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Confidence intervals for multiple correlation coefficients are generated using the RSqNB() function from the betaNB package. In this example, we use the data set and the model used in betaNB: Example Using the BetaNB Function.

df <- betaNB::nas1982

Regression

Fit the regression model using the lm() function.

object <- lm(QUALITY ~ NARTIC + PCTGRT + PCTSUPP, data = df)

Nonparametric Bootstrap

nb <- NB(object)

Multiple Correlation Coefficients

Normal-Theory Approach

out <- RSqNB(nb, alpha = 0.05)

Methods

summary

Summary of the results of RSqNB().

Percentile Confidence Intervals

summary(out, type = "pc")
#>        est     se    R   2.5%  97.5%
#> rsq 0.8045 0.0537 5000 0.6879 0.8997
#> adj 0.7906 0.0576 5000 0.6656 0.8925

Bias Corrected Confidence Intervals

summary(out, type = "bc")
#>        est     se    R   2.5%  97.5%
#> rsq 0.8045 0.0537 5000 0.6428 0.8809
#> adj 0.7906 0.0576 5000 0.6173 0.8724

Bias Corrected and Accelerated Confidence Intervals

summary(out, type = "bca")
#>        est     se    R   2.5%  97.5%
#> rsq 0.8045 0.0537 5000 0.6359 0.8792
#> adj 0.7906 0.0576 5000 0.6099 0.8706

coef

Return the vector of estimates.

coef(out)
#>       rsq       adj 
#> 0.8045263 0.7905638

vcov

Return the sampling covariance matrix.

vcov(out)
#>             rsq         adj
#> rsq 0.002886954 0.003093165
#> adj 0.003093165 0.003314105

confint

Return confidence intervals.

Percentile Confidence Intervals

confint(out, level = 0.95, type = "pc")
#>         2.5 %    97.5 %
#> rsq 0.6878976 0.8996817
#> adj 0.6656046 0.8925161

Bias Corrected Confidence Intervals

confint(out, level = 0.95, type = "bc")
#>         2.5 %    97.5 %
#> rsq 0.6428499 0.8808777
#> adj 0.6173392 0.8723690

Bias Corrected and Accelerated Confidence Intervals

confint(out, level = 0.95, type = "bca")
#>         2.5 %    97.5 %
#> rsq 0.6359172 0.8791906
#> adj 0.6099113 0.8705613

References