# Applied Multivariate Statistical Analysis (6th edition) Textbook Solutions Chapter 4 Problem 29

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#### Problem

Given the air-pollution data in table 1.5, examine the pairs *X*_{5} = NO_{2} and *X*_{6} = O_{3} for bivariate normality.

(a) Calculate statistical distances where

(b) Determine the proportion of observation , falling within the approximate 50% probability contour of a bi variate normal distribution.

(c) Construct a chi-square plot of the ordered distances in part a

#### Solution

Generalized distances are as follows:

0.4607 0.6592 2.3771 1.6283 0.4135 0.4761 1.1849

10.6392 0.1388 0.8162 1.3566 0.6228 5.6494 0.3159

0.4135 0.1225 0.8988 4.7647 3.0089 0.6592 2.7741

1.0360 0.7874 3.4438 6.1489 1.0360 0.1388 0.8856

0.1380 2.2489 0.1901 0.4607 1.1472 7.0857 1.4584

0.1225 1.8985 2.7783 8.4731 0.6370 0.7032 1.80 14

**(b).** The number of observations whose generalized distances are less than X2(0.5) = 1.39 is 26.

So the proportion is 26/42=0.6190.

**(c).**

** CHI-SQUARE PLOT FOR (X1>X2)**

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