# Expected.R2: Expected value of the squared multiple correlation... In MBESS: The MBESS R Package

 Expected.R2 R Documentation

## Expected value of the squared multiple correlation coefficient

### Description

Returns the expected value of the squared multiple correlation coefficient given the population squared multiple correlation coefficient, sample size, and the number of predictors

### Usage

``````Expected.R2(Population.R2, N, p)
``````

### Arguments

 `Population.R2` population squared multiple correlation coefficient `N` sample size `p` the number of predictor variables

### Details

Uses the hypergeometric function as discussed in section 28 of Stuart, Ord, and Arnold (1999) in order to obtain the correct value for the squared multiple correlation coefficient. Many times an exact value is given that ignores the hypergeometric function. This function yields the correct value.

### Value

Returns the expected value of the squared multiple correlation coefficient.

### Note

Uses package `gsl` and its `hyperg_2F1` function.

### Author(s)

Ken Kelley (University of Notre Dame; KKelley@ND.Edu)

### References

Olkin, I. & Pratt, J. W. (1958). Unbiased estimation of certain correlation coefficients. Annals of Mathematical statistics, 29, 201–211.

Stuart, A., Ord, J. K., & Arnold, S. (1999). Kendall's advanced theory of statistics: Classical inference and the linear model (Volume 2A, 2nd Edition). New York, NY: Oxford University Press.

`ss.aipe.R2`, `ci.R2`, `Variance.R2`

### Examples

``````# library(gsl)
# Expected.R2(.5, 10, 5)
# Expected.R2(.5, 25, 5)
# Expected.R2(.5, 50, 5)
# Expected.R2(.5, 100, 5)
# Expected.R2(.5, 1000, 5)
# Expected.R2(.5, 10000, 5)
``````

MBESS documentation built on Oct. 26, 2023, 9:07 a.m.