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

#### Problem

Given the air-pollution data in table 1.5, examine the pairs X5 = NO2 and X6 = O3 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) If you happen to run into some problem while following the steps, please make sure to let us know in the comment section below, and we’ll do our best to solve it. Apart from that, you can contact us on Facebook and Twitter, however we can’t guarantee a rapid reaction time over those platform

Categories: AMSA 6e solutions