# RsqDist

##### The distribution of R squared (as obtained in a regression analysis)

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

- Keywords
- univar

##### Usage

```
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.

##### See Also

##### Examples

```
# NOT RUN {
### Generate 10 random R Squared values
### with 2 predictors and 100 participants
rRsq(10, 2, 100);
### Probability of finding an R Squared of
### .15 with 4 predictors and 100 participants
pRsq(.15, 4, 100, lower.tail = FALSE);
### Probability of finding an R Squared of
### .15 with 15 predictors and 100 participants
pRsq(.15, 15, 100, lower.tail=FALSE);
# }
```

*Documentation reproduced from package userfriendlyscience, version 0.7.2, License: GPL (>= 3)*