ABSTRACT

Example I: Financial Data. ln this chapter we make a repeated use of the following data set, which we refer to as the financial data. The data set was collected and thoroughly analyzed by Jeff M. Semansein (a student in one of the authors' applied regression methods class) using Standard & Poor's Compustat PC Plus. The purpose of using the data here is only to illustrate the methods presented in this chapter. There are several variables in the data set, but for illustrative purposes we consider only a subset consisting of the following three variables:

X1: Book value in dollars per share at the end of 1992 X2: Net sales in millions of dollars in 1992 X3: Sales-to-assets ratio in 1992

Let us first think of this data set as a lrivariate data. Figure l shows the trivariate scatter plot after it has been rotated to show the outliers in the data. The four outlying points marked on the graph are detected by the multivariate outliers detection method presented here. The mean and covariance matrix of the data are

(

22.06) 5.86

0.24 and

(

168.14 2:3.44

23.44 35.24 -0.62

0.18 (l)

respectively. When the outliers are deleted, mean and covariance matrix become

and (

125.24 32.59 -0.45

32.59 18.47

-O.lJ

(2)

respectively. Note the dramatic effects of outliers on the estimated variances and covariances. To illustrate how the conf]dence regions can change substantially because of let us examine the bivariate scatkr plot of versus The scatter

Table I Financial Data for 29 Financial Companies

Number Xl x2 X:1 Number Xl )(2 X:1

14.58 26.96.1 0.17 14 2.46 0.217 0.26 2 21.15 4.816 0.15 15 15.75 2.213 0.09 3 19.26 3.394 0.08 16 25.19 2.825 0.09 4 39.93 5.455 0.08 17 34.30 7.281 0.07 5 6.12 1.495 L52 l8 39.26 7.382 O.JO 6 32.25 9.ll2 0.09 19 30.80 9.228 0.08 7 32.43 11.078 0.08 20 B.5l 3.364 0.14 8 8.30 0.806 0.28 21 15.96 3.840 0.08 9 16.68 4.461 0.08 22 6.7;) 0.196 0.16 10 24.79 14.5;)9 0.09 23 31.84 lS.372 0.12 ll 19.26 1.114 1.82 24 1..52 0.909 0.17 12 19.42 4.190 0.09 25 17.70 5.099 0.2:3 13 27.02 2.009 O.OB 26 57.41-5.067 0.10

~26

FigureIFinancialdata:TrivariateScatterplotofX1,X2,andX3withtheoutliersindicated bytheirnumbers.