confintr (version 0.1.0)

ci_rsquared: Confidence Interval for the Population R-Squared

Description

This function calculates parametric confidence intervals for the population R-squared. It is based on confidence intervals for the non-centrality parameter Delta of the F distribution, found by test inversion. Delta values are mapped to R-squared by R-squared = Delta / (Delta + df1 + df2 + 1), where df1 and df2 are the degrees of freedom of the F test statistic. A positive lower (1-alpha)*100%-confidence limit for the R-squared 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 degree of freedom. Only used if x is a test statistic.

df2

The denominator degree of freedom. Only used if x is a test statistic.

probs

Error probabilites. The default c(0.025, 0.975) gives a symmetric 95% confidence interval.

Value

A list with class cint containing these components:

• parameter: The parameter in question.

• interval: The confidence interval for the parameter.

• estimate: The estimate for the parameter.

• probs: A vector of error probabilities.

• type: The type of the interval.

• info: An additional description text for the interval.

Details

According to ?pf, the results might be unreliable for very large F values. Note that we do not provide bootstrap confidence intervals here to keep the input interface simple.

References

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

See Also

ci_f_ncp.

Examples

# NOT RUN {
fit <- lm(Sepal.Length ~ ., data = iris)
summary(fit)$r.squared
ci_rsquared(fit)
ci_rsquared(fit, probs = c(0.05, 1))
ci_rsquared(fit, probs = c(0, 0.95))
ci_rsquared(188.251, 5, 144)
# }