By Ravindra Khattree

Real-world difficulties and information units are the spine of this booklet, which supplies a special method of the subject, integrating statistical tools, info research, and purposes. Now greatly revised, the ebook contains new information regarding combined results versions, purposes of the combined strategy, regression diagnostics with the corresponding IML method code, and covariance buildings. The authors' method of the knowledge will relief professors, researchers, and scholars in quite a few disciplines and industries. vast SAS code and the corresponding high-resolution output accompany pattern difficulties, and transparent reasons of SAS approaches are integrated. Emphasis is on right interpretation of the output to attract significant conclusions. that includes either the theoretical and the sensible, themes lined comprise multivariate research of experimental info and repeated measures facts, graphical illustration of knowledge together with biplots, and multivariate regression. moreover, a brief creation to the IML process with certain connection with multivariate information comes in an appendix. SAS courses and output built-in with the textual content make it effortless to learn and stick with the examples.

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**Example text**

00 C1:Contrast N-E-W+S C2:Contrast N-S C3:Contrast E-W are usually used for writing descriptive comments. The scatter plot matrix is a useful way of representing multivariate data on a single two-dimensional display. It simultaneously identifies the relationships between various variables. In this sense it is a graphic analog of a correlation matrix. However, it may sometimes be more effective in that apart from the strength of linear relationships, any nonlinearities can also be easily spotted.

For example, the scatter plot of the three variables N, S, and E indicates that the points have an increasing pattern not only in the horizontal plane but also in the perpendicular direction. This seems to indicate that there is a positive correlation between the variables (N,S), between (S,E), and between (N, E). 3. R. Rao (1948)’; footnote1 j=l ’C1:Contrast N-E-W+S’ j=r ’C2:Contrast N-S’; footnote2 j=r ’C3:Contrast E-W’; proc g3d data=cork; scatter c1*c2=c3; run; This scatter plot seems to show weak or no correlation among the three contrasts except perhaps between C2 and C3.

There are various variations of scatter plots for a variety of special purposes. For example, scatter plots have been used to examine the symmetry of distribution of the univariate data (Gnanadesikan, 1997). We will briefly discuss this approach. Suppose y1 , . . , yn are n observations on a variable y. R. Rao (1948) 100 90 80 D i r e c t i o n : N o r t h 70 60 50 40 30 20 30 40 50 60 70 80 Direction: East metric, we order the data from smallest to largest as y(1) ≤, . . , ≤ y(n) . Then, if the distribution of y is symmetric about a number, say µ, then the scatter plot of the paired data, (y(1) , y(n) ), (y(2) , y(n−1) ), .