II
3S Chapter 1 Aspects of Multivariate Analysis
.1.2. A morning newspaper lists the following used-car prices for a foreign compact with age
XI measured in years and selling price X2 measured in thousands of dollars:
1 2 3 3 4 5 6 8 9 11
18.95 19.00 17.95 15.54 14.00 12.95 8.94 7.49 6.00 3.99
(a) Construct a scatter plot of the data and marginal dot diagrams.
(b) Infer the sign of the sampkcovariance sl2 from the scatter plot.
(c) Compute the sample means XI and X2 and the sample variartces SI I and S22′ Compute the sample covariance SI2 and the sample correlation coefficient ’12’ Interpret
these quantities.
(d) Display the sample mean array i, the sample variance-covariance array Sn, and the
sample correlation array R using (I-8).
1.3. The following are five measurements on the variables Xl’ X2, and X3:
XI 9 2 6 5 8
X2 12 8 6 4 10
X3 3 4 0 2
Find the arrays i, Sn, and R.
1.4. The world’s 10 largest companies yield the following data:
The World’s 10 Largest Companiesl
Company
Citigroup
General Electric
American Int! Group
Bank of America
HSBCGroup
ExxonMobil
Royal Dutch/Shell
BP
INGGroup
Toyota Motor
Xl = sales
(billions)
108.28
152.36
95.04
65.45
62.97
263.99
265.19
285.06
92.01
165.68
X2 = profits
(billions)
17.05
16.59
10.91
14.14
9.52
25.33
18.54
15.73
8.10
11.13
X3 = assets
(billions)
1,484.10
750.33
766.42
1,110.46
1,031.29
195.26
193.83
191.11
1,175.16
211.15
IFrom www.Forbes.compartiallybasedonForbesTheForbesGlobaI2000,
April 18,2005.
(a) Plot the scatter diagram and marginal dot diagrams for variables Xl and X2′ Comment on the appearance of the diagrams.
(b) Compute Xl> X2, su, S22, S12, and ’12’ Interpret ’12’
1.5. Use the data in Exercise 1.4.
(a) Plot the scatter diagrams and dot diagrams for (X2, X3) and (x], X3)’ Comment on
thepattems.
(b) Compute the i, Sn, and R arrays for (XI’ X2, X3).
Exercises 39
1.6. The data in Table 1.5 are 42 measurements on air-pollution variables recorded at 12:00
noon in the Los Angeles area on different days. (See also the air-pollution data on the
web at www.prenhall.com/statistics.)
(a) Plot the marginal dot diagrams for all the variables.
(b) Construct the i, Sn, and R arrays, and interpret the entries in R.
Table 1.5 Air-Pollution Data
Solar
Wind (Xl) radiation (X2) CO (X3) NO (X4) N02 (xs) 0 3 (X6) HC(X7)
8 98 7 2 12 8 2
7 107 4 3 9 5 3
7 103 4 3 5 6 3
10 88 5 2 8 15 4
6 91 4 2 8 10 3
8 90 5 2 12 12 4
9 84 7 4 12 15 5
5 72 6 4 21 14 4
7 82 5 1 11 11 3
8 64 5 2 13 9 4
6 71 5 4 10 3 3
6 91 4 2 12 7 , 3
7 72 7 4 18 10 3
10 70 4 2 11 7 3
10 72 4 1 8 10 3
9 77 4 1 9 10 3
8 76 4 1 7 7 3
8 71 5 3 16 4 4
9 67 4 2 13 2 3
9 69 3 3 9 5 3
10 62 5 3 14 4 4
9 88 4 2 7 6 3
8 80 4 2 13 11 4
5 30 3 3 5 2 3
6 83 5 1 10 23 4
8 84 3 2 7 6 3
6 78 4 2 11 11 3
8 79 2 1 7 10 3
6 62 4 3 9 8 3
10 37 3 1 7 2 3
8 71 4 1 10 7 3
7 52 4 1 12 8 4
5 48 6 5 8 4 3
6 75 4 1 10 24 3
10 35 4 1 6 9 2
8 85 4 1 9 10 2
5 86 3 1 6 12 2
5 86 7 2 13 18 2
7 79 7 – 4 9 25 3
7 79 5 2 8 6 2
6 68 6 2 11 14 3
8 40 4 3 6 5 2
Source: Data courtesy of Professor O. C. Tiao.