# ci_rsquared: Confidence Interval for the Population R-Squared In confintr: Confidence Intervals

## 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

 `1` ```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.

## 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.

## 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.

## References

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

`ci_f_ncp`.
 ```1 2 3 4 5 6``` ```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) ```