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

2. 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

3. Plot of Fairway % vs Drive Distance with Marginal Histograms

4. Plot of Fairway % vs Drive Distance with Marginal Densities

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

6. Setting up and rotating the ellipse

7. Adding the Major and Minor Axes and Data Points