By Richard A. Johnson, Dean W. Wichern
This industry best textual content is acceptable for classes that educate statistical equipment for describing and interpreting multivariate information in depts. of information, math, advertising, and within the organic, actual, and social sciences. The 4th version makes extra large use of SAS and SPSS output with an emphasis on interpretation. positive aspects comprise extra routines, info units, and photographs to demonstrate issues. a variety of strategies corresponding to MANOVA and Discriminate research, Correspondence research, and Biplots are built-in extra completely.
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Assume the distance along a street between two intersections in either the NS or EW direction is 1 unit. Define the distance between any two intersections (points) on the grid to be the "city block" distance. (For example, the distance between intersections (D, 1) and (C, 2), which we might call d((D, 1), (C, 2)), is given by d((D, 1), (C, 2)) = d ((D , 1), (D, 2)) + d ( (D, 2), (C, 2)) = 1 + 1 = 2. ) B r---+---+---,_--� C t---t-----1f--+- -�FP2n D r---+---+---,_--� E Locate a supply facility (warehouse) at an intersection such that the sum of the distances from the warehouse to the three retail stores is minimized.
The assignment of variables to facial features is done by the experimenter, and differ ent choices produce different results. Some iteration is usually necessary before sat isfactory representations are achieved. Chernoff faces appear to be most useful for verifying (1) an initial grouping suggested by subject-matter knowledge and intuition or (2) final groupings pro duced by clustering algorithms. 5, the 22 public utility companies were represented as Chernoff faces. We have the following correspondences: Variable Xl : Fixed-charge coverage Xz : Rate of return on capital X3 : Cost per KW capacity in place X4 : Annual load factor ("\ i· iI Xs : Peak KWH demand growth from 1974 X6 : Sales (KWH use per year) X7 : Percent nuclear Xs : Total fuel costs (cents per KWH) , .
4 . . . . . 5 . Max . . · · . 4 .... . : : ·· · . · . . . 135. 1 . . , . T . ;- . 76 Max . . . . . . . . • . . �. . . � Cll . . l · ·' . . . ·:. : .. . . t . . Strength (CD) . . . . . .. - . . . . . . . . . Med .. . 70 . . 5 . 2 . 93 Sec. 4 Data Displays and Pictorial Representations 19 [xli] p points i n n dimensions. The n observations o f the p variables can also be regarded as p points in n-dimensional space. Each column of X determines one of the points.
Applied Multivariate Statistical Analysis, Fourth Edition by Richard A. Johnson, Dean W. Wichern