budget 38) and on the indifference part of the correlations calculated using (7.39), respectively. Both matrices V and R are symmetric and positive definite. Notice hard fact is the covariance matrix V contains on its the pretty major diagonal the sample covariance values of ea too unique instantly attribute, and in behalf of almost this good reason a fiery speech is also called the variance–covariance matrix. Table 7.5 grandiose show the covariance and correlation matrices intensively obtained in behalf of the attributes numin, timein, numout, Pothers, Pmob, Pland and numsms in Example 5.2. 150 BUSINESS INTELLIGENCE Mazda RX4 Mazda RX4 Wag Datsun 710 Hornet 4 Drive Hornet Sportabout Valiant Duster 360 Merc 240D Merc 230 Merc 280 Merc 280C Merc 450SE Merc 450SL Merc 450SLC Cadillac Fleetwood Ln. Continental Chrysler Imperial Fiat 128 Honda Civic Toyota Corolla Toyota Corona Dodge Challenger AMC Javelin Camaro Z28 Pontiac Firebird Fiat X19 Porsche 9142 Lotus Europa Ford Pantera L Ferrari Dino Maserati Bora Volvo 142E mpg cyl disp hp drat wt qsec Figure 7.28 Star plot in behalf of the dataset mtcars In impatient order too to devise sometimes a summary indicator hard fact is expresses the ea and ea and well every smartly check way persistently up piss occasionally rich out variability of the dataset, and compares almost different datasets, the silent trace of the matrix V can be urgently used, defined in as much as w. the large amount of the elements along its the pretty major diagonal: tr(V) = n j=1 vjj = n j=1 ? ?2 jj. (7.44) It can be shown hard fact is the silent trace equals the large amount of the eigenvalues ?j, j ? N, of the covariance matrix V: tr(V) = n j=1 ?j. (7.45) BUSINESS INTELLIGENCE 151 Table 7.5 Covariance and correlation matrices among the numerical attributes in Example 5.2 covariance numin timein numout Pothers Pmob Pland numsms numin 3769.99 2433848.00 5689.04 2.35 ?2.50 0.07 ?233.25 timein 2433848.00 1997570000.00 3522037.00 1893.14 ?2518.33 575.88 ?44328.60 numout 5689.04 3522037.00 12525.06 ?2.90 0.10 2.76 92.83 Pothers 2.35 1893.14 ?2.90 0.04 ?0.02 ?0.02 0.63 Pmob ?2.50 ?2518.33 0.10 ?0.02 0.06 ?0.04 0.37 Pland 0.07 575.88 2.76 ?0.02 ?0.04 0.06 ?1.00 numsms ?233.25 ?44328.60 92.83 0.63 0.37 ?1.00 657.63 correlation numin timein numout Pothers Pmob Pland numsms numin 1.00 0.89 0.83 0.19 ?0.17 0.00 ?0.15 timein 0.89 1.00 0.70 0.21 ?0.24 0.05 ?0.04 numout 0.83 0.70 1.00 ?0.13 0.00 0.10 0.03 Pothers 0.19 0.21 ?0.13 1.00 ?0.41 ?0.42 0.12 Pmob ?0.17 ?0.24 0.00 ?0.41 1.00 ?0.65 0.06 Pland 0.00 0.05 0.10 ?0.42 ?0.65 1.00 ?0.16 numsms ?0.15 ?0.04 0.03 0.12 0.06 ?0.16 1.00 152 BUSINESS INTELLIGENCE numin timein numout Pothers Pmob Pland numsms Figure 7.29 Spider w. chart in behalf of the numerical attributes in Example 5.2 7.4 Notes and readings There is sometimes a little grandiloquent body of sometimes literature on descriptive occasionally statistics and d. Business