ci_rsquared {confintr}

CI for the Population R-Squared

Description

This function calculates parametric CIs for the population R^2. It is based on CIs for the non-centrality parameter \Delta of the F distribution found by test inversion. Values of \Delta are mapped to R^2 by R^2 = \Delta / (\Delta + \textrm{df}_1 + \textrm{df}_2 + 1), where the \textrm{df}_j are the degrees of freedom of the F test statistic. A positive lower (1 - \alpha) \cdot 100\%-confidence limit for the R^2 goes hand-in-hand with a significant F test at level \alpha.

Usage

ci_rsquared(x, df1 = NULL, df2 = NULL, probs = c(0.025, 0.975))

Arguments

x

The result of stats::lm() or the F test statistic.

df1

The numerator df. Only used if x is a test statistic.

df2

The denominator df. Only used if x is a test statistic.

probs

Lower and upper probabilities, by default c(0.025, 0.975).

Details

According to stats::pf(), the results might be unreliable for very large F values. Note that we do not provide bootstrap CIs here to keep the input interface simple.

Value

An object of class "cint", see ci_mean() for details.

References

Smithson, M. (2003). Confidence intervals. Series: Quantitative Applications in the Social Sciences. New York, NY: Sage Publications.

See Also

ci_f_ncp()

Examples

fit <- lm(Sepal.Length ~ ., data = iris)
summary(fit)$r.squared
ci_rsquared(fit)
ci_rsquared(fit, probs = c(0.05, 1))