# RsqDist: The distribution of R squared (as obtained in a regression... In userfriendlyscience: Quantitative Analysis Made Accessible

## Description

These functions use the beta distribution to provide the R Squared distribution.

## Usage

 1 2 3 4 dRsq(x, nPredictors, sampleSize, populationRsq = 0) pRsq(q, nPredictors, sampleSize, populationRsq = 0, lower.tail = TRUE) qRsq(p, nPredictors, sampleSize, populationRsq = 0, lower.tail = TRUE) rRsq(n, nPredictors, sampleSize, populationRsq = 0)

## Arguments

 x, q Vector of quantiles, or, in other words, the value(s) of R Squared. p Vector of probabilites (p-values). nPredictors The number of predictors. sampleSize The sample size. n The number of R Squared values to generate. populationRsq The value of R Squared in the population; this determines the center of the R Squared distribution. This has not been implemented yet in this version of userfriendlyscience. If anybody knows how to do this and lets me know, I'll happily integrate this of course. lower.tail logical; if TRUE (default), probabilities are the likelihood of finding an R Squared smaller than the specified value; otherwise, the likelihood of finding an R Squared larger than the specified value.

## Details

The functions use convert.omegasq.to.f and convert.f.to.omegasq to provide the Omega Squared distribution.

## Value

dRsq gives the density, pRsq gives the distribution function, qRsq gives the quantile function, and rRsq generates random deviates.

## Note

These functions are based on the Stack Exchange (Cross Validated) post at http://stats.stackexchange.com/questions/130069/what-is-the-distribution-of-r2-in-linear-regression-under-the-null-hypothesis. Thus, the credits go to Alecos Papadopoulos, who provided the answer that was used to write these functions.