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Confidence interval for squared multiple correlation

Source: R/statpsych2.R
ci.rsqr.Rd

Computes an approximate confidence interval for a population squared multiple correlation in a linear model with random predictor variables. This function uses the scaled central F approximation method. An approximate standard error is recovered from the confidence interval.

For more details, see Section 2.4 of Bonett (2021, Volume 2)

Usage

ci.rsqr(alpha, r2, s, n)

Arguments

alpha

alpha value for 1-alpha confidence

r2

estimated unadjusted squared multiple correlation

s

number of predictor variables

n

sample size

Value

Returns a 1-row matrix. The columns are:

  • R-squared - estimate of unadjusted R-squared (from input)

  • adj R-squared - bias adjusted R-squared estimate

  • SE - recovered standard error

  • LL - lower limit of the confidence interval

  • UL - upper limit of the confidence interval

References

Helland IS (1987). “On the interpretation and use of R2 in regression analysis.” Biometrics, 43(1), 61–69. doi:10.2307/2531949 .

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

ci.rsqr(.05, .247, 4, 150)
#>  R-squared adj R-squared      SE     LL     UL
#>      0.247        0.2262 0.06024 0.1152 0.3514

# Should return:
# R-squared adj R-squared      SE      LL     UL  
#     0.247        0.2262 0.06024  0.1152 0.3514