# confidenceEllipse: Bivariate Normal Confidence Ellipse In douglaswhitaker/MVQuickGraphs: Quick Multivariate Graphs

## Description

Draws a (1-`alpha`)100% confidence ellipse (two dimensional) for a multivariate normal distribution using the eigendecomposition of the covariance matrix.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```confidenceEllipse( X.mean = c(0, 0), eig, n, p, xl = NULL, yl = NULL, axes = TRUE, center = FALSE, lim.adj = 0.02, alpha = 0.05, ... ) ```

## Arguments

 `X.mean` a column matrix giving the mean of the two dimensions of the p-dimensional multivariate normal distribution. `eig` the eigenvalues and eigenvectors of the covariance matrix. This should be of the same form as the output of `eigen`, namely a list with two components: `values` and `vectors`. It is assumed that the largest eigenvalue is given first. `n` the number of observations. `p` the number of dimensions of the multivariate normal distribution. (The resulting graph will always be a two-dimensional confidence region for the two dimensions of a p-dimensional multivaraite normal distribution under consideration.) `xl` a vector giving the lower and upper limits of the x-axis for plotting. If `xl = NULL` (default), then reasonable values are computed automatically. `yl` a vector giving the lower and upper limits of the y-axis for plotting. If `yl = NULL` (default), then reasonable values are computed automatically. `axes` logical. If `axes = TRUE` (default) then the major and minor axes of the ellipse are plotted. `center` logical. If `axes = TRUE` then the center of the ellipse is indicated with a point and dashed lines are drawn to the x-axis and y-axis. `lim.adj` a value giving an adjustment to the x-axis and y-axis limits computed if either `xl = NULL` or `yl = NULL`. Essentially this is a way to have some coarse control over these limits for quick graphing: positive values will increase the distance between the upper and lower limits (making the ellipse appear smaller) while negative values will decrease the distance (and make the ellipse appear larger). `alpha` a value giving the value of alpha to be used when computing the contour. Contours are drawn at the `1-alpha` level. `...` other arguments to be passed to the graphing functions.

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## References

Johnson, R. A., & Wichern, D. W. (2007). Applied multivariate statistical analysis (6th ed). Pearson Prentice Hall.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10``` ```# 90% Confidence Ellipse for Reading and Vocab from ability.cov x.bar <- ability.cov\$center[5:6] Sigma <- ability.cov\$cov[5:6,5:6] n <- ability.cov\$n.obs p <- length(ability.cov\$center) confidenceEllipse(X.mean = x.bar, eig = eigen(Sigma), n = n, p = p, alpha = 0.10) ```

douglaswhitaker/MVQuickGraphs documentation built on Sept. 18, 2021, 7:17 p.m.