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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")
#> Call:
#> RSqNB(object = nb, alpha = 0.05)
#> 
#> R-squared and adjusted R-squared
#> type = "pc"
#>        est     se    R   2.5%  97.5%
#> rsq 0.8045 0.0527 5000 0.6943 0.8981
#> adj 0.7906 0.0565 5000 0.6725 0.8908

Bias Corrected Confidence Intervals

summary(out, type = "bc")
#> Call:
#> RSqNB(object = nb, alpha = 0.05)
#> 
#> R-squared and adjusted R-squared
#> type = "bc"
#>        est     se    R   2.5%  97.5%
#> rsq 0.8045 0.0527 5000 0.6527 0.8805
#> adj 0.7906 0.0565 5000 0.6279 0.8719

Bias Corrected and Accelerated Confidence Intervals

summary(out, type = "bca")
#> Call:
#> RSqNB(object = nb, alpha = 0.05)
#> 
#> R-squared and adjusted R-squared
#> type = "bca"
#>        est     se    R   2.5%  97.5%
#> rsq 0.8045 0.0527 5000 0.6428 0.8786
#> adj 0.7906 0.0565 5000 0.6172 0.8700

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 0.002779805 0.002978362
#> adj 0.002978362 0.003191102

confint

Return confidence intervals.

Percentile Confidence Intervals

confint(out, level = 0.95, type = "pc")
#>         2.5 %    97.5 %
#> rsq 0.6943138 0.8981104
#> adj 0.6724791 0.8908325

Bias Corrected Confidence Intervals

confint(out, level = 0.95, type = "bc")
#>         2.5 %    97.5 %
#> rsq 0.6527384 0.8804724
#> adj 0.6279340 0.8719347

Bias Corrected and Accelerated Confidence Intervals

confint(out, level = 0.95, type = "bca")
#>         2.5 %    97.5 %
#> rsq 0.6427639 0.8786374
#> adj 0.6172470 0.8699687

References