Confidence Ellipse for Bivariate Normal Data LPGA Driving Distance and Fairway Percent – 2008 Season

Overview of Method Obtain Bivariate Data on n Units Compute the Estimated Means and Variance-Covariance Matrix Obtain the Eigenvalues and Eigenvectors of the Estimated Variance- Covariance Matrix Choose the Confidence Coefficient for the Ellipsoid and obtain the critical value corresponding to it for the Chi-Square Distribution with df=2 Form a grid of angles from 0 to 2p radians (equivalently, 0 to 360 degrees) Obtain the Base of the Ellipse scaling the cosine of the angle for “X” and the sine of the angle for “Y” Rotate the ellipse Center the Ellipse Add Major and Minor Axes

Plot of Fairway % vs Drive Distance with Marginal Histograms

Plot of Fairway % vs Drive Distance with Marginal Densities

Sample Means, Variance-Covariance Matrix, and Eigenvalues/Eigenvectors

Setting up and rotating the ellipse

Adding the Major and Minor Axes and Data Points