The numbered Exercises are from Johnson & Wichern, Applied Multivariate Statistical Analysis, 4th edition.
(a) Draw a perspective plot of the bivariate normal
probability density function.
(b) Find and graph the marginal density of X1 and the conditional density of X1 given X2 = x2, for x2 = 8, 10, 12.
(c) Plot the ellipses of concentration for 50%, 90%, 95% and 99% concentration. Add both regression lines to this plot.
Repeat Question 1 for a bivariate distribution uniform on an ellipse, with the same mean and covariance matrix as the bivariate normal distribution in Question 1.
[Hint: Find the mean and covariance matrix for a random variable V with distribution uniform on the unit circle centred at the origin, then find the distribution of X = m + BV, then find what B you need to give X the specified covariance matrix.]
Consider the bivariate density function
f(x1, x2) = x1 (x1 - x2)/8 when 0 < x1 < 2, -x1 < x2 <x1 and 0 otherwise.
(a) Find and graph the marginal and conditional distributions.
(b) Find and graph the regression of X1 on X2 and the regression of X2 on X1.
4.4
4.10 - 4.14
4.35 Also, see if Box-Cox transformations will help to improve normality.