF`, but you do have the test statistic.

For details about the model, see the help for `regressionBF`, and the references therein.

The Bayes factor is computed via Gaussian quadrature.

## Value

If `simple` is `TRUE`, returns the Bayes factor (against the intercept-only null). If `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.

## Author(s)

Richard D. Morey (richarddmorey@gmail.com) and Jeffrey N. Rouder (rouderj@missouri.edu)

## 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. http://pcl.missouri.edu/bayesfactor

`integrate`, `lm`; see `lmBF` for the intended interface to this function, using the full data set.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ```## 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']]) ```